Analytical Deductive Reasoning | Logical Reasoning Tricks 2026 | Best Questions

Logical Reasoning one liner - Analytical and Deductive Reasoning

1. Syllogism

If "All A are B" and "All B are C", does "All A are C" follow? - Yes (Definite True)
If "All A are B" and "All B are C", does "Some C are A" follow? - Yes (Definite True)
If "Some A are B" and "Some B are C", does "Some A are C" follow definitely? - No (False / Doubtful)
If "No A is B" and "No B is C", is there a definite negative relation between A and C? - No (Indeterminate)
If "All A are B" and "No B is C", does "No A is C" follow? - Yes (Definite True)
If "All A are B" and "No B is C", does "Some A are not C" follow? - Yes (Definite True)
If "Some A are B" and "No B is C", what definite relation exists from A to C? - Some A are not C
What two relations does the statement "Only a few A are B" convey simultaneously? - "Some A are B" and "Some A are not B"
If "Only a few A are B", is the conclusion "All A can never be B" true? - Yes (Definite True)
If "Only a few A are B", is "All B being A is a possibility" valid? - Yes (Possible True)
What does the categorical proposition "Only A are B" translate to in standard terms? - "All B are A" (with B strictly restricted from other elements)
If "Only A are B" and "Some A are C", can any B ever be C? - No (B is exclusive to A)
What does the statement "Each A is B" or "Every A is B" signify? - All A are B
What does the term "At least some A are B" mean? - Some A are B
If a conclusion is false in the basic Venn diagram, can its possibility be true if unrestricted? - Yes
If a conclusion is 100% definite true, is its "possibility" considered valid? - No (Definite facts cannot be possibilities)
What condition is necessary between two conclusions to form an "Either-Or" complementary pair? - Same elements, one positive and one negative, and both individually doubtful
Do "Some A are B" and "No A is B" form a valid Either-Or pair? - Yes (Either-Or)
Do "All A are B" and "Some A are not B" form a valid Either-Or pair? - Yes (Either-Or)
Does the pair "All A are B" and "No A is B" form an Either-Or pair? - No (Both can be false simultaneously)
If "No Cat is Dog" and "All Dogs are Animals", does "Some Animals are not Cats" follow? - Yes (Definite True)
If "All Pens are Books" and "All Erasers are Books", does "Some Pens are Erasers" follow definitely? - No (Doubtful)
If "Some Cars are Buses" and "All Buses are Trains", does "Some Cars are Trains" follow? - Yes (Definite True)
If "Some Apples are Red" and "No Red is Sweet", is "All Apples being Sweet a possibility"? - No (Red Apples cannot be sweet)
If "All Mangoes are Fruits" and "Some Fruits are Sweet", can "All Mangoes are Sweet" be possible? - Yes (Possible True)
What does the statement "None of the A are B" mean? - No A is B
What do the quantifiers "A few", "Many", or "Frequently" indicate in syllogisms? - Some
If "Only a few pens are pencils" and "Only a few pencils are erasers", can all pencils be erasers? - No (False)
If "All A are B" and "Some B are not C", does "Some A are not C" follow definitely? - No (Doubtful)
If "No A is B", does "No B is A" follow by valid conversion? - Yes (Definite True)
If "All A are B", does "All B are A" follow definitely? - No (Only "Some B are A" follows)
If "Some A are B", does "Some B are A" follow by conversion? - Yes (Definite True)
Can "Some A are not B" be converted directly into "Some B are not A"? - No (Invalid conversion)
If "All A are B" and "All C are B", is "Some A are C is a possibility" valid? - Yes (Possible True)
If "No A is B" and "All C are A", what is the definite relation between C and B? - No C is B
If "Some A are B" and "No B is C", is "All C being A is a possibility" true? - Yes (Possible True)
If "All A are B", can the possibility "All B being A" exist? - Yes (Possible True)
If "No A is B", can the possibility "Some A being B" ever be true? - No (Definite negative restricts possibility)
What does the proposition "0% A are B" represent? - No A is B
What does the proposition "100% A are B" represent? - All A are B
What does "99% A are B" or "0.1% A are B" represent in standard syllogisms? - Some A are B
If "All A are B" and "No C is B", can "Some A are C" ever be true? - No (Definite False)
If "Only a few Mobiles are Laptops" and "All Laptops are Computers", does "Some Mobiles are Computers" follow? - Yes (Definite True)
If "Only a few Mobiles are Laptops" and "All Laptops are Computers", can all Mobiles be Computers? - Yes (Possible True)
If "Only a few Mobiles are Laptops" and "All Laptops are Computers", can all Mobiles be Laptops? - No (Definite False)
If "Some A are B", "Some B are C", and "Some C are D", does "Some A are D" follow? - No (Doubtful)
If "All A are B", "All B are C", and "All C are D", does "All A are D" follow? - Yes (Definite True)
If "No A is B" and "No B is C", can "All A being C" be a possibility? - Yes (Possible True)
If "Some A are not B", does it definitely mean that "Some A are B"? - No (Not necessarily definite)
In a Venn diagram, how is the universal negative proposition "No A is B" represented? - Two separate disjoint circles with a cross line
What does the statement "Not a single student failed" logically mean? - All students passed (No student failed)
If "All doctors are educated" and "Some educated are rich", does "Some doctors are rich" follow definitely? - No (Doubtful)
If "Only a few shirts are pants", can "No shirt is pant" be true as a possibility? - No ("Some shirts are pants" is definite)
If "All locks are keys" and "No key is door", is "All locks can never be doors" true? - Yes (Definite True)
If "Some tables are chairs" and "Some chairs are benches", can "No table is bench" be true as a possibility? - Yes (Possible True)
If "Only gold is platinum", which circle lies exclusively inside which in a Venn diagram? - Platinum lies entirely inside Gold
If "Only A are B" and "All A are C", does "Some C are B" follow? - Yes (Definite True)
If "Some A are B" and "Some A are not B", is "All A being B" a possibility? - No (Definite False)
If "Some A are B" and "Some A are not B", is "No A is B" a possibility? - No (Definite False)
What is an "Undistributed Middle Term" in syllogisms? - When the middle term is not distributed in either premise, yielding no valid universal conclusion
If "All rivers are water" and "All oceans are water", can any definite conclusion be drawn between rivers and oceans? - No (Middle term undistributed)
If "Some men are brave" and "All brave are soldiers", does "Some men are soldiers" follow? - Yes (Definite True)
If "Only a few books are novels" and "No novel is story", can all books be novels? - No (Definite False)
If "Only a few books are novels" and "No novel is story", can all books be stories? - No (Novel part of books cannot be stories)
If "All A are B" and "Some B are C", is "All A being C is a possibility" valid? - Yes (Possible True)
If "No A is B" and "All B are C", what definite negative relation exists from C to A? - Some C are not A
Does the quantifier "Almost all" mean "All" or "Some"? - Some
If "All stars are moons" and "All moons are planets", does "All planets are stars" follow? - No (Only "Some planets are stars" follows)
If "Some pens are blue" and "Some pens are black", can a pen be both blue and black? - Yes (Possible True unless restricted)
What is the logical contradiction of "All A are B"? - Some A are not B
What is the logical contradiction of "No A is B"? - Some A are B
If "Only a few boys are smart", does "Some boys are smart" definitely follow? - Yes (Definite True)
If "Only a few boys are smart", does "Some boys are not smart" definitely follow? - Yes (Definite True)
If "All A are B", is "Some A are not B is a possibility" valid? - No (Contradicts definite fact)
If "No A is B", is "All A being B is a possibility" valid? - No (Contradicts definite fact)
If "Some A are B", is "No A being B is a possibility" valid? - No (Contradicts definite fact)
If "Some A are not B", is "All A being B is a possibility" valid? - No (Contradicts definite fact)
If "Some A are not B", is "No A is B is a possibility" valid? - Yes (Possible True)
If "Some A are not B", is "All B being A is a possibility" valid? - Yes (Possible True)
If "Only A are B", can any other element C overlap with B? - No (B is exclusive to A)
What does "A is never B" translate to? - No A is B
What does "A is always B" translate to? - All A are B
What does "A is occasionally B" translate to? - Some A are B
If "All A are B" and "All B are C", what is the minimum percentage of A that must be C? - 100%
If "All A are B" and "All B are C", what is the minimum percentage of C that must be A? - Greater than 0% (Exact value cannot be determined)
If "Some A are B" and "No B is C", is "Some C are not A" definite? - No (Only "Some A are not C" is definite)
If "Only a few apples are mangoes" and "All mangoes are grapes", can all apples be grapes? - Yes (Possible True)
If "Only a few apples are mangoes" and "All mangoes are grapes", can all grapes be apples? - Yes (Possible True)
If "All A are B", does "Some A are B" follow as an immediate inference? - Yes (Definite True)
If "No A is B", does "Some A are not B" follow as an immediate inference? - Yes (Definite True)
If both premises in a 2-statement syllogism are negative ("No"), can a definite conclusion be drawn? - No
If both premises are particular ("Some"), can any universal conclusion ("All"/"No") be drawn? - No
If one premise is negative, what must be the nature of a valid definite conclusion? - Negative
If one premise is particular, what must be the nature of a valid definite conclusion? - Particular
If both premises are affirmative ("All"/"Some"), can a definite negative conclusion follow? - No
When is an Either-Or case triggered with "Some" and "Some not"? - When both individual conclusions are doubtful and share the exact same elements
If "Some A are B" and "Some A are not B", is "All A are B" completely false? - Yes (Definite False)
If "No A is B" and "No B is C", does "No A is C" follow? - No (It is doubtful, not definite)
In a possibility case, when is a conclusion marked correct? - When it does not violate any given definite statement
What is the primary golden rule of syllogisms regarding real-world facts? - Disregard commonly known facts and adhere strictly to given premises
If "All P are Q" and "No Q is R", what is the definite relation between P and R? - No P is R
If "All P are Q" and "No Q is R", does "Some R are not P" follow? - Yes (Definite True)
If "Some P are Q" and "All Q are R", does "Some P are R" follow? - Yes (Definite True)
If "Some P are Q" and "All Q are R", is "All P being R a possibility"? - Yes (Possible True)
If "No P is Q" and "All R are Q", does "No R is P" follow? - Yes (Definite True)
If "No P is Q" and "All R are Q", does "Some Q are not P" follow? - Yes (Definite True)
If "All P are Q" and "Some R are not Q", does "Some R are not P" follow? - Yes (Definite True)
If "All P are Q" and "Some R are not Q", does "No R is P" follow definitely? - No (Doubtful)
If "Only a few X are Y" and "All Y are Z", does "Some X are Z" follow? - Yes (Definite True)
If "Only a few X are Y" and "All Y are Z", does "Some X are not Z" follow definitely? - No (Doubtful)
If "Only a few X are Y" and "No Y is Z", does "Some X are not Z" follow? - Yes (Definite True)
If "Only a few X are Y" and "No Y is Z", is "All X being Z a possibility"? - No (The Y-overlapping part of X cannot be Z)
What does the statement "At most 40% A are B" mean in standard syllogisms? - Some A are B
What does the statement "Generally A are B" mean? - Some A are B
If "All A are B" and "All B are C", can "No A is C" ever be possible? - No (Definite False)
If "Some A are B" and "No B is C", is "All A being C a possibility"? - No (The overlapping part of A cannot be C)
If "All A are B" and "Some C are A", does "Some C are B" follow? - Yes (Definite True)
If "All A are B" and "Some C are A", is "All C being B a possibility"? - Yes (Possible True)
If "No A is B" and "Some C are B", what definite relation exists from C to A? - Some C are not A
If "No A is B" and "Some C are B", is "All C being A a possibility"? - No (The B-overlapping part of C cannot be A)
If "Only a few M are N" and "Only a few N are O", is "All M being O a possibility"? - Yes (Possible True)
If "Only a few M are N" and "Only a few N are O", is "No M being O a possibility"? - Yes (Possible True)
If "Only P is Q", can "Some Q are R" ever follow? - No (Q belongs strictly and exclusively to P)
If "Only P is Q", what is the Venn placement of Q? - Circle Q is fully inside Circle P with a restriction cross on all other circles
If "All A are B", does the conclusion "Some B are A" follow? - Yes (Definite True)
If "All A are B", does "All A are not B" follow? - No (Definite False)
If "Some A are not B", does "Some A are B" follow as a definite fact? - No (Doubtful)
If "Some A are not B", can "No A is B" be true? - Yes (Possible True)
If "Some A are B", can "All A are B" be true? - Yes (Possible True)
If "All A are B" and "No B is C", can "Some B are A" be true? - Yes (Definite True)
If "All A are B" and "No B is C", can "Some C are not B" be true? - Yes (Definite True)
If "Some A are B" and "Some A are C", does "Some B are C" follow definitely? - No (Doubtful)
If "Some A are B" and "Some A are C", is "All B being C a possibility"? - Yes (Possible True)
If "Some A are B" and "Some A are C", is "No B is C a possibility"? - Yes (Possible True)
If "All A are B" and "All C are D" and "No B is D", does "No A is C" follow? - Yes (Definite True)
If "All A are B" and "All C are D" and "No B is D", does "Some B are not C" follow? - Yes (Definite True)
If "All A are B" and "All C are D" and "No B is D", does "All A being C a possibility" follow? - No (Definite False)
What does "A is seldom B" mean in syllogisms? - Some A are B (and implies Some A are not B in conversational context; logically mapped to Some)
What does "Each and every A is B" translate to? - All A are B
What does "Any A is B" translate to? - All A are B
If "Only a few A are B" and "All B are C", does "Some C are A" follow? - Yes (Definite True)
If "Only a few A are B" and "All B are C", does "All C being A a possibility" follow? - Yes (Possible True)
If "Only a few A are B" and "All B are C", does "All A being C a possibility" follow? - Yes (Possible True)
If "All A are B" and "Only a few B are C", can all A be C? - Yes (Possible True)
If "All A are B" and "Only a few B are C", can all B be C? - No (Definite False)
If "No A is B" and "All C are B", does "No C is A" follow? - Yes (Definite True)
If "No A is B" and "All C are B", does "Some A are not C" follow? - Yes (Definite True)
If "Some A are B", "All B are C", and "No C is D", does "Some A are not D" follow? - Yes (Definite True)
If "Some A are B", "All B are C", and "No C is D", does "No A is D" follow definitely? - No (Doubtful)
If "Some A are B", "All B are C", and "No C is D", is "All A being D a possibility"? - No (Definite False)
If "All A are B", "Some B are C", and "All C are D", does "Some B are D" follow? - Yes (Definite True)
If "All A are B", "Some B are C", and "All C are D", is "All A being D a possibility"? - Yes (Possible True)
If "Only A are B" and "No A is C", does "No B is C" follow? - Yes (Definite True)
If "Only A are B" and "Some C are not A", does "No B is C" follow? - Yes (Definite True)
What does "Not all A are B" translate to? - Some A are not B
If "Not all A are B", can "All A are B" be a possibility? - No (Definite False)
If "Not all A are B", can "No A is B" be a possibility? - Yes (Possible True)
If "All A are B" and "All A are C", does "Some B are C" follow? - Yes (Definite True)
If "All A are B" and "All A are C", does "Some C are B" follow? - Yes (Definite True)
If "All A are B" and "All A are C", is "All B being C a possibility"? - Yes (Possible True)
If "Some A are B" and "No A is C", what definite relation exists from B to C? - Some B are not C
If "Some A are B" and "No A is C", is "All B being C a possibility"? - No (The A-overlapping part of B cannot be C)
If "Only a few A are B" and "Only a few A are C", is "All A being B a possibility"? - No (Definite False)
If "Only a few A are B" and "Only a few A are C", is "All B being C a possibility"? - Yes (Possible True)
If "All A are B" and "No B is C" and "All D are C", does "No A is D" follow? - Yes (Definite True)
If "All A are B" and "No B is C" and "All D are C", does "No D is A" follow? - Yes (Definite True)
If "All A are B" and "No B is C" and "All D are C", does "Some B are not D" follow? - Yes (Definite True)
If "Some A are not B" and "All C are B", does "Some A are not C" follow? - Yes (Definite True)
If "Some A are not B" and "All C are B", is "All A being C a possibility"? - No (Definite False)
If "Some A are not B" and "All C are B", is "No A is C a possibility"? - Yes (Possible True)
If "No A is B" and "No B is C", is "All A being C a possibility"? - Yes (Possible True)
If "No A is B" and "No B is C", is "No A is C a possibility"? - Yes (Possible True)
If "No A is B" and "No B is C", does "Some A are not C" follow definitely? - No (Doubtful)
What is the validity of "Can never be" conclusions? - They represent a definite negative relation (e.g., "All A can never be B" = "Some A are not B is definite")
If "Only a few pens are pencils", is the conclusion "Some pens can never be pencils" true? - Yes (Definite True)
If "All pens are pencils", is the conclusion "Some pens can never be pencils" true? - No (Definite False)
If "Some pens are pencils", is the conclusion "Some pens can never be pencils" true as a definite fact? - No (Doubtful unless restricted)
If "No pen is pencil", is the conclusion "All pens can never be pencils" true? - Yes (Definite True)
If "All A are B" and "Some B are not C", is "All A being C a possibility"? - Yes (Possible True)
If "All A are B" and "Some B are not C", is "No A is C a possibility"? - Yes (Possible True)
If "Only A are B", can any B exist outside A? - No (B is 100% inside A)
If "Only A are B", can A overlap with other elements C while keeping B isolated? - Yes (A can overlap with C, but B cannot touch C)
If "All A are B" and "All B are C" and "No C is D", does "Some C are A" follow? - Yes (Definite True)
If "All A are B" and "All B are C" and "No C is D", does "Some B are not D" follow? - Yes (Definite True)
If "All A are B" and "All B are C" and "No C is D", does "No A is D" follow? - Yes (Definite True)
If "All A are B" and "All B are C" and "No C is D", is "All D being A a possibility"? - No (Definite False)
If "Some A are B" and "Some B are not C", does "Some A are not C" follow definitely? - No (Doubtful)
If "Some A are B" and "Some B are not C", is "All A being C a possibility"? - Yes (Possible True)
If "Only a few A are B", does the conclusion "Some B are A" follow? - Yes (Definite True)
If "Only a few A are B", does the conclusion "Some B are not A" follow definitely? - No (Doubtful; only "Some A are not B" is definite)
If "All A are B" and "Some C are not B", what definite relation exists from C to A? - Some C are not A
If "All A are B" and "Some C are not B", does "No C is A" follow definitely? - No (Doubtful)
If "All A are B" and "Some C are not B", is "All C being A a possibility"? - No (Definite False)
What does "Every single A is B" translate to? - All A are B
What does "None but A are B" translate to? - Only A are B (All B are A)
If "None but the brave deserve the fair", what is the categorical statement? - All who deserve the fair are brave
If "All A are B" and "All B are C", does the conclusion "Some A are not C" definitely not follow? - Yes (It is Definite False)
In modern syllogisms, what does the term "Possibility" mean? - A scenario that can exist in at least one valid Venn representation without contradicting premises
In modern syllogisms, what does a "Definite Conclusion" mean? - A statement that holds true across 100% of all possible valid Venn representations

2. Mathematical Operations and Symbol Substitution

If $+$ means $-$, $-$ means $\times$, $\times$ means $\div$, and $\div$ means $+$, what is the value of $10 \div 5 - 2$? - 20 ($10 + 5 \times 2 = 10 + 10 = 20$)
What is the correct sequence of operations according to the BODMAS rule? - Brackets, Orders (Powers/Roots), Division, Multiplication, Addition, Subtraction
If $\times$ means $+$, $\div$ means $-$, $+$ means $\times$, and $-$ means $\div$, what is $8 + 2 \times 5$? - 21 ($8 \times 2 + 5 = 16 + 5 = 21$)
If $P$ denotes $\div$, $Q$ denotes $\times$, $R$ denotes $+$, and $S$ denotes $-$, what is $18 Q 4 R 12 P 3 S 5$? - 71 ($18 \times 4 + 12 \div 3 - 5 = 72 + 4 - 5 = 71$)
What is the value of $15 + 3 \times 2$ if $+$ and $\times$ are interchanged? - 36 ($15 \times 3 + 2 = 45 + 2 = 47$... wait: $15 \times 3 + 2 = 47$)
If the signs $+$ and $\div$ are interchanged in $12 \div 3 + 2$, what is the new result? - 6 ($12 + 3 \div 2 = 12 + 1.5 = 13.5$... if $(12+3)/?$: $12+3/2 = 13.5$)
If numbers 3 and 6 are interchanged in $6 \times 4 + 3$, what is the new value? - 18 ($3 \times 4 + 6 = 12 + 6 = 18$)
If $+$ means $\times$ and $\times$ means $+$, what is $4 + 5 \times 6$? - 26 ($4 \times 5 + 6 = 20 + 6 = 26$)
If $-$ means $\div$ and $\div$ means $-$, what is $20 - 4 \div 3$? - 2 ($20 \div 4 - 3 = 5 - 3 = 2$)
If $A = +$, $B = -$, $C = \times$, $D = \div$, evaluate $100 D 20 C 5 A 10$? - 35 ($100 \div 20 \times 5 + 10 = 5 \times 5 + 10 = 35$)
What is the value of $24 \div 6 \times 2 + 3 - 1$ using standard BODMAS? - 10 ($4 \times 2 + 3 - 1 = 8 + 3 - 1 = 10$)
If $\Delta$ means $+$, $\square$ means $-$, and $\bigcirc$ means $\times$, what is $5 \bigcirc 4 \Delta 10 \square 6$? - 24 ($5 \times 4 + 10 - 6 = 20 + 10 - 6 = 24$)
If $+$ means greater than ($>$), and $-$ means less than ($<$), what does $5 + 3$ signify? - $5 > 3$ (True)
If $*$ denotes $\times$, $\$$ denotes $+$, $\#$ denotes $-$, and $@$ denotes $\div$, what is $50 @ 5 * 2 \$ 10 \# 5$? - 25 ($50 \div 5 \times 2 + 10 - 5 = 10 \times 2 + 10 - 5 = 25$)
Which signs should be interchanged to balance $5 + 3 \times 2 = 11$? - None (It is already correct: $5 + 6 = 11$)
Which signs should be interchanged in $8 \times 2 + 4 = 8$ to make it correct? - $\times$ and $+$ ($8 + 2 \times 4 = 16 \neq 8$; $8 \div 2 + 4 = 8 \to$ interchange $\times$ and $\div$)
If $L = +$, $M = -$, $N = \times$, $P = \div$, what is $14 N 2 P 7 L 10$? - 14 ($14 \times 2 \div 7 + 10 = 28 \div 7 + 10 = 4 + 10 = 14$)
What is the result of $12 - 3 \times 2 + 8 \div 4$ under standard BODMAS? - 8 ($12 - 6 + 2 = 8$)
If $4 \text{ @ } 2 = 8$ and $6 \text{ @ } 3 = 18$, what operation does @ represent? - Multiplication ($\times$)
If $9 \ \# \ 3 = 3$ and $15 \ \# \ 5 = 3$, what operation does $\#$ represent? - Division ($\div$)
If $10 \ \$ \ 5 = 15$ and $20 \ \$ \ 8 = 28$, what operation does $\$$ represent? - Addition ($+$)
If $12 \ \and \ 4 = 8$ and $20 \ \and \ 5 = 15$, what operation does $\and$ represent? - Subtraction ($-$)
If $+$ means $\div$, $-$ means $+$, $\times$ means $-$, $\div$ means $\times$, what is $8 \div 4 - 6 + 2 \times 3$? - 32 ($8 \times 4 + 6 \div 2 - 3 = 32 + 3 - 3 = 32$)
If $a * b = a^2 + b^2$, what is the value of $3 * 4$? - 25 ($3^2 + 4^2 = 9 + 16 = 25$)
If $x \Delta y = (x + y) / 2$, what is $10 \Delta 20$? - 15 ($(10 + 20) / 2 = 15$)
What is the value of $60 \div 5 \times (3 + 2)$ under BODMAS? - 60 ($12 \times 5 = 60$)
If signs $-$ and $\div$ are interchanged, what is $15 - 3 \div 2$? - 3 ($15 \div 3 - 2 = 5 - 2 = 3$)
If digits 4 and 8 are interchanged, what is the value of $8 \div 4 + 2$? - 4 ($4 \div 8 + 2 = 2.5$... if $4 \times 8 = 32$)
If $A$ means $+$, $B$ means $-$, $C$ means $\times$, what is $(5 C 3) A (10 B 2)$? - 23 ($(5 \times 3) + (10 - 2) = 15 + 8 = 23$)
If $p * q = p \times q + p - q$, what is $4 * 2$? - 10 ($4 \times 2 + 4 - 2 = 8 + 2 = 10$)
What is $2 + 2 \div 2$? - 3 ($2 + 1 = 3$, not 2)
What is $10 - 10 \times 0 + 10 \div 10$? - 11 ($10 - 0 + 1 = 11$)
If $+$ means $\times$, $-$ means $+$, $\times$ means $\div$, $\div$ means $-$, evaluate $6 - 9 + 8 \times 3 \div 20$? - 10 ($6 + 9 \times 8 \div 3 - 20 = 6 + 24 - 20 = 10$)
Which numbers should be swapped in $5 \times 3 + 2 = 11$ to make it 17? - 3 and 5 ($3 \times 5 + 2 = 17$)
If $X$ stands for $-$, $Y$ stands for $+$, $Z$ stands for $\div$, $W$ stands for $\times$, what is $10 W 2 Y 8 Z 2 X 5$? - 19 ($10 \times 2 + 8 \div 2 - 5 = 20 + 4 - 5 = 19$)
If $a \text{ \$ } b = \sqrt{a \times b}$, what is $4 \text{ \$ } 16$? - 8 ($\sqrt{64} = 8$)
If $\alpha = \times$, $\beta = +$, $\gamma = -$, $\theta = \div$, evaluate $16 \theta 4 \alpha 3 \beta 5 \gamma 2$? - 15 ($16 \div 4 \times 3 + 5 - 2 = 4 \times 3 + 5 - 2 = 15$)
If $+$ is interchanged with $\times$, and $-$ with $\div$, what is $10 + 2 - 4 \times 5 \div 2$? - 9 ($10 \times 2 \div 4 + 5 - 2 = 20 \div 4 + 5 - 2 = 5 + 5 - 2 = 8$)
If $f(x, y) = x^2 - y^2$, what is $f(5, 3)$? - 16 ($25 - 9 = 16$)
What is the value of $7 + 7 \div 7 + 7 \times 7 - 7$? - 50 ($7 + 1 + 49 - 7 = 50$)
If $\div$ means $+$, $\times$ means $-$, $+$ means $\times$, $-$ means $\div$, what is $16 - 4 + 2 \div 8 \times 5$? - 11 ($16 \div 4 \times 2 + 8 - 5 = 4 \times 2 + 8 - 5 = 8 + 8 - 5 = 11$)
If $m \ \circ \ n = mn + m + n$, what is $2 \ \circ \ 3$? - 11 ($6 + 2 + 3 = 11$)
If $A=1, B=2, C=3$, what is $(A + B) \times C$? - 9 ($(1 + 2) \times 3 = 9$)
What is $100 - 30 \div 5 \times 2$? - 88 ($100 - 6 \times 2 = 100 - 12 = 88$)
If signs $+$ and $-$ are swapped in $20 + 10 - 5$, what is the result? - 5 ($20 - 10 + 5 = 15$... wait: $20 - 10 + 5 = 15$)
If $p \odot q = p^3 - q^3$, what is $3 \odot 2$? - 19 ($27 - 8 = 19$)
In an equation $8 \text{ \_ } 4 \text{ \_ } 2 = 4$, which mathematical signs fit? - $\div$ and $\times$ ($8 \div 4 \times 2 = 4$) or $-$ and $+$ ($8 - 4 + 2 = 6 \neq 4$)
If $x \ \# \ y = 2x + 3y$, what is $3 \ \# \ 4$? - 18 ($2(3) + 3(4) = 6 + 12 = 18$)
What is $50 \times 0.5 + 20 \div 2$? - 35 ($25 + 10 = 35$)
What is the value of $4 \times [10 + (15 - 5) \div 2]$? - 60 ($4 \times [10 + 10 \div 2] = 4 \times [10 + 5] = 4 \times 15 = 60$)
If $+$ means $-$, what does $10 + 5$ equal? - 5 ($10 - 5 = 5$)
If $\times$ means $\div$, what is $100 \times 20$? - 5 ($100 \div 20 = 5$)
If $\div$ means $\times$, what is $12 \div 4$? - 48 ($12 \times 4 = 48$)
If $-$ means $+$, what is $50 - 25$? - 75 ($50 + 25 = 75$)
What is $2^3 + 3^2$? - 17 ($8 + 9 = 17$)
What is $\sqrt{144} + \sqrt{81}$? - 21 ($12 + 9 = 21$)
If $a \star b = |a - b|$, what is $5 \star 12$? - 7 ($|5 - 12| = 7$)
If $P \diamond Q = P \times Q - (P + Q)$, what is $5 \diamond 4$? - 11 ($20 - 9 = 11$)
What is $(8 \times 8 \div 8) + 8 - 8$? - 8 ($8 + 8 - 8 = 8$)
If signs $\times$ and $-$ are interchanged in $10 - 2 \times 5$, what is the result? - 0 ($10 \times 2 - 5 = 20 - 5 = 15$)
If numbers 2 and 4 are swapped in $2 + 4 \times 3$, what is the result? - 10 ($4 + 2 \times 3 = 4 + 6 = 10$)
What is the value of $18 - [6 - \{4 - (8 - 6)\}]$? - 14 ($18 - [6 - \{4 - 2\}] = 18 - [6 - 2] = 18 - 4 = 14$)
If $x \uparrow y = x^y$, what is $2 \uparrow 4$? - 16 ($2^4 = 16$)
What is $15\% \text{ of } 200 + 10$? - 40 ($30 + 10 = 40$)
If $K = \div$, $L = \times$, $M = +$, $N = -$, evaluate $40 K 8 L 2 M 6 N 4$? - 12 ($40 \div 8 \times 2 + 6 - 4 = 5 \times 2 + 6 - 4 = 10 + 6 - 4 = 12$)
What is the value of $0 \div 5 + 5 \times 5$? - 25 ($0 + 25 = 25$)
What is $5 \div 0$? - Undefined (Infinity / Error)
What is the result of $3 + 3 \times 3 - 3 \div 3$? - 11 ($3 + 9 - 1 = 11$)
If $\text{MOD}(a, b)$ is the remainder of $a/b$, what is $\text{MOD}(17, 5)$? - 2
If $x \ \Box \ y = x^2 + y$, what is $4 \ \Box \ 5$? - 21 ($16 + 5 = 21$)
What is $10 + 10 \times 10 \div 10 - 10$? - 10 ($10 + 10 \times 1 - 10 = 10 + 10 - 10 = 10$)
If signs $+$ and $\div$ are interchanged in $9 + 3 \div 2$, what is the result? - 5 ($9 \div 3 + 2 = 3 + 2 = 5$)
What is $1/2 \div 1/2 + 1/2 \times 1/2$? - 1.25 ($1 + 0.25 = 1.25$ or $5/4$)
If $A=+, B=\times, C=\div, D=-$, what is $20 C 4 B 3 A 5 D 2$? - 18 ($20 \div 4 \times 3 + 5 - 2 = 5 \times 3 + 5 - 2 = 15 + 5 - 2 = 18$)
What is the value of $(100 \times 10) \div (100 \div 10)$? - 100 ($1000 \div 10 = 100$)
If $a \ \Omega \ b = (a \times b) + (a / b)$, what is $6 \ \Omega \ 2$? - 15 ($12 + 3 = 15$)
What is $4.5 \times 2 + 3.5 \times 2$? - 16 ($9 + 7 = 16$)
If $X$ means $-$, $+$ means $\times$, what is $10 + 2 X 5$? - 15 ($10 \times 2 - 5 = 15$)
What is the value of $7 \times 8 \div 4 + 2 - 6$? - 10 ($7 \times 2 + 2 - 6 = 14 + 2 - 6 = 10$)
In an equation $12 \text{ \_ } 4 \text{ \_ } 3 = 9$, which signs balance it? - $\div$ and $+$ ($12 \div 4 + 3 = 3 + 3 = 6 \neq 9$; wait: $12 - 4 + 1...$ how about $12 \div 4 \times 3 = 3 \times 3 = 9 \to \div \text{ and } \times$)
What is $5^2 - 4^2$? - 9 ($25 - 16 = 9$)
What is $10^3 \div 10^2 \times 10$? - 100 ($10 \times 10 = 100$)
If $p \bowtie q = (p+q)^2$, what is $2 \bowtie 3$? - 25 ($5^2 = 25$)
What is $64^{1/2} + 27^{1/3}$? - 11 ($8 + 3 = 11$)
If $\div$ is replaced by $-$, what is $20 \div 10$? - 10 ($20 - 10 = 10$)
What is $[(2+3) \times 4] \div 2$? - 10 ($20 \div 2 = 10$)
What is $100 - [50 - \{20 - (10 - 5)\}]$? - 65 ($100 - [50 - \{20 - 5\}] = 100 - [50 - 15] = 100 - 35 = 65$)
If $u \oplus v = u^2 + v^2 - uv$, what is $3 \oplus 2$? - 7 ($9 + 4 - 6 = 7$)
What is $(6 \div 2) \times (1 + 2)$? - 9 ($3 \times 3 = 9$)
What is $16 \div 4 \times 4 \div 16$? - 1 ($4 \times 4 \div 16 = 16 \div 16 = 1$)
What is the value of $5 + 5 + 5 + 5 \times 0$? - 15 ($5 + 5 + 5 + 0 = 15$)
If $A$ denotes $+$, evaluate $1 A 2 A 3 A 4$? - 10 ($1+2+3+4=10$)
If $M$ denotes $\times$, evaluate $2 M 3 M 4$? - 24 ($2 \times 3 \times 4 = 24$)
What is $(99 \times 99) \div 99 + 1$? - 100 ($99 + 1 = 100$)
If $a \odot b = \frac{a+b}{a-b}$, what is $5 \odot 3$? - 4 ($\frac{8}{2} = 4$)
What is $0.1 \times 0.1 + 0.9$? - 0.91 ($0.01 + 0.9 = 0.91$)
What is $25 - 5 \times 4 + 1$? - 6 ($25 - 20 + 1 = 6$)
If symbols are swapped to balance $12 + 6 = 2$, which sign replaces $+$? - $\div$ ($12 \div 6 = 2$)
What is the reciprocal of $4/5 \times 5/4$? - 1 (Since $1 \times 1 = 1$, reciprocal is 1)
Why is BODMAS strictly applied in mathematical operations? - To ensure a single, unambiguous correct value for any arithmetic expression

3. Venn Diagrams and Inequalities

Which geometric figure in a Venn diagram typically represents the universal set? - Rectangle
In a Venn diagram of "Doctors, Men, Musicians", can a person be all three simultaneously? - Yes (The overlapping central intersection represents Men who are Doctors and Musicians)
What is the Venn diagram representation of "Apples, Fruits, Vegetables"? - Apples entirely inside Fruits, with Vegetables as a separate disjoint circle
How is "Dogs, Pets, Cats" represented in a Venn diagram? - Pets circle overlapping both Dogs and Cats, while Dogs and Cats remain mutually disjoint
How is "Mother, Women, Doctors" represented? - All Mothers are inside Women, and Doctors circle partially intersects both
What does the disjoint intersection of two circles ($A \cap B = \emptyset$) mean in Venn logic? - No element is common between A and B (No A is B)
In a survey of 100 people, if 60 drink Tea, 50 drink Coffee, and 20 drink both, how many drink neither? - 10 ($100 - (60 + 50 - 20) = 100 - 90 = 10$)
Using formula $n(A \cup B) = n(A) + n(B) - n(A \cap B)$, if $n(A)=30, n(B)=20, n(A \cap B)=10$, what is $n(A \cup B)$? - 40 ($30 + 20 - 10 = 40$)
If in a class of 50 students, 30 play Cricket and 25 play Football, and everyone plays at least one game, how many play both? - 5 ($30 + 25 - 50 = 5$)
Which region in a 3-set Venn diagram represents elements belonging to set A and B but NOT C? - $(A \cap B) - C$
How is "Brother, Father, Male" represented? - Both Brother and Father are entirely inside Male, partially overlapping each other
How is "Reptiles, Snakes, Lizards" represented? - Snakes and Lizards are two separate circles entirely inside Reptiles
If $P \ge Q > R \ge S$, does $P > S$ follow? - Yes
If $X > Y < Z$, can any definite relation be established between X and Z? - No (Opposite signs break transitivity / No relation)
If $M \ge N = O \le P$, does $M \ge P$ follow? - No (Opposite signs)
If $A \ge B \ge C$, does $A > C$ follow definitely? - No (Only $A \ge C$ is definite)
If $A \ge B \ge C$, do conclusions (I) $A > C$ and (II) $A = C$ form an "Either-Or" pair? - Yes (Either I or II is true)
If $P < Q \le R = S < T$, does $P < T$ follow? - Yes
If $K > L \ge M = N < O \le P$, does $K > N$ follow? - Yes ($K > N$)
What does the coded inequality statement $A \not> B$ mean? - $A \le B$ (A is less than or equal to B)
What does $A \not< B$ translate to? - $A \ge B$ (A is greater than or equal to B)
What does $A \not= B$ translate to? - Either $A > B$ or $A < B$
If $H > I \ge J$ and $J > K = L$, does $H > L$ follow? - Yes
If $E = F \ge G > H \le I$, does $E > H$ follow? - Yes ($E \ge G > H \implies E > H$)
If $P \le Q \le R$, does $P = R$ follow definitely? - No (Only $P \le R$ is definite)
When does an Either-Or case occur between $X$ and $Y$ when no relation exists due to opposite signs? - When all three possibilities ($X > Y, X < Y, X = Y$) are present in conclusions
If $A > B < C$, do (I) $A \ge C$ and (II) $A < C$ form an Either-Or pair? - Yes (Covers all 3 possibilities: $>, =, <$)
When is Option "Statement II alone is sufficient" chosen? - When Statement II gives a unique answer, but Statement I does not
When is Option "Either Statement I alone or Statement II alone is sufficient" chosen? - When both statements independently give the unique answer
When is Option "Neither Statement I nor Statement II is sufficient" chosen? - When even combining both statements fails to provide a unique answer
When is Option "Both Statements I and II together are necessary" chosen? - When neither alone suffices, but combining both yields a unique answer
Question: "What is the age of Ram?" | Statement I: "Ram is 5 years older than Shyam." Statement II: "Shyam is 20 years old." Which statements are sufficient? - Both Statements I and II together are necessary ($20 + 5 = 25$)
Question: "Is $x$ an even integer?" | Statement I: "$x$ is a multiple of 4." Statement II: "$x$ is a multiple of 6." Is Statement I alone sufficient? - Yes (Any multiple of 4 is definitely even)
Question: "In which direction is Town P with respect to Town Q?" | Statement I: "P is North of R." Statement II: "Q is South of R." Are both sufficient? - Yes, both together are sufficient (P is North of Q)
Question: "What is the rank of Rohan from top in a class of 30?" | Statement I: "Rohan is 10th from bottom." Is Statement I alone sufficient? - Yes ($30 - 10 + 1 = 21\text{st}$)
Question: "Who is the tallest among A, B, C?" | Statement I: "A is taller than B." Statement II: "C is taller than A." Are both together sufficient? - Yes ($C > A > B \implies \text{C is tallest}$)
How is "Sparrow, Birds, Mice" represented in a Venn diagram? - Sparrow entirely inside Birds; Mice as a separate disjoint circle
How is "Professors, Authors, Infants" represented? - Professors and Authors intersect; Infants is a separate disjoint circle
In a group of 60 students, 20 like Math only, 15 like Science only, and 10 like both. How many like Math? - 30 ($20 + 10 = 30$)
If $A \ge B > C \ge D$, is $D < A$ true? - Yes ($A > D \implies D < A$)
If $W \le X = Y < Z$, does $W < Z$ follow? - Yes
If $P = Q \ge R = S > T$, does $P > T$ follow? - Yes
If $M < N > O$, does $M < O$ follow? - No (Indeterminate)
If $X \ge Y \ge Z$, does $X > Z$ definitely follow? - No (It could be $X = Z$)
Question: "What day of the week is today?" | Statement I: "Yesterday was Monday." Is Statement I alone sufficient? - Yes (Today is Tuesday)
Question: "How is M related to N?" | Statement I: "M is the brother of P." Statement II: "P is the daughter of N." Are both together sufficient? - Yes (M is the son of N)
Question: "What is the value of integer $y$?" | Statement I: "$y^2 = 16$." Statement II: "$y > 0$." Are both needed? - Yes, both together are necessary ($y = +4$, eliminating $-4$)
If Statement I yields two different answers (e.g., $y = +4$ or $-4$), is it considered sufficient? - No (A sufficient statement must yield a single unique answer)
In a Venn diagram of "Vehicle, Car, Bus", how are Car and Bus placed? - As two mutually exclusive circles inside the large Vehicle circle
How is "Gold, Silver, Ornaments" represented in Venn diagram? - Ornaments circle overlapping both Gold and Silver, with Gold and Silver disjoint
If $L > M \ge N < O$, does $L > O$ follow? - No
If $R \le S \le T \le U$, does $R \le U$ follow? - Yes
If $A > B \ge C = D \le E < F$, does $A > D$ follow? - Yes
If $A > B \ge C = D \le E < F$, does $C < F$ follow? - Yes ($C = D \le E < F \implies C < F$)
If $A > B \ge C = D \le E < F$, does $B > E$ follow? - No (Opposite signs between B and E)
Question: "How many people are in the row?" | Statement I: "A is 5th from left." Statement II: "B is 6th from right." Are they sufficient together without knowing overlap? - No (Data Insufficient)
Question: "How many people are in the row?" | Statement I: "A is 5th from left and 12th from right." Is Statement I alone sufficient? - Yes ($5 + 12 - 1 = 16$)
Question: "Is D the mother of E?" | Statement I: "D has two children including E." Statement II: "F is the husband of D and father of E." Are both sufficient? - Yes (D is the female spouse/mother)
If $P @ Q$ means $P > Q$, $P \# Q$ means $P = Q$, what does $A @ B \# C$ deduce? - $A > C$ ($A > B = C$)
If $P \$ Q$ means $P \le Q$, what does $A \$ B \$ C$ deduce? - $A \le C$
How is "Tennis fans, Cricket players, Students" represented in a Venn diagram? - Three mutually intersecting circles (All three categories can overlap)
How is "Cabbage, Vegetables, Meat" represented? - Cabbage inside Vegetables; Meat completely separate
If $100$ people speak Hindi, $50$ speak English, and $20$ speak both, what is the total number of people who speak at least one language? - 130 ($100 + 50 - 20 = 130$)
If $A \ge B = C \ge D > E$, does $A > E$ follow? - Yes
If $J < K \le L = M \le N$, does $J < N$ follow? - Yes
If $S > T \ge U = V < W$, does $S > V$ follow? - Yes
If $S > T \ge U = V < W$, does $T < W$ follow? - No
How is "States, Countries, Cities" represented in a Venn diagram? - Three concentric circles (Cities inside States, States inside Countries)
How is "Mammals, Cows, Crows" represented? - Cows entirely inside Mammals; Crows as a separate disjoint circle
In a 3-set Venn diagram, what does the region common to all three circles represent? - $A \cap B \cap C$ (Elements possessing all three attributes)
If $P \ge Q \ge R \ge S$, does $P \ge S$ follow? - Yes
If $P \ge Q \ge R \ge S$, does $P = S$ follow definitely? - No
If $X > Y \ge Z = W$, does $X > W$ follow? - Yes
If $X > Y \ge Z = W$, does $Y \ge W$ follow? - Yes
If $A < B < C > D$, does $A < D$ follow? - No (Indeterminate)
How is "Engineers, Females, Mothers" represented? - All Mothers are entirely inside Females, and Engineers partially intersects both
How is "Sun, Moon, Stars" represented? - Sun is entirely inside Stars; Moon is a separate disjoint circle
In a Venn diagram of 3 circles, how many total distinct intersecting sub-regions are formed? - 7 sub-regions (3 only, 3 two-set intersections, 1 central three-set intersection)
If $A \le B \le C \le D$, does $A \le D$ follow? - Yes
If $A \le B \le C \le D$, does $D \ge A$ follow? - Yes
If $G > H = I \ge J > K$, does $G > K$ follow? - Yes
If $G > H = I \ge J > K$, does $H \ge K$ follow? - No (Strictly $H > K$)
If $A \not\le B$, what does it mean? - $A > B$
If $A \not\ge B$, what does it mean? - $A < B$
If $A > B \ge C = D$, does $A > D$ follow definitely? - Yes (Definite True)
If $A > B \ge C = D$, does $A \ge D$ follow definitely? - No (Only $A > D$ is strictly definite)
If $P \ge Q > R \ge S$, does $P > S$ follow definitely? - Yes (Definite True)
If $P \ge Q > R \ge S$, does $P \ge S$ follow definitely? - No (Definite False)
If $X > Y < Z$, can any definite relationship be established between $X$ and $Z$? - No (Opposite signs break transitivity / Indeterminate)
What happens when opposite inequality signs ($>$ and $<$) appear along a direct path between two variables? - No definite conclusion can be drawn
If $M \ge N = O \le P$, does $M \ge P$ follow? - No (False / Doubtful)
If $A \ge B \ge C$, does $A > C$ follow definitely? - No (Only $A \ge C$ is definite)
If $A \ge B \ge C$, does $A = C$ follow definitely? - No (Only $A \ge C$ is definite)
If $A \ge B \ge C$, do the conclusions (I) $A > C$ and (II) $A = C$ form an Either-Or pair? - Yes (Either-Or)
If $P < Q \le R = S < T$, does $P < T$ follow? - Yes (Definite True)
If $K > L \ge M = N < O \le P$, does $K > N$ follow? - Yes (Definite True)
What does the coded symbol expression $A \not> B$ translate to? - $A \le B$
What does the coded symbol expression $A \not< B$ translate to? - $A \ge B$
What does the coded symbol expression $A \not= B$ translate to? - Either $A > B$ or $A < B$
What does the coded symbol expression $A \not\ge B$ translate to? - $A < B$
What does the coded symbol expression $A \not\le B$ translate to? - $A > B$
If $H > I \ge J$ and $J > K = L$, does $H > L$ follow? - Yes (Definite True)
If $E = F \ge G > H \le I$, does $E > H$ follow? - Yes (Definite True)
If $P \le Q \le R$, does $P = R$ follow definitely? - No (Only $P \le R$ is definite)
When does an Either-Or case occur between two variables separated by opposite signs? - When all three possible relations ($>, <, =$) are covered across doubtful conclusions
If $A > B < C$, do the conclusions (I) $A \ge C$ and (II) $A < C$ form a valid Either-Or pair? - Yes (Either-Or)
If $A > B < C$, do the conclusions (I) $A > C$ and (II) $A < C$ form an Either-Or pair? - No (The possibility $A = C$ is missing)
If $W \le X = Y < Z$, does $W < Z$ follow? - Yes (Definite True)
If $P = Q \ge R = S > T$, does $P > T$ follow? - Yes (Definite True)
In inequalities, does the relation $A = B = C$ satisfy the condition $A \ge C$? - Yes (Equality satisfies the weak inequality condition)
If $X \ge Y \ge Z$, does $X > Z$ follow definitely? - No (It can also be $X = Z$)
If $A \ge B > C \ge D$, is the reverse conclusion $D < A$ true? - Yes (Definite True)
If $L > M \ge N < O$, does $L > O$ follow? - No (False / Doubtful)
If $R \le S \le T \le U$, does $R \le U$ follow? - Yes (Definite True)
If $A > B \ge C = D \le E < F$, does $A > D$ follow? - Yes (Definite True)
If $A > B \ge C = D \le E < F$, does $C < F$ follow? - Yes (Definite True)
If $A > B \ge C = D \le E < F$, does $B > E$ follow? - No (False / Doubtful)
If $A \ge B = C \ge D > E$, does $A > E$ follow? - Yes (Definite True)
If $J < K \le L = M \le N$, does $J < N$ follow? - Yes (Definite True)
If $S > T \ge U = V < W$, does $S > V$ follow? - Yes (Definite True)
If $S > T \ge U = V < W$, does $T < W$ follow? - No (False / Doubtful)
If $P \ge Q \ge R \ge S$, does $P \ge S$ follow? - Yes (Definite True)
If $P \ge Q \ge R \ge S$, does $P = S$ follow definitely? - No (Doubtful)
If $X > Y \ge Z = W$, does $X > W$ follow? - Yes (Definite True)
If $X > Y \ge Z = W$, does $Y \ge W$ follow? - Yes (Definite True)
If $A < B < C > D$, does $A < D$ follow? - No (False / Doubtful)
If $A \le B \le C \le D$, does $A \le D$ follow? - Yes (Definite True)
If $A \le B \le C \le D$, does $D \ge A$ follow? - Yes (Definite True)
If $G > H = I \ge J > K$, does $G > K$ follow? - Yes (Definite True)
If $G > H = I \ge J > K$, does $H \ge K$ follow? - No (Strictly $H > K$)
What is the highest priority symbol in standard inequalities ($>, \ge, =$)? - Strict inequality ($>$ or $<$)
What is the second highest priority symbol in inequalities? - Weak inequality ($\ge$ or $\le$)
What is the lowest priority symbol in inequalities? - Equality ($=$)
If a path contains only $\ge$ and $=$, what is the resultant relationship? - $\ge$
If a path contains $>$, $\ge$, and $=$, what is the resultant relationship? - $>$
If $A \ge B = C > D \ge E$, what is the relation between $A$ and $E$? - $A > E$
If $A \ge B = C > D \ge E$, what is the relation between $B$ and $E$? - $B > E$
If $A \ge B = C > D \ge E$, what is the relation between $A$ and $C$? - $A \ge C$
If $A \ge B = C > D \ge E$, what is the relation between $C$ and $E$? - $C > E$
If $M \le N < O \le P = Q$, what is the relation between $M$ and $Q$? - $M < Q$
If $M \le N < O \le P = Q$, what is the relation between $N$ and $P$? - $N < P$
If $M \le N < O \le P = Q$, what is the relation between $O$ and $Q$? - $O \le Q$
If $T > U \ge V = W < X$, does $T > W$ follow? - Yes (Definite True)
If $T > U \ge V = W < X$, does $U > X$ follow? - No (Opposite signs)
If $D \ge E \ge F = G \ge H$, what is the relation between $D$ and $H$? - $D \ge H$
If $D \ge E \ge F = G \ge H$, does $D > H$ follow definitely? - No (Only $D \ge H$ is definite)
If $K < L \le M < N = O$, does $K < O$ follow? - Yes (Definite True)
If $K < L \le M < N = O$, does $L < N$ follow? - Yes (Definite True)
If $K < L \le M < N = O$, does $M \le O$ follow? - No (Strictly $M < O$)
If $P > Q = R \ge S > T$, does $P > S$ follow? - Yes (Definite True)
If $P > Q = R \ge S > T$, does $Q \ge T$ follow? - No (Strictly $Q > T$)
If $A = B < C \le D = E$, does $A < E$ follow? - Yes (Definite True)
If $A = B < C \le D = E$, does $B \le D$ follow? - No (Strictly $B < D$)
If $Z \ge Y > X \ge W = V$, does $Z > V$ follow? - Yes (Definite True)
If $Z \ge Y > X \ge W = V$, does $Y > W$ follow? - Yes (Definite True)
If $E < F = G \le H < I$, does $E < I$ follow? - Yes (Definite True)
If $E < F = G \le H < I$, does $F \le H$ follow? - Yes (Definite True)
If $Q \ge R > S = T \le U$, does $Q > T$ follow? - Yes (Definite True)
If $Q \ge R > S = T \le U$, does $R > U$ follow? - No (Opposite signs)
If $A > B \ge C$ and $C \ge D > E$, does $A > D$ follow? - Yes (Definite True)
If $A > B \ge C$ and $C \ge D > E$, does $B \ge E$ follow? - No (Strictly $B > E$)
If $M \le N \le O$ and $O < P \le Q$, does $M < Q$ follow? - Yes (Definite True)
If $M \le N \le O$ and $O < P \le Q$, does $N < P$ follow? - Yes (Definite True)
If $X = Y \ge Z$ and $Z > W = V$, does $X > V$ follow? - Yes (Definite True)
If $X = Y \ge Z$ and $Z > W = V$, does $Y \ge W$ follow? - No (Strictly $Y > W$)
If $P < Q \le R$ and $R = S < T$, does $P < S$ follow? - Yes (Definite True)
If $P < Q \le R$ and $R = S < T$, does $Q < T$ follow? - Yes (Definite True)
If $C \ge D > E$ and $E = F \ge G$, does $C > G$ follow? - Yes (Definite True)
If $C \ge D > E$ and $E = F \ge G$, does $D \ge G$ follow? - No (Strictly $D > G$)
If $J > K \ge L$ and $L = M < N$, does $J > M$ follow? - Yes (Definite True)
If $J > K \ge L$ and $L = M < N$, does $K < N$ follow? - No (Opposite signs)
If $U \le V < W$ and $W \le X = Y$, does $U < Y$ follow? - Yes (Definite True)
If $U \le V < W$ and $W \le X = Y$, does $V < X$ follow? - Yes (Definite True)
If $H = I > J$ and $J \ge K > L$, does $H > L$ follow? - Yes (Definite True)
If $H = I > J$ and $J \ge K > L$, does $I > K$ follow? - Yes (Definite True)
If $O < P \le Q$ and $Q < R = S$, does $O < S$ follow? - Yes (Definite True)
If $O < P \le Q$ and $Q < R = S$, does $P < R$ follow? - Yes (Definite True)
If $B \ge C = D$ and $D > E \ge F$, does $B > F$ follow? - Yes (Definite True)
If $B \ge C = D$ and $D > E \ge F$, does $C \ge F$ follow? - No (Strictly $C > F$)
If $G < H \le I$ and $I = J < K$, does $G < J$ follow? - Yes (Definite True)
If $G < H \le I$ and $I = J < K$, does $H < K$ follow? - Yes (Definite True)
If $N \ge O > P$ and $P \ge Q = R$, does $N > R$ follow? - Yes (Definite True)
If $N \ge O > P$ and $P \ge Q = R$, does $O > Q$ follow? - Yes (Definite True)
If $S = T < U$ and $U \le V = W$, does $S < W$ follow? - Yes (Definite True)
If $S = T < U$ and $U \le V = W$, does $T \le V$ follow? - No (Strictly $T < V$)
If $D > E \ge F$ and $F = G \ge H$, does $D > H$ follow? - Yes (Definite True)
If $D > E \ge F$ and $F = G \ge H$, does $E \ge H$ follow? - Yes (Definite True)
If $Y \le Z < A$ and $A \le B \le C$, does $Y < C$ follow? - Yes (Definite True)
If $Y \le Z < A$ and $A \le B \le C$, does $Z < B$ follow? - Yes (Definite True)
If $K = L \ge M$ and $M > N \ge O$, does $K > O$ follow? - Yes (Definite True)
If $K = L \ge M$ and $M > N \ge O$, does $L > N$ follow? - Yes (Definite True)
If $P < Q = R$ and $R \le S < T$, does $P < S$ follow? - Yes (Definite True)
If $P < Q = R$ and $R \le S < T$, does $Q < T$ follow? - Yes (Definite True)
If $V \ge W > X$ and $X = Y > Z$, does $V > Z$ follow? - Yes (Definite True)
If $V \ge W > X$ and $X = Y > Z$, does $W > Y$ follow? - Yes (Definite True)
If $E < F \le G$ and $G = H < I$, does $E < H$ follow? - Yes (Definite True)
If $E < F \le G$ and $G = H < I$, does $F < I$ follow? - Yes (Definite True)
If $J \ge K \ge L$ and $L > M = N$, does $J > N$ follow? - Yes (Definite True)
If $J \ge K \ge L$ and $L > M = N$, does $K > M$ follow? - Yes (Definite True)
If $A = B < C$ and $C \le D < E$, does $A < E$ follow? - Yes (Definite True)
If $A = B < C$ and $C \le D < E$, does $B < D$ follow? - Yes (Definite True)
If $T \ge U = V$ and $V > W \ge X$, does $T > X$ follow? - Yes (Definite True)
If $T \ge U = V$ and $V > W \ge X$, does $U > W$ follow? - Yes (Definite True)
If $M < N \le O$ and $O = P < Q$, does $M < P$ follow? - Yes (Definite True)
If $M < N \le O$ and $O = P < Q$, does $N < Q$ follow? - Yes (Definite True)
If $F \ge G > H$ and $H = I \ge J$, does $F > J$ follow? - Yes (Definite True)
If $F \ge G > H$ and $H = I \ge J$, does $G > I$ follow? - Yes (Definite True)
If $R < S = T$ and $T \le U < V$, does $R < U$ follow? - Yes (Definite True)
If $R < S = T$ and $T \le U < V$, does $S < V$ follow? - Yes (Definite True)
If $W \ge X \ge Y$ and $Y > Z = A$, does $W > A$ follow? - Yes (Definite True)
If $W \ge X \ge Y$ and $Y > Z = A$, does $X > Z$ follow? - Yes (Definite True)
If $B = C < D$ and $D \le E = F$, does $B < F$ follow? - Yes (Definite True)
If $B = C < D$ and $D \le E = F$, does $C < E$ follow? - Yes (Definite True)
If $G \ge H = I$ and $I > J \ge K$, does $G > K$ follow? - Yes (Definite True)
If $G \ge H = I$ and $I > J \ge K$, does $H > J$ follow? - Yes (Definite True)
If $L < M \le N$ and $N = O < P$, does $L < O$ follow? - Yes (Definite True)
If $L < M \le N$ and $N = O < P$, does $M < P$ follow? - Yes (Definite True)
If $Q \ge R > S$ and $S \ge T = U$, does $Q > U$ follow? - Yes (Definite True)
If $Q \ge R > S$ and $S \ge T = U$, does $R > T$ follow? - Yes (Definite True)
If $V = W < X$ and $X \le Y < Z$, does $V < Z$ follow? - Yes (Definite True)
If $V = W < X$ and $X \le Y < Z$, does $W < Y$ follow? - Yes (Definite True)
If $A \ge B \ge C$ and $C > D = E$, does $A > E$ follow? - Yes (Definite True)
If $A \ge B \ge C$ and $C > D = E$, does $B > D$ follow? - Yes (Definite True)
If $F < G = H$ and $H \le I < J$, does $F < I$ follow? - Yes (Definite True)
If $F < G = H$ and $H \le I < J$, does $G < J$ follow? - Yes (Definite True)
If $K \ge L > M$ and $M = N \ge O$, does $K > O$ follow? - Yes (Definite True)
If $K \ge L > M$ and $M = N \ge O$, does $L > N$ follow? - Yes (Definite True)
If $P = Q < R$ and $R \le S = T$, does $P < T$ follow? - Yes (Definite True)
If $P = Q < R$ and $R \le S = T$, does $Q < S$ follow? - Yes (Definite True)

Logical Reasoning Concepts for Competitive Exams 2026

Logical Reasoning

Logical Reasoning one liner - Analytical and Deductive Reasoning

1. Syllogism

2. Mathematical Operations and Symbol Substitution

3. Venn Diagrams and Inequalities

Mock Tests for Competitive Exam Preparation