Reasoning

Data Sufficiency

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MEDIUM

Who among A, B, C, D, E and F is the tallest?
I. Only two of them are taller than C.
II. D is shorter than F.
III. C is taller than A but shorter than F and B.

Only I and II

Only II and III

Only I and III

Data inadequate

Explanation

From I and III we can determine the order of height.

MEDIUM

Who is the daughter-in-law of D?
I. K is brother of F. U is wife of L's nephew.
II. T is brother of P. V is son of P. U is mother of V.
III. D is wife of F. F is father of P. F has two children.

Only I and III

Only II and III

Only I and either II or III

Only I and II

Explanation

Even after using all three statements, insufficient information is provided.

MEDIUM

Consider the following statements regarding seating arrangement properties:

In linear arrangements facing North, the 'Left' corresponds to the West direction.
In linear arrangements facing South, the relative directions are identical to North-facing arrangements.
In circular arrangements where individuals face the center, their relative positions (left/right) are determined by their orientation toward the center.

Which of the statements given above are correct?

1 and 2 only

2 and 3 only

1 and 3 only

1, 2, and 3

Explanation

🌟 Quick Verification

Direct Answer: The correct answer is 1 and 3 only.
Core Concept: Understanding Directional Orientation in seating arrangements.

🧠 Concept Blueprint

Linear North vs South:
- When facing North, your left hand points West and your right points East.
- When facing South (the opposite), your left hand points East and your right points West. This means the directions are reversed compared to North-facing arrangements, making statement 2 incorrect.
Circular Arrangement:
- In a circular table where people face the center, the 'left' of any person is their clockwise direction, and 'right' is their counter-clockwise direction relative to their position.

📊 Fact Spotlight

Arrangement Type	Facing Direction	Left Orientation	Right Orientation
Linear	North	West	East
Linear	South	East	West
Circular	Center	Clockwise	Counter-clockwise

💡 Exam Strategy & Trivia

Tip

Common Pitfall: Always visualize the person sitting at the table. If you are facing the center of a clock, your left hand is moving towards the next hour mark (clockwise).

MEDIUM

On which day starting from Monday did Mayank visit Chennai?
I. Mayank took leave on Wednesday.
II. Mayank visited Chennai the day after his mother's visit to his house.
III. Mayank's mother visited Mayank's house neither on Monday nor or Thursday.

II and III

I and II

I and III

All I, II and III are required

Explanation

From II and III, we can determine the day.

MEDIUM

City A is in which direction with respect to City E?
I. A is to the north of F, which is to the west of C.
II. A is to the north-west of C.
III. F is to the north-west of E.

Any two of the given three

Only I and II

Only II and III

Only I and III

Explanation

Combining II and III, we can find the position of A and E.

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MEDIUM

Ten persons are sitting in a straight row and facing north. How many persons sitting to the right of V?
I. S sits third to the right of M and none of them sits at end of the row. Only two persons are sitting between V and S.
II. V sits second to the left of A, who sits from either ends of the row.

If the data in statement I alone is sufficient

If the data in statement II alone is sufficient

If the data either in statement I alone or in statement II alone are sufficient

If the data in both statement I and II together are not sufficient

Explanation

Both statements are necessary to determine the arrangement.

MEDIUM

How is L related to N?
I. K is daughter of L, and N is daughter of M.
II. K is mother of N, who is sister of O.

Only I is sufficient

Only II is sufficient

Either I or II is sufficient

Both I and II are necessary

Explanation

Combining both: K is daughter of L. K is mother of N. N is daughter of M. Thus, L is related to N. Both statements are required.

MEDIUM

In a five-floor building, on which floor does Manav live? (Starting from first floor going up to fifth floor)
I. Manav lives just above Kriti's flat, whose flat is just above Rakesh's flat.
II. Umesh lives on top floor.
III. Deepak lives just above Manav's flat. Rakesh lives on the first floor.

Only I is sufficient

Only II is sufficient

Both II and III are sufficient

Both I and III are sufficient

Explanation

By combining I and III, Manav's floor can be determined.

MEDIUM

Consider the following statements regarding the methodology of solving Data Sufficiency questions in logical reasoning:

While analyzing Statement II, the information provided in Statement I must be incorporated to ensure all variables are accounted for.
In Data Sufficiency, the primary objective is to check if the provided data is sufficient to reach a unique solution, not necessarily to calculate the final numerical or logical result.
If neither statement individually provides a solution, the data from both statements should be combined to attempt a solution.

Which of the statements given above are correct?

1 and 2 only

2 and 3 only

1 and 3 only

1, 2, and 3

Explanation

🌟 Quick Verification

Direct Answer: The correct answer is 2 and 3 only.
Core Concept: Understanding the independent nature of evaluating statements in Data Sufficiency.

🧠 Concept Blueprint

Independent Evaluation:
- When evaluating Statement I, it must be assessed entirely on its own merit.
- Similarly, Statement II must be evaluated independently. Incorporating data from Statement I while checking Statement II violates the fundamental rule of Data Sufficiency methodology.
Logical Threshold:
- The goal is Sufficiency Determination (can we find the answer?), not Calculation (what is the specific answer?).
- If individual statements fail, Combination (I + II) is the mandatory next logical step.

📊 Fact Spotlight

Rule	Action	Significance
Independence	Analyze I and II separately	Prevents bias from overlapping information
Goal	Sufficiency > Final Answer	Saves time by stopping once determined
Strategy	Combine only if necessary	Last resort for logic extraction

💡 Exam Strategy & Trivia

Tip

Common Trap: A classic mistake is assuming that if Statement I gives a number and Statement II gives a number, you must combine them. Always check if one is sufficient alone before moving to combination.

MEDIUM

P, Q, R, S and T are the five persons in the group. How many persons are taller than T?
I. P is taller than Q, who was only shorter than P and T.
II. R is shorter than P, who was shorter than T.

Only Statement I is sufficient to answer.

Only Statement II is sufficient to answer.

Either Statement I or Statement II is sufficient to answer.

Neither Statement I nor Statement II is sufficient to answer.

Explanation

From Statement I: 'Q was only shorter than P and T' means P, T > Q. No information about R, S. However, from the structure, only P is definitely taller than T.

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MEDIUM

Among P, Q, R, S, T and U each having a different weight, who is the heaviest?
I. P is lighter than S, who is lighter than R.
II. R is lighter than only T.
III. S is heavier than U.

Only I and II

Only II and III

Only I and III

All I, II and III together

Explanation

All are required. From II, T is the heaviest.

MEDIUM

Consider the following scenario involving ranking:
'Madan's rank is 24 less than Nandan's rank (M = N - 24) and Nisha's rank is 38 more than Madan's rank (Ni = M + 38).'

Which of the following statements is true regarding this scenario?

The rank of Madan can be determined if the rank of Nandan is known.

The rank of Madan can be determined if the rank of Nisha is known.

Both of the above are true.

The rank of Madan cannot be determined in any case.

Explanation

🌟 Quick Verification

Direct Answer: Both of the above are true.
Core Concept: Variable Dependence in Algebraic Ranking.

🧠 Concept Blueprint

The Equations:
- Equation 1: $M = N - 24$
- Equation 2: $Ni = M + 38$
Logical Deduction:
- If $N$ is known, $M$ is fixed by the first equation.
- If $Ni$ is known, $M$ is fixed by rearranging the second equation ( $M = Ni - 38$ ).

📊 Fact Spotlight

Condition	Effect on Madan's Rank
Nandan's Rank Known	$M$ is solvable
Nisha's Rank Known	$M$ is solvable
Unknown Ranks	$M$ is indeterminate

💡 Exam Strategy & Trivia

Tip

Memory Aid: In Data Sufficiency, look for the 'Bridge Variable'. Here, Madan ( $M$ ) is the bridge variable. If you define the bridge, you solve the puzzle.

MEDIUM

Assertion (A): Madan's rank in a class cannot be determined using the information that his rank is 24 less than Nandan's, and Nisha's rank is 38 more than Madan's.

Reason (R): In a linear ranking system, establishing a relative rank difference between variables is insufficient to derive an absolute rank without at least one fixed numerical anchor point.

Both (A) and (R) are true and (R) is the correct explanation of (A)

Both (A) and (R) are true but (R) is not the correct explanation of (A)

(A) is true but (R) is false

(A) is false but (R) is true

Explanation

🌟 Quick Verification

Direct Answer: The correct answer is Both (A) and (R) are true and (R) is the correct explanation of (A).

🧠 Concept Blueprint

Mathematical Logic:
- Let M be Madan's rank and N be Nandan's rank: M = N - 24.
- Let Ni be Nisha's rank: Ni = M + 38.
- To solve for M, one needs a concrete value for either N, Ni, or the total class size. Without this, the equations remain interdependent variables (e.g., M = M + 4 in some configurations), leading to an indeterminate system.
Exam Strategy: Always look for an 'absolute value' in ranking questions. If only relative differences are provided, the problem is almost certainly 'data insufficient'.

MEDIUM

What does 'important' represent in the given code language?
I. 'sa ri mn pa' means 'work out important problems'
II. 'fe ze pi' means 'very intelligent girl'
III. 'ze mn sa' means 'very important work'

Only I and III

Only I and II

Either I and II or I and III

All I, II and III together are sufficient

Explanation

From I and III: Code for 'important' can be derived (between mn, sa).

MEDIUM

Eight friends A, B, C, D, E, F, G and H are sitting around a circular table facing the center. Who is opposite to A?
I. D sits second to right of F and opposite to E. A is an immediate neighbor of B and C.
II. G sits third to right of E, who sits second to right of A.

if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

if the data either in statement I alone or in statement II alone are sufficient to answer the question.

if the data in both the statements I and II together are not sufficient to answer the question.

Explanation

Both statements are necessary.

MEDIUM

Six teachers i.e. A, B, C, D, E and F who all take lecture from Monday to Saturday on different topic i.e. Math's, Physics, Chemistry, Biology, Economics and English but not necessarily in the same order. Who among the following teaches Economics on which of the following day?
I. Only three teachers take classes between B and the one who takes class of Biology. Economy lecture is taken immediately before Biology Class. B does not take lecture on Saturday. Only one person takes lecture between E and C, who takes lecture on the last day but not of Biology.
II. E takes lecture immediately after the one who takes lecture of English. Only one person takes lecture between E and D. Only two person takes lecture between C and A, who takes lecture between C and the one who takes lecture of Economics subject. D takes lecture of Economics.

If statement I alone is sufficient to answer the question, but statement II alone is not sufficient to answer the question.

If statement II alone is sufficient to answer the question, but statement I alone is not sufficient to answer the question.

If statement either I or II is sufficient to answer the question.

If both the statements I and II taken together are not sufficient to answer the questions.

Explanation

The question is on which day the Economics lecture is taken. Using statement I, we can determine the order of teachers as there is a gap of 3 between B and Biology, and Economy (Economics) is immediately before Biology. Hence, I is sufficient.

MEDIUM

In queue arrangement problems, why is the identification of individuals who are 'NOT at the extremes' considered a high-value inference?

It proves the queue has an even number of people.

It eliminates two possible positions for that individual immediately, narrowing down the potential permutations for others.

It forces the individual to the center of the queue.

It implies the individual is the shortest in the queue.

Explanation

🌟 Quick Verification

Direct Answer: It eliminates two possible positions for that individual immediately, narrowing down the potential permutations for others.
Core Concept: Constraint Propagation.

🧠 Concept Blueprint

Reasoning:
- In a queue of length 'n', there are 'n' spots. 'Extremes' are position 1 and position 'n'.
- Identifying someone is NOT at these two spots provides a concrete constraint (Position ≠ 1 AND Position ≠ n).
- This constraint allows you to prune the search space for that specific entity, making subsequent logic steps (like 'A is behind B') easier to solve.

📊 Fact Spotlight

Constraint Type	Logical Value
Not at Ends	Eliminates 2 positions
First Position	Fixes 1 position
Between X and Y	Creates a relative block (e.g., X, Z, Y)

💡 Exam Strategy & Trivia

Tip

Common Trap: Students often wait for 'absolute' positions (e.g., 'C is at 3rd') before doing anything. Use 'negative' constraints (e.g., 'not at ends') to start filling the diagram immediately.

Trivia: In computer science, this is similar to constraint satisfaction problem solving.

MEDIUM

As per instructions: Office X is in which direction with respect to Office Y?
I. X is to the east of Z, which is to the north of Y.
II. W is to the east of Y and to the south of X.

Only I is sufficient

Only II is sufficient

Either I or II is sufficient

Both I and II are necessary

Explanation

From Statement I, X is to the east of Z, and Z is to the north of Y. Thus, X is to the north-east of Y. This is sufficient.

MEDIUM

Who is the lightest amongst A, B, C, D and E?
I. D is heavier than C and lighter than A.
II. B is heavier only than E.

if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

if the data either in statement I alone or in statement II alone are sufficient to answer the question.

if the data in both the statements I and II together are not sufficient to answer the question.

Explanation

Both statements are necessary.

MEDIUM

Conclusion:
I. Some hands are not Socks.
II. No legs are socks.
Statement:
I. All legs are Hands. Some Shoes are legs. No Legs are fingers.
II. Some watches are arm. All arms are fingers. All legs are Hands.
III. No Socks are Shoes. All legs are Shoes. Some Hands are finger.

If the data in statement I and II together are sufficient to answer the question, while the data in statement III are not required to answer the question.

If the data in statement I and III together are sufficient to answer the question, while the data in statement II are not required to answer the question.

If the data in statement II and III are sufficient to answer the question, while the data in statement I are not required to answer the question.

If the data in all three statements I, II and III together are necessary to answer the question.

Explanation

Statements I and III are sufficient to verify the conclusions.

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