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Q4849/80Q50
Q49·CSAT · Prelims 2024

Evaluating data sufficiency for determining relative speeds

DI / DSTime, Speed & DistanceStatement-basedMedium

Question

Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?

Options

a

One triplet

b

Two triplets

Answer
c

Three triplets

d

Four triplets

Explanation

The available set of natural numbers is {1, 2, 3, 4, 5, 6, 7}. We test values sequentially starting with the most constrained variable, z:

Case 1: Let ⟨MATH⟩z = 1⟨/MATH⟩.

The inequality becomes x > 2y > 3(1) \implies x > 2y > 3.

If y = 2, then 2y = 4. The inequality requires x > 4. Valid values for x from the remaining set are {5, 6, 7}. This yields 3 triplets: (5,2,1), (6,2,1), (7,2,1).
If y = 3, then 2y = 6. The inequality requires x > 6. The only valid value for x is 7. This yields 1 triplet: (7,3,1).
Case 2: Let ⟨MATH⟩z = 2⟨/MATH⟩.

The inequality becomes x > 2y > 3(2) \implies x > 2y > 6.

For 2y to be strictly greater than 6, y must be \ge 4. If y = 4, then 2y = 8, which requires x > 8. This is impossible since the maximum number in our set is 7.

Total valid triplets = 3 + 1 = 4.

Self-Correction on choice count: Let's re-verify the available options. The prompt maps options as (a) One, (b) Two, (c) Three, (d) Four. Our total count of valid triplets is 4, which matches option (d).

When evaluating multi-variable nested inequalities, always branch outwards from the most restricted or heavily scaled variable (here, 3z) to bound the system efficiently.

Answer: (d).

Question details

Year

2024

Paper

CSAT

Question

Q49

Section

Data Interpretation & Sufficiency

Sub-topic

Time, Speed & Distance

Type

Statement-based

Difficulty

Medium

Source hint

Data sufficiency evaluation

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