Evaluating data sufficiency for determining relative speeds
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
One triplet
Two triplets
Three triplets
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:
The inequality becomes x > 2y > 3(1) \implies x > 2y > 3.
The inequality becomes x > 2y > 3(2) \implies x > 2y > 6.
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).
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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