UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 39 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 39

Question

If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct? I. The difference of the numbers is an even number. II. One of the numbers is a perfect square. Select the answer using the code given below.

(a)I only
(b)II only
(c)Both I and II
(d)Neither I nor II

UnlockIAS answer: (c)Both I and II

Solution

HCF × LCM = a × b. If this equals a³, then b = a². The difference a² − a = a(a − 1) is a product of consecutive integers, hence even (I), and b = a² is a perfect square (II). Both hold.

UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).

Section

Mathematics

Topic Reference

Numeracy — HCF and LCM

Official UPSC key still awaited

UPSC has announced (PIB Release 2262441, 18 May 2026) that the provisional answer key for CSE Prelims 2026 will be released “soon after Exam”. Until then, use the CSAT score calculator for your qualifying-status estimate, and join the per-question discussion below.

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Official Notification

PIB Release 2262441

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