SSC CGL 2024 Tier-I · 11 September 2024, Shift 2 · Quantitative Aptitude · Question 10 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the quotient, when the mean proportional of 7 1⁄5 and 245 is divided by an even prime number.

(a)21
(b)36
(c)49
(d)42

Answer

Why

Correct — A. The mean proportional of two numbers is their geometric mean, √(ab).

7 1⁄5 = 36⁄5 = 7.2
7.2 × 245 = 36 × 49 = 1764
√1764 = 42

The only even prime is 2, so that is the divisor.
42 ÷ 2 = 21 → option (a)

Why the others are wrong

(b)
36 — 36 is one factor of the product, since 7 1⁄5 × 245 = 36 × 49. It is a step inside the working, not the mean proportional, which is √1764 = 42.
(c)
49 — 49 is the other factor of 1764, because 245 ÷ 5 = 49. Like 36 it appears while forming the product; the mean proportional is the square root of the whole product.
(d)
42 — 42 is the mean proportional itself. The question asks for it divided by an even prime, and the only even prime is 2, so one more step gives 21.

Concept

The mean proportional of a and b is the number x for which a : x = x : b. That forces x² = ab, so x = √(ab) — the geometric mean, not the average.

The second hook is verbal. 2 is the only even prime, because every other even number has 2 as a proper factor and so is composite.

The arithmetic is built to close: 7.2 × 245 = 1764 = 42². If your product is not a perfect square, check the mixed-fraction conversion before anything else.

The phrase 'an even prime number' carries the whole second step. A candidate who reads past it is left with no divisor at all and stops at 42.

Key facts

The mean proportional of a and b is √(ab), the geometric mean, not (a + b)⁄2.
2 is the only even prime number.
7 1⁄5 = 36⁄5 = 7.2, and 7.2 × 245 = 1764 = 42².

Study next

Third proportional and fourth proportionalGeometric mean versus arithmetic mean in ratio questionsSquare roots of four-digit numbers by prime factorisation

Common traps

Averaging 7.2 and 245 instead of multiplying them.
Stopping at 42, the mean proportional, without dividing by the even prime.
Reading 'even prime' as any even number and dividing by 4 or by 10.

SSC hides one step behind a definition — 'mean proportional' here, 'even prime' immediately after — so the arithmetic is trivial once both are decoded. Quant Q.18 of this same shift uses the same tactic, asking for the average of the primes between 50 and 76.

Related PYQs

No directly related past PYQ was found.