SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 10 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What is the average of all integers between 300 and 450 that are exactly divisible by 13?

(a)277
(b)377
(c)477
(d)577

Answer

Why

Correct — B. List the multiples of 13 that fall between 300 and 450.

First: 13 × 23 = 299 is below 300, so start at 13 × 24 = 312
Last: 13 × 35 = 455 is above 450, so stop at 13 × 34 = 442

Multiples of 13 are equally spaced, so average = (first + last) ÷ 2
= (312 + 442) ÷ 2 = 754 ÷ 2 = 377 → option (b)

Why the others are wrong

(a)
277 — 277 is below 300, yet every number being averaged lies between 312 and 442. An average can never be smaller than the smallest value in the set.
(c)
477 — 477 is above 450, beyond even the largest multiple, 442. The average of a set cannot exceed its largest member, so it is ruled out before any division.
(d)
577 — 577 is more than 450, the upper limit printed in the question. Averaging numbers that run from 312 to 442 cannot give a result outside that range.

Concept

Multiples of a fixed number are equally spaced: 312, 325, 338 … 442, each 13 more than the last. Such a list is an arithmetic progression (AP).

In an AP the terms pair off from both ends — 312 with 442, 325 with 429 — and every pair has the same sum, 754. So the average is (first + last) ÷ 2, and you never add all eleven terms.

With an odd count the average is also the middle term: the 6th of 11 is 13 × 29 = 377.

Neither 300 nor 450 is a multiple of 13, so the word between needs no inclusive-or-exclusive decision here.

A range check alone settles it: 377 is the one option that lies between 312 and 442.

Key facts

The multiples of 13 between 300 and 450 run from 312 (13 × 24) to 442 (13 × 34), eleven numbers in all.
The average of an arithmetic progression is (first term + last term) ÷ 2.
An average always lies between the smallest and the largest value averaged.

Study next

Counting the multiples of a number in a range: (last − first) ÷ common difference + 1Sum of an arithmetic progression as number of terms × averageAverage of consecutive odd or even numbers in a range

Common traps

Averaging the limits themselves: (300 + 450) ÷ 2 = 375, but neither 300 nor 450 is a multiple of 13.
Taking 13 × 23 = 299 as the first term, although it lies below 300.

The same average-of-multiples question appears at 12 Sep 2025, 09:00, Quant Q.7 (multiples of 11 between 100 and 250, average 176) and 15 Sep 2025, 12:30, Quant Q.5 (multiples of 25 between 1000 and 1300, average 1150).

Related PYQs

No directly related past PYQ was found.

Topic: Averages — all 53 SSC CGL questions on it, every solved shift.