SSC CGL 2025 Tier-I · 12 September 2025, Shift 1 · Quantitative Aptitude · Question 7 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 11 September 2026.

Where this paper and its answers come from

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 100 and 250 that are exactly divisible by 11?

(a)176
(b)186
(c)196
(d)146

Answer

Why

Correct — A. Find the first and last multiples of 11 inside the range.

First: 11 × 9 = 99 is below 100, so start at 11 × 10 = 110
Last: 11 × 23 = 253 is above 250, so stop at 11 × 22 = 242

Multiples of 11 are evenly spaced, so average = (first + last) ÷ 2
(110 + 242) ÷ 2 = 352 ÷ 2 = 176 → option (a)

Why the others are wrong

(b)
186 — 186 is not a multiple of 11 (11 × 17 = 187). The list has 13 terms, an odd count, so its average is the middle term, itself a multiple of 11.
(c)
196 — 196 is not a multiple of 11 either (11 × 18 = 198), so it cannot be the middle term of 110, 121, … 242.
(d)
146 — 146 = 11 × 13 + 3, so it is not a multiple of 11 and cannot be the middle term. It sits 30 below the true average.

Concept

Multiples of 11 form an arithmetic progression: each is 11 more than the last. For any arithmetic progression the average is (first + last) ÷ 2, so you never add all the terms.

With an odd number of terms the average is also the middle term. Here there are 22 − 10 + 1 = 13 terms, and the 7th is 11 × 16 = 176.

Neither endpoint divides by 11 (100 = 11 × 9 + 1 and 250 = 11 × 22 + 8), so whether 'between' includes 100 and 250 makes no difference here.

Key facts

Average of an arithmetic progression = (first term + last term) ÷ 2.
Multiples of 11 from 110 to 242 number 22 − 10 + 1 = 13.
With an odd number of terms the average is the middle term: 11 × 16 = 176.

Study next

Sum of an arithmetic progression = number of terms × averageCounting multiples in a range: ⌊250⁄11⌋ − ⌊100⁄11⌋ = 22 − 9 = 13Averages of consecutive odd or even numbers

Common traps

Averaging the range endpoints, (100 + 250) ÷ 2 = 175, which is one short of the answer.
Starting the list at 99 (11 × 9), which lies below 100.

The first-plus-last rule also settles 18 Sep 2024, 16:00, Quant Q.3 (average of the first 125 natural numbers, 63). Primes are not evenly spaced, so 11 Sep 2024, 12:30, Quant Q.18 (average of the primes between 50 and 76) needs a full sum instead.

Related PYQs

No directly related past PYQ was found.

Topic: Averages — all 40 SSC CGL questions on it, every solved shift.