SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 16 of 99

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 13 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.

The average of a group of 11 numbers is 61. If the first six numbers have an average of 57 and the last six numbers have an average of 65, what is the sixth number?

(a)62
(b)61
(c)64
(d)60

Answer

Why

Correct — B. Turn each average into a total.

All 11 numbers: 11 × 61 = 671
First six (1st to 6th): 6 × 57 = 342
Last six (6th to 11th): 6 × 65 = 390

The two groups fill 12 places from 11 numbers, so the 6th sits in both.
342 + 390 = 732
6th number = 732 − 671 = 61 → option (b)

Why the others are wrong

(a)
62 — If the 6th were 62, the eleven numbers would total 732 − 62 = 670, an average of about 60.9, not 61.
(c)
64 — A 6th number of 64 leaves 732 − 64 = 668 for the eleven, an average of about 60.7, not the 61 given.
(d)
60 — With 60, the eleven would total 732 − 60 = 672, an average of about 61.1. A total of exactly 671 forces the 6th to be 61.

Concept

Sum = average × count turns every average into a total you can add and subtract.

When two groups overlap, the shared item is inside both group totals. Add the two groups, subtract the whole, and only that item is left.

When the groups leave a gap instead, the missing item is the whole minus the two groups.

Deviation check from 61: the first six sum to 6 × (−4) = −24 and the last six to 6 × (+4) = +24. All eleven sum to 0 about their own average, so the 6th's deviation is −24 + 24 − 0 = 0, and the 6th number is 61.

Key facts

Sum = average × number of items
Of 11 numbers, the first six (1st to 6th) and last six (6th to 11th) share only the 6th
Overlap item = sum of group 1 + sum of group 2 − sum of all

Study next

The gap version: first five and last five of eleven, where the 6th is left outReplacing one item and finding its value from the change in the averageAverage of consecutive numbers or of an arithmetic progression

Common traps

Averaging 57 and 65 to 61 and stopping: it lands on the key only because (57 + 65) ÷ 2 equals the overall 61, and fails whenever it does not
Using the gap formula here: 671 − 732 is negative, the sign that the groups overlap

12 Sep 2025, 16:00, Quant Q.9 runs the gap version: the first five and last five of 11 numbers leave the 6th out, so it is 748 − 315 − 360 = 73.

The overlap version, as here, is 9 Sep 2024, 12:30, Quant Q.9: the first and last sixteen days of January share the 16th, whose temperature is 352 + 416 − 744 = 24°C.

Related PYQs

No directly related past PYQ was found.

Topic: Averages — all 76 SSC CGL questions on it, every solved shift.