SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 9 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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The average of 11 numbers is 68. If the average of the first five is 63 and the average of the last five is 72, find the 6th number.

(a)73
(b)74
(c)75
(d)76

Answer

Why

Correct — A. Turn each average into a total.

All 11 numbers: 11 × 68 = 748
First five: 5 × 63 = 315
Last five: 5 × 72 = 360

The first five are numbers 1–5 and the last five are 7–11, so the 6th is the one left out.
6th number = 748 − 315 − 360 = 73 → option (a)

Why the others are wrong

(b)
74 — With 74 in 6th place the eleven numbers total 749, one more than 11 × 68 = 748, so their average would be about 68.09, not 68.
(c)
75 — 75 makes the total 750, two over 748, and the average about 68.18. Only a 6th number of exactly 73 brings the eleven to 748.
(d)
76 — 76 pushes the total to 751, three over 748, for an average of about 68.27. Each extra unit in the 6th number lifts the total by one.

Concept

Sum = number of items × average. Once every average is turned into a sum, the blocks can be added and subtracted like ordinary amounts.

Here the first five (numbers 1–5) and the last five (numbers 7–11) do not overlap, and together they cover every number except the 6th. So the 6th is the whole total minus the two block totals.

A quicker check uses deviations from 68. The first five run 5 below 68 each, 25 short in all; the last five run 4 above, 20 over. Net 5 short, so the 6th must be 5 above 68: 73.

Key facts

Sum = number of items × average: 11 × 68 = 748.
Numbers 1–5 and 7–11 leave the 6th uncounted.
Deviation check: the first five are 25 below 68 in total and the last five 20 above, so the 6th is 5 above 68.

Study next

Overlapping blocks, where a middle item is counted in both averagesReplacing one item and finding the new averageThe deviation method for averages of large numbers

Common traps

Averaging the two block averages: (63 + 72) ÷ 2 = 67.5 says nothing about the 6th number.
Treating the blocks as overlapping: with 11 numbers, the first five and the last five share no number, so nothing is counted twice.

Here the two blocks leave one number out. At 9 Sep 2024, 12:30, Quant Q.9 they overlap instead: the first and last sixteen days of a 31-day January share the 16th, so its temperature is the two block totals minus the month's total, 24°C.

Related PYQs

No directly related past PYQ was found.

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