SSC CGL 2025 Tier-I · 16 September 2025, Shift 2 · Quantitative Aptitude · Question 6 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 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.

There are 6 consecutive integers and 5 consecutive integers. The average of the 6 integers is 2 less than the average of the 5 integers. The sum of the 5 integers is 4 more than the sum of the 6 integers. Find the average of the 6 integers.

(a)6
(b)5
(c)4
(d)3

Answer

Why

Correct — A. Let the average of the 6 integers be x, and turn both conditions into sums.

Average of the 5 integers: x + 2
Sum of the 6 integers: 6x
Sum of the 5 integers: 5(x + 2) = 5x + 10

Sum condition: 5x + 10 = 6x + 4
Subtract 5x and 4 from both sides: x = 6 → option (a)

Why the others are wrong

(b)
5 — With x = 5 the sums are 35 and 30, a gap of 5, not 4. The gap works out to 10 − x, so it is 4 at x = 6.
(c)
4 — With x = 4 the sums are 30 and 24, a gap of 6, not 4. Each drop of 1 in x widens the gap by 1.
(d)
3 — With x = 3 the sums are 25 and 18, a gap of 7, not 4. The gap is 10 − x, so a smaller x moves it further from 4.

Concept

Sum = count × average. The stem gives one condition on averages and one on sums. Rewrite the averages as sums and a single unknown is left.

Six numbers averaging x sum to 6x, and five averaging x + 2 sum to 5x + 10. The five-integer sum is 4 more, so 5x + 10 − 6x = 4, giving x = 6.

The stem does not fully cohere. Six consecutive integers n, n + 1, …, n + 5 sum to 6n + 15, an odd number, so their average n + 2.5 always ends in .5 (1 to 6 averages 3.5). No six consecutive integers average 6, or any whole number.

The key's 6 comes from the two numerical conditions alone, and it is the option that satisfies them. The five-integer side does work: average 8 gives 6, 7, 8, 9, 10.

Key facts

Sum of a set = number of items × average.
Six consecutive integers n to n + 5 sum to 6n + 15, so their average is n + 2.5.
For an odd count of consecutive integers the average is the middle number: 6, 7, 8, 9, 10 average 8.

Study next

Sum and average of consecutive integers, consecutive even numbers and consecutive odd numbersWhy an even count of consecutive integers never has a whole-number averageTwo-group average problems solved by converting averages to sums

Common traps

Writing the five-integer sum as 5x + 2 instead of 5(x + 2) = 5x + 10. The extra 2 applies to each of the five integers.
Hunting for six consecutive integers that average 6. None exist, so solve with the two equations.

15 Sep 2025, 12:30, Quant Q.6 has the same two-condition build with 5 consecutive even and 4 consecutive odd numbers: the sum gap m + 25 = 30 gives m = 5, and four consecutive odd numbers cannot average 5 either.

Related PYQs

No directly related past PYQ was found.

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