SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 23 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 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The least number which must be subtracted from 7278745 so as to obtain a sum that is divisible by 11 is:

(a)1
(b)3
(c)5
(d)2

Answer

Why

Correct — A. Test 7278745 with the alternating digit sum, counting from the right.

Odd places (1st, 3rd, 5th, 7th from the right): 5 + 7 + 7 + 7 = 26
Even places (2nd, 4th, 6th): 4 + 8 + 2 = 14
Difference = 26 − 14 = 12

For divisibility by 11 that difference must itself be a multiple of 11, and 12 is one past 11.

Dropping the units digit by k drops the difference by k, so k = 1:
7278745 − 1 = 7278744 = 11 × 661704 → option (a)

Why the others are wrong

(b)
3 — Subtracting 3 leaves 7278742, whose alternating difference is 12 − 3 = 9. Nine is not a multiple of 11, so the result is still not divisible.
(c)
5 — Subtracting 5 leaves 7278740 and an alternating difference of 7. It also fails the question's word 'least', since 1 already works.
(d)
2 — Subtracting 2 leaves 7278743 and an alternating difference of 10, one short of 11. Only a reduction of exactly 1 brings the difference of 12 down onto a multiple of 11.

Concept

A number is divisible by 11 exactly when the alternating sum of its digits is a multiple of 11, counting 0 as a multiple.

That gives you the remainder for free. For 7278745 the alternating difference is 12, which is 11 + 1, so the number is 1 more than a multiple of 11. The least number to subtract is that remainder, 1.

Read the direction carefully. To SUBTRACT, you take the remainder. To ADD, you take 11 minus the remainder, which here would be 10.

The stem says 'a sum that is divisible by 11'. It means the number left after the subtraction, not an addition of digits — reproduce SSC's wording, but read it as the resulting number.

Key facts

A number is divisible by 11 when the alternating sum of its digits is a multiple of 11, including 0.
For 7278745 that sum is (5 + 7 + 7 + 7) − (4 + 8 + 2) = 12.
7278745 leaves remainder 1 on division by 11.
7278744 = 11 × 661704.

Study next

The least number to ADD, which is 11 minus the remainder rather than the remainder itselfDigit-placeholder divisibility, finding the missing digit that makes a number divisible by 11Divisibility by 7 and 13 through three-digit grouping from the right

Common traps

Subtracting the alternating difference itself, 12, instead of the remainder, 1.
Starting the alternating sum from the left when the digit count is even, which flips the sign of the difference.
Treating a difference of 11 as a failure because it is not 0 — any multiple of 11 passes.

SSC dresses this rule as a missing digit to hunt, as an odd number to spot, and — here — as a subtraction.

9 Sep 2024, 16:00, Quant Q.9 asks for K in 7845K854, and 17 Sep 2024, 16:00, Quant Q.10 for P in 6954P. The odd-one-out form appears at 19 Sep 2024, 12:30, Quant Q.19 and at 12 Sep 2024, 12:30, Quant Q.21.

Related PYQs

No directly related past PYQ was found.