SSC CGL 2024 Tier-I · 12 September 2024, Shift 2 · Quantitative Aptitude · Question 21 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 6 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.

Which of following numbers is NOT divisible by 11?

(a)109153
(b)5445
(c)80124
(d)128041

Answer

Why

Correct — D. Rule: add the digits in odd places counting from the right, add the digits in even places, subtract. A number is divisible by 11 only if that difference is 0 or a multiple of 11.

128041
Odd places: 1 + 0 + 2 = 3
Even places: 4 + 8 + 1 = 13
Difference = 3 − 13 = −10

−10 is not a multiple of 11, so 128041 is not divisible → option (d).
Long division agrees: 11 × 11640 = 128040, remainder 1.

Why the others are wrong

(a)
109153 — Divisible, so not the answer. Odd places 3 + 1 + 0 = 4 against even places 5 + 9 + 1 = 15, a difference of −11, and 109153 = 11 × 9923.
(b)
5445 — Divisible, so not the answer. 5 + 4 = 9 against 4 + 5 = 9, a difference of 0, which always passes, and 5445 = 11 × 495.
(c)
80124 — Divisible, so not the answer. Odd places 4 + 1 + 8 = 13 against even places 2 + 0 = 2, a difference of 11 exactly, and 80124 = 11 × 7284.

Concept

The test for 11 comes from 10 ≡ −1 (mod 11). Each place value alternates in sign, so a number reduces to (sum of digits in odd places) − (sum of digits in even places).

If that alternating sum is 0, ±11, ±22 and so on, the number is divisible. Otherwise the alternating sum is the remainder, up to a multiple of 11 — here −10, which is the same as remainder 1.

Direction does not matter. Starting the count from the left flips the sign of the difference, and a multiple of 11 stays a multiple of 11 either way.

The question asks which number is NOT divisible, so three of the four options are built to pass the test and only the odd one out is the answer.

Key facts

Divisibility by 11: (sum of digits in odd places from the right) − (sum in even places) must be 0 or a multiple of 11.
The rule follows from 10 ≡ −1 (mod 11), which makes consecutive place values alternate in sign.
128041 gives 3 − 13 = −10, so it leaves remainder 1 on division by 11.
The other three divide exactly: 109153 = 11 × 9923, 5445 = 11 × 495, 80124 = 11 × 7284.

Study next

Divisibility by 7, 11 and 13 together, using three-digit blocks with alternating signsFinding a missing digit that makes a number divisible by 11Reading the remainder off the alternating sum instead of only the yes-or-no verdict

Common traps

Adding all the digits, which is the test for 3 and 9 rather than for 11.
Losing the sign and passing −10 because 10 looks close to 11.
Answering with the first number that divides, when the question asks for the one that does not.

The commoner form supplies a missing digit: 7845K854 on 9 Sep 2024, 16:00, Quant Q.9 and 6954P on 17 Sep 2024, 16:00, Quant Q.10. The pick-the-one-that-fails form is asked on 19 Sep 2024, 12:30, Quant Q.19.

Related PYQs

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