SSC CGL 2025 Tier-I · 14 September 2025, Shift 1 · General Intelligence and Reasoning · Question 19 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.

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.

Identify the number which does not satisfy: Sum of digits is a divisor of the number

(a)21
(b)30
(c)36
(d)39

Answer

Why

Correct — D. Test each number against the condition.

Rule: the digit sum must divide the number exactly.

21: 2 + 1 = 3, and 21 ÷ 3 = 7 ✓
30: 3 + 0 = 3, and 30 ÷ 3 = 10 ✓
36: 3 + 6 = 9, and 36 ÷ 9 = 4 ✓
39: 3 + 9 = 12, and 39 ÷ 12 = 3.25 ✗

39 fails the condition, option (d).

Why the others are wrong

(a)
21 — 21 has digit sum 3, and 21 = 3 × 7, so the sum divides it. It satisfies the condition, and the stem asks for the number that does not.
(b)
30 — 30 has digit sum 3, and 30 = 3 × 10. The condition holds, so 30 is not the number that fails.
(c)
36 — 36 has digit sum 9, and 36 = 9 × 4. The condition holds, so 36 is not the answer.

Concept

The condition is that the digit sum divides the number. Numbers with this property are called Harshad or Niven numbers.

When the digit sum is 3 or 9, the condition holds automatically, by the divisibility rules for 3 and 9. That clears 21, 30 and 36 at a glance.

39 fails before any division: it is odd, and its digit sum 12 is even. An even number cannot divide an odd one.

The stem asks for the number that does not satisfy the condition, so the answer is the single failure among the four.

Key facts

Digit sums: 21 → 3, 30 → 3, 36 → 9, 39 → 12.
A number whose digit sum is 3 or 9 is divisible by that sum, by the divisibility rules for 3 and 9.
An odd number has no even divisor, so 12 cannot divide 39.

Study next

Divisibility rules for 3, 9 and 11Two-digit numbers defined by their digit sum and their reversalOdd-one-out on number properties such as primes and squares

Common traps

Missing the NOT in the stem and picking a number that satisfies the condition.
Confusing divisible by 3 with divisible by the digit sum: 39 = 3 × 13, but its digit sum is 12, and 12 does not divide 39.

A digit-sum condition also decides 14 Sep 2025, 12:30, Reasoning Q.25, where 24 = 4 × 6 with 6 its digit sum, and its reversal 42 = 24 + 18.

Related PYQs

No directly related past PYQ was found.

Topic: Symbolic/Number Classification — all 45 SSC CGL questions on it, every solved shift.