SSC CGL 2024 Tier-I · 25 September 2024, Shift 3 · Quantitative Aptitude · Question 18 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.

Which of the following numbers is divisible by 6?

(a)62233
(b)438750
(c)12581
(d)128530

Answer

Why

Correct — B. Divisible by 6 means divisible by 2 and by 3 — both tests, every time.

Test for 2: 438750 ends in 0, so it is even.
Test for 3: its digit sum is 4+3+8+7+5+0 = 27, a multiple of 3.

Both pass, so 438750 clears 6 → option (b). Direct check: 438750 ÷ 6 = 73125.

Why the others are wrong

(a)
62233 — 62233 ends in 3. An odd number fails the test for 2 straight away, and no odd number is divisible by 6 however its digits add up.
(c)
12581 — 12581 ends in 1, odd again, so it fails the same test for 2. Its digit sum, 17, is not a multiple of 3 either.
(d)
128530 — 128530 is even, which is what makes it tempting, but its digit sum is 1+2+8+5+3+0 = 19, not a multiple of 3. It is divisible by 2 and by 5, not by 6.

Concept

A number is divisible by 6 exactly when it is divisible by 2 and by 3 at the same time, because 2 and 3 are coprime and their product is 6.

The two tests are independent and both are cheap: read the last digit for 2, add all the digits for 3.

That cheapness is the trap. An even number is only half-qualified, and running one test instead of two is how a ten-second mark is lost.

The same two tests, set the harder way round, ask you to supply a missing digit rather than pick a whole number — 217924k at 09 Sep 2024, 09:00, Quant Q.11 and 249k876 at 17 Sep 2024, 09:00, Quant Q.20.

Key facts

Divisibility by 6 needs both tests to pass: the last digit even, and the digit sum a multiple of 3.
438750 has digit sum 27 and 438750 ÷ 6 = 73125.
128530 is divisible by 2 and by 5 but not by 3, so it is not divisible by 6.
Failing either test is enough to rule a number out for 6.

Study next

Divisibility tests for 8 and 11, which read the last three digits or the alternating digit sumFinding the missing digit that makes a number divisible by 6Divisibility by 12 and 15, which combine two coprime tests the same way

Common traps

Stopping at even — 128530 is even and still not divisible by 6.
Misadding a six-digit digit sum. Recount 4+3+8+7+5+0 = 27.
Assuming a number ending in 0 must clear 6 because it clears 10.

SSC sets this both ways: pick the divisible number from four, as here, or supply the missing digit. The missing-digit form is asked at 09 Sep 2024, 09:00, Quant Q.11 (217924k) and 17 Sep 2024, 09:00, Quant Q.20 (249k876), and both still come down to the 2-test and the 3-test run together.

Related PYQs

No directly related past PYQ was found.