SSC CGL 2024 Tier-I · 13 September 2024, Shift 2 · Quantitative Aptitude · Question 8 of 99

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 digits should come in the place of x and y, respectively, if the number 62684xy is divisible by both 8 and 5?

(a)0 and 5
(b)4 and 0
(c)5 and 0
(d)2 and 0

Answer

Why

Correct — B. Two divisibility conditions, applied in order.

Divisible by 5 → the last digit y must be 0 or 5.
Divisible by 8 → the last three digits, 4xy, must be a multiple of 8, and every multiple of 8 is even.

Even, and 0 or 5, forces y = 0.

Now test the block 4x0 with each x on offer:
x = 4 → 440 ⁄ 8 = 55, exact
x = 5 → 450 ⁄ 8 = 56.25
x = 2 → 420 ⁄ 8 = 52.5

So x = 4 and y = 0 → option (b), and 6268440 ⁄ 40 = 156,711 exactly.

Why the others are wrong

(a)
0 and 5 — y = 5 makes the last three digits 405, an odd number, and no odd number is divisible by 8. Satisfying the 5-rule alone is not enough.
(c)
5 and 0 — With x = 5 the block is 450, and 450 ⁄ 8 = 56.25. The 5-rule is met by y = 0, but the 8-rule fails on the three-digit block.
(d)
2 and 0 — With x = 2 the block is 420, and 420 ⁄ 8 = 52.5. That number is divisible by 4 — the last-two-digits rule — but 4 is not 8.

Concept

Both tests read only the tail of the number, which is why the first five digits 62684 never matter.

Divisible by 8 means the last three digits are divisible by 8, because 1000 is itself a multiple of 8. Divisible by 5 means the number ends in 0 or 5.

Imposed together, the two conditions mean the number is a multiple of LCM(8, 5) = 40, and every multiple of 40 ends in 0. So y = 0 before you test anything.

That leaves one three-digit block to check, 4x0, and only 440 among the blocks the options offer divides by 8.

The paper writes the unknowns as x and y in the seventh and sixth positions of a seven-digit number, so the block being tested for 8 is 4xy, not xy.

Key facts

A number is divisible by 8 when its last three digits are divisible by 8, since 1000 is a multiple of 8.
A number is divisible by 5 when it ends in 0 or 5.
Divisible by both 8 and 5 means divisible by 40, so the number must end in 0.
Of the blocks the options produce — 405, 440, 450 and 420 — only 440 is a multiple of 8.

Study next

Divisibility rules for 4, 8 and 16 read off the trailing digitsCombining two divisibility conditions through their LCMDivisibility by 11 from the alternating digit sum

Common traps

Stopping at the 5-rule and accepting y = 5.
Testing divisibility by 8 on the last two digits, which is the rule for 4.
Dividing the whole seven-digit number when only the last three digits decide it.

SSC reuses this stem almost word for word. Quant Q.16 of the 10 Sep 2024, 16:00 sitting prints the very same 62684 with the unknowns written as * and #, and Quant Q.1 of the 12 Sep 2024, 09:00 sitting swaps the digits to 72864 under the same two conditions.

Related PYQs

No directly related past PYQ was found.