SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 10 of 98

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.

If P is a digit such that 6954P is divisible by 11, then P equals:

(a)2
(b)6
(c)8
(d)7

Answer

Why

Correct — A. The divisibility test for 11 compares the two alternating digit groups of 6954P.

Odd places, counting from the right: P, 5, 6 → sum = P + 11
Even places, counting from the right: 4, 9 → sum = 13

Difference = (P + 11) − 13 = P − 2
This has to be 0 or a multiple of 11. P − 2 = 11 would need P = 13, which is not a digit.

So P − 2 = 0 → P = 2 → option (a).
Check: 69542 ÷ 11 = 6322 exactly.

Why the others are wrong

(b)
6 — P = 6 makes the number 69546, whose alternating difference is 6 − 2 = 4. Four is neither 0 nor a multiple of 11, so the number fails the test.
(c)
8 — P = 8 gives an alternating difference of 6. The gap has to close to 0 or 11, and 6 does neither, so 69548 is not divisible by 11.
(d)
7 — P = 7 leaves a difference of 5. Only a difference that is 0 or a multiple of 11 works, and 5 misses both.

Concept

A number is divisible by 11 when the alternating sum of its digits is 0 or a multiple of 11: add the digits in the odd places, add the digits in the even places, and subtract.

The rule comes from powers of 10 alternating between +1 and −1 modulo 11. With one unknown digit it turns a divisibility question into a one-line equation, which is why SSC prefers this shape over asking you to divide.

6954P has an odd number of digits, so counting places from the left instead of the right lands on the same two groups. On a number with an even digit count the groups swap and the difference changes sign, which is harmless because only 'multiple of 11' is being tested.

Key facts

A number is divisible by 11 when (sum of digits in odd places) − (sum of digits in even places) equals 0 or a multiple of 11.
In 6954P the odd-place digits from the right are P, 5 and 6, and the even-place digits are 4 and 9.
The equation P − 2 = 0 has the single digit solution P = 2, because P − 2 = 11 would force P = 13.
69542 = 11 × 6322, the check worth doing once the digit is found.

Study next

Least number to add or subtract to make a given number divisible by 11Divisibility tests for 7, 11 and 13 taken together on a six-digit numberRemainder of a large number modulo 11 without performing the division

Common traps

Adding all five digits and testing that total against 11. Digit-sum tests belong to 3 and 9, not to 11.
Forgetting that the alternating difference may be a multiple of 11 rather than 0, and so not checking whether a second digit works.
Applying the rule for 4 by mistake, which looks only at the last two digits: 4P divisible by 4 admits P = 0, 4 or 8, and 8 is on the option list.

One unknown digit, as here, also appears at 9 Sep 2024, 16:00, Quant Q.9 (7845K854).

SSC also prints four whole numbers and asks which one fails the test — 12 Sep 2024, 12:30, Quant Q.21 and 19 Sep 2024, 12:30, Quant Q.19.

And it asks for the least number to subtract, at 23 Sep 2024, 12:30, Quant Q.23.

Related PYQs

No directly related past PYQ was found.