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ItsMeHudd
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When the positive integer k is divided by the positive integer n 03 Aug 2026, 18:48
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Thank you that makes sense. I'll have to increase my base understanding on common math formulas for the gmat it seems
egmat
Hi ItsMeHudd,

Good question. The q isn't pulled out of nowhere; it's just a name the solutions gave to the quotient - the whole-number part of a division.

Whenever you divide one positive integer by another, you can always write:

dividend = divisor × quotient + remainder

For this question that's:

k = n·q + 11

Here q is simply "how many whole times n goes into k." Bunuel introduced the letter q to stand for that number before we know its value. Then dividing both sides by n gives:

k/n = q + 11/n

Now compare that to what you're told: k/n = 81.2 = 81 + 0.2.

- The whole-number part, 81, must be q (the quotient).
- The leftover fraction, 0.2, must be the 11/n piece.

Thereforeq = 81, and 11/n = 0.2, which gives n = 55.

A tiny concrete check

Take something you can see instantly: 17 ÷ 5 = 3.4.
- The quotient is the whole part: 3 - that's your q.
- 5 × 3 = 15, and 17 - 15 = 2, the remainder.
- So 17 = 5·3 + 2, and 17/5 = 3 + 2/5 = 3.4. ✓

Notice how the whole number (3) is the quotient and the decimal (0.4 = 2/5) is remainder-over-divisor. That's exactly the same split used with 81.2 in this problem - q is just the label for that whole-number quotient.

Answer: C


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