Bunuel wrote:

When a positive integer is divided by 4, the remainder is r; when divided by 9, the remainder is R. What is the greatest possible value of r^2+R?

A. 23

B. 21

C. 17

D. 13

E. 11

Using the concept of divisibility, you can get the answer with minimum calculation.

When a number is divided by 4, the maximum value of r can be 3.

When a number is divided by 9, the maximum value of R can be 8.

Now all we need to figure out is whether we can have a number such that when divided by 4, it gives remainder 3 and when divided by 9, it gives remainder 8.

Imagine the number split into groups of 9 and 8 leftover. When the same is divided by 4, the 8 leftover will be evenly split into groups of 4. From each group of 9, we will make 2 groups of 4 each such that 1 is leftover from each group of 9. We want 3 to be leftover when we divide by 4 and this will be possible if we have 3 groups of 9.

So basically such a number could be 3*9 + 8 = 35 etc

Hence, maximum value of r^2 + R = 3^2 + 8 = 17

Answer (C)

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Karishma

Veritas Prep GMAT Instructor

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