What is the remainder when positive integer x is divided by 52?

Question

(1) When x is divided by 4, the remainder is 3

(2) When x is divided by 13, the remainder is 1

akshayk · Answer

S1 -> x = 4Q + 3
=> x = 3, 7, 11, 15, 19, 23, 27,...
Multiple values for r when divided by 52.
Insufficient.

S2 -> x = 13A + 1
=> x = 1, 14, 27,....
Multiple values for r when divided by 52.
Insufficient.

(S1 + S2)
x = 27, 79,...
R = 27
Sufficient --> C is the answer IMO

GMATinsight · Answer

Question  : remainder when positive integer x is divided by 52?

52 = 13*4

Statement 1 : When x is divided by 4, the remainder is 3 
We don't know the remainder x is divided by 13 hence 
NOT SUFFICIENT

Statement 2 : When x is divided by 13, the remainder is 1 
We don't know the remainder x is divided by 4 hence 
NOT SUFFICIENT

Combining the statement

Now we know that the remainder is of the form 4a+3 form and also
Now we know that the remainder is of the form 13b+1 form 
The number which satisfies to both condition is 27

Hence, The remainder will be 27 
SUFFICIENT

Answer: Option C

studybuddy7 · Answer

I have an additional question regarding this one:

In this case the only prime factors of 52 were 7 and 2, and both were accounted for in the provided statements (4 and 7). What about a composite number with 3 PFs? Suppose instead of 52 we have a number with PFs 2, 5, and 7. Would two statements not be enough because we don’t know about the behavior with the 3rd PF? Or do we only need to know about two? How does this work mathematically?

studybuddy7 · Answer

Question here -- did you solve the system of equations 4a + 3 and 13b + 1 or is that impossible? Did you just go the "listing numbers for each statement and compare" route, or did you actually solve for 27 in a different way?

Louis14 · Answer

I had to search a lot to help you. So, here is the best way to solve these kinda questions: https://gmatclub.com/forum/positive-int ... 93752.html (Read Bunuel's explanation).

bumpbot · Answer

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What is the remainder when positive integer x is divided by 52?

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What is the remainder when positive integer x is divided by 52?

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