If n is a positive integer, what is the remainder when n is divided by

Question

FRESH GMAT CLUB TESTS QUESTION

If n is a positive integer, what is the remainder when n is divided by 5?

(1) The remainder when n^2 is divided by 5 is 4
(2) The remainder when n + 10 is divided by 5 is 3

M36-37

Bunuel · Accepted Answer

Official Solution:

If  n  is a positive integer, what is the remainder when  n  is divided by 5? 
 
(1) The remainder when  n^2  is divided by 5 is 4
 
 n^2 = 5q + 4 
 
Since  n  is a positive integer then  n^2 , which is the square of an integer, can be 4, 9, 49, ... So,  n  can be 2, 3, 7, ... The remainders upon division these values by 5 can respectively be 2, 3, 2, ... Not sufficient.
 
(2) The remainder when  n + 10  is divided by 5 is 3
 
 n + 10 = 5p + 3 
 
 n = 5(p - 2) + 3 
 
 5(p - 2)   is divisible by 5 and 3 divided by 5 gives the remainder of 5. Sufficient.

Answer: B

Shorub · Answer

Squares of n - 1,4,9,16,25,36, 49,64,81,100,121,144,169....

Reminders when divided by 5

1,4,4,1,0,1,4,4,1,0,1....

A alone not sufficient

With only B, we have 3,8,13,18...

A Combined with B, the only number with n+10 divided by 5 and reminder 3 is "3".

Hence option C.

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Archit3110 · Answer

#1
n=2 or 3
so n^2 = 4 remainder possible insufficient
#2
n=3,13,23,33,8,18 we get remainder 3 dividing by 5 value of n+10..

from 1 & 2
n=3 only possible
IMO C

solikon · Answer

The question is what is the reminder when  n  is divided by 5.

From statement B it is clear that regardless if the figure is 3, 13, 18 or 8 (as other users proposed) the reminder will always be N/3 = X + 3

So statement  B  is enough to answer the question

RupamPaul13 · Answer

In statement 2 if n+10 is divided by 5 remainder is 3. So as 10 is a multiple of 5 hence n when divided by 5 remainder should always be 3. and statement b should be sufficient to answer the question. Why the OA is 3. Can you please explain Bunuel

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luvbb23 · Answer

I am still unclear why B is sufficient.

if n=3 -> 3/5 has a remainder of 5. if n=13 -> 13/5 has a reminder of 3.

Bunuel · Answer

3 divided by 5 gives the remainder of 3, not 5.

When the divisor (5 in your case) is more than dividend (3 in your case) then the reminder equals to the dividend.

For example:
3 divided by 24 yields a reminder of 3 -->  3=0*24+3 ;
or:
5 divided by 6 yields a reminder of 5 -->  5=0*6+5 ,
or example from your post:
2 divided by 5 yields a reminder of 2 -->  2=0*5+2 .

Hope it's clear.

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If n is a positive integer, what is the remainder when n is divided by

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