What is the remainder when X is divided by Y?

Question

What is the remainder when positive integer X is divided by another positive integer Y?

(1) Y = 3*a + 10, and X = 3*b + 15. 'a' and 'b' are positive integers.

(2) a is a factor of b.

MikeHelios · Answer

do the equations of X and Y apply to statement 2 as well?

amanvermagmat · Answer

Hello

This is Data Sufficiency. So we first have to look at statement 1 alone, and see whether it answers the question or not. Then we have to look at statement 2 alone, and see whether it answers the question. 
Only if none of the two statements are alone sufficient to answer, then we will combine the two statements. And yes, combining means we will take data of both statements together, and thus the equations of X/Y will apply...

niks18 · Answer

Essentially  X=Yk+R , where  k  is the quotient and  R  is the remainder. We need the value of  R

Statement 1:  implies  3b+15=(3a+10)k+R , from this relation we cannot calculate the value of  R  because we have three unknown variables;  a,b  &  k .  Insufficient

Statement 2:  No relation between  X  &  Y  is given. the statement implies  b=aq  for some constant  q .  Insufficient

Combining 1 & 2:  we have  3aq+15=3ak+10k+R . From this value of  R  cannot be calculated.  Insufficient

Option  E

aserghe1 · Answer

Can solve this by plugging numbers.

Statement 1
 \frac{X}{Y}=\frac{3b+15}{3a+10} 
If a=1, b=1, then Y/X=18/13. Remainder = 5.
If a=2, b=1, then Y/X=18/16. Remainder = 2.
Cant arrive at unique solution. Not sufficient.

Statement 2
Since a is a factor of b, there exists an integer n such that b=an.
No info about X and Y. Not sufficient.

Combining 1&2
 \frac{Y}{X}=\frac{3an+15}{3a+10} 
If n=1, a=1, then Y/X=18/13. Remainder = 5.
If n=2, a=1, then Y/X=21/13. Remainder = 8.
Cant arrive at unique solution. Not sufficient.

Answer: E

ritikajain1988 · Answer

equations of X and Y apply to statement 2?

amanvermagmat · Answer

Yes of course, when you combine the statements, you have to take them together only.

What is the remainder when X is divided by Y?

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GMAT Data Sufficiency (DS) Questions

What is the remainder when X is divided by Y?

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