When x is divided by 13, the answer is y with a remainder of

Question

When x is divided by 13, the answer is y with a remainder of 3. When x is divided by 7, the answer is z with a remainder of 3. If x, y, and z are all possible integers, what is the remainder of yz/13?

(A) 0
(B) 3
(C) 4
(D) 7
(E) None of these

aniruddhawarang29 · Accepted Answer

We see that x = 13y + 3 and x = 7z+3

Equating the two equations we see 13 y + 3 = 7z + 3

==> 13y = 7z
==> z is a multiple of 13.

Hence, when yz/13 , the Remainder will be 0.

MathRevolution · Answer

x = 13y + 3   then x = 3, 16, 29....
x = 7z + 3   then x = 3, 10, 17....

First overlapping number: 3.
Next overlapping number: 3 + LCM(13,7 = 91) = 94

=> 94 = 13 * 7 + 3. Therefore, y = 7
=> 94 = 7 * 13 + 3. Therefore, z = 13

=>  \frac{yz }{ 13} = \frac{7 * 13 }{ 13}  will give remainder '0'.

Answer A

Scuven · Answer

From the text you can reason that:

x= 13y + 3 (when x is divided by 13 it gives a quotient of y a remainder of 3)
x= 7z + 3 (when x is divided by 7 it gives a quotient of z and it gives a remainder of 3)

Now reverse the equations to find y and z

y=(x-3)/13
z= (x-3)/7

You know that x, y and z are INTEGERS thus the product YZ is divisible by (13*7)=81 because it's a multiple of it.

But 81 is divisible by 13 thus the remainder is 0.

sarthak1701 · Answer

x/13 = y + 3/13 and x/7 = z + 3/7

Multiply these 2 equations by 13 and 7 respectively

We get

x = 13y + 3 and x = 7z + 3

13y = 7z

y = 7z/13

The question asks remainder when yz is divided by 13

taking the value of y above we get = 7z/13*z = 7z^2/13, the remainder is 0 since z is an integer.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

When x is divided by 13, the answer is y with a remainder of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

When x is divided by 13, the answer is y with a remainder of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards