Problem Solving

If x, y, and z are positive integers, x : y = 1 : 3, and z : y = 2 : 5, then x + z COULD equal

A) 46
B) 50
C) 54
D) 62
E) 66

Answer: E

Source: www.gmatprepnow.com
Difficulty level: 600 - 650

Brent@GMATPrepNow wrote:If x, y, and z are positive integers, x : y = 1 : 3, and z : y = 2 : 5, then x + z COULD equal

A) 46
B) 50
C) 54
D) 62
E) 66

Given: x : y = 1 : 3
y : z = 5 : 2

To COMBINE these ratios, their shared term (the y-value) must be the same in each ratio.

So, take x : y = 1 : 3 and multiply both parts by 5 to get an EQUIVALENT RATIO: x : y = 5 : 15
Likewise, take y : z = 5 : 2 and multiply both parts by 3 to get: y : z = 15 : 6
We can now COMBINE the ratios to get: x : y : z = 5 : 15 : 6
This means the ratio x : z = 5 : 6

Since x and z are positive integers, x + z must be a MULTIPLE of 5 + 6
In other words, x + z must be a MULTIPLE of 11

Answer: E

Cheers,
Brent