If x, y, and z are integers, y + z = 13, and xz = 9, which of the foll

Question

If x, y, and z are integers, y + z = 13, and xz = 9, which of the following must be true?

(A) x is even
(B) x = 3
(C) y is odd
(D) y > 3
(E) z < x

Chethan92 · Answer

XZ = 9.

Possible numbers are (1,9) (3,3) or (9,1)

Then Y+Z = 13.

Taking Z as 1,3 or 9.

Y becomes 12,10 or 4.

In all cases Y is greater than 3.

D is the answer

Posted from my mobile device

CounterSniper · Answer

we have y + z = 13
This is possible when 
odd + even = odd
which means 
one of x or y is odd and the other is even.

xz = 9
This is possible when both x and z are odd

we finally have in terms of odd or even 
x= odd
so answer choice A and C are out.

since x , y and z are integers 
in xz=9
x can hold following values
1,3,9
and so can z

answer choice B and E are out

Finally , greatest possible value of z can be 9
thus the smallest possible value of x is 13-9 = 4 > 3
D should be the answer

GulfTube · Answer

Realize that x and z have to be both odd and hence y is even.

A & C are out.

9=9*1 or 3*3 but latter is not possible since x and z are different integers. B is out.

either of x or z could be greater, hence E is out.

if z=1, y=12, if z=9, y=4, in both cases y>3 correct ans is D

Prep Toolkit