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

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
If x, y, and z are integers, y + z = 13, and xz = 9, which of the foll  [#permalink]

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31 Aug 2018, 00:07
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92% (01:39) correct 8% (01:45) wrong based on 43 sessions

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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

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Re: If x, y, and z are integers, y + z = 13, and xz = 9, which of the foll  [#permalink]

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31 Aug 2018, 00:18
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.

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Re: If x, y, and z are integers, y + z = 13, and xz = 9, which of the foll  [#permalink]

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31 Aug 2018, 00:30
Bunuel wrote:
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

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
Re: If x, y, and z are integers, y + z = 13, and xz = 9, which of the foll   [#permalink] 31 Aug 2018, 00:30
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