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# If x + y = z where x, y and z are positive integers, what is the ratio

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Math Expert
Joined: 02 Sep 2009
Posts: 58430
If x + y = z where x, y and z are positive integers, what is the ratio  [#permalink]

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01 Jan 2018, 01:33
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Difficulty:

45% (medium)

Question Stats:

70% (02:08) correct 30% (01:19) wrong based on 36 sessions

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If x + y = z where x, y and z are positive integers, what is the ratio of x to y?

(1) xz = 40
(2) y = 3

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If x + y = z where x, y and z are positive integers, what is the ratio  [#permalink]

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01 Jan 2018, 04:57
Bunuel wrote:
If x + y = z where x, y and z are positive integers, what is the ratio of x to y?

(1) xz = 40
(2) y = 3

Statement 1: $$xz=40=> x(x+y)=40$$ (substitute the value of $$z$$)

$$=>x^2+yx=40$$. two variable one equation, values cannot be calculated. Insufficient

Statement 2: nothing mentioned about $$x$$. insufficient

Combining 1 & 2: we get $$x^2+3x-40=0$$ (substituting the value of $$y$$ from Statement 2)

therefore $$x=-8$$ or $$5$$. As $$x$$ is positive so $$x=5$$ & $$y=3$$

Hence $$x:y=5:3$$. Sufficient

Option C
If x + y = z where x, y and z are positive integers, what is the ratio   [#permalink] 01 Jan 2018, 04:57
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