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If w, x, y and z are positive, is the value of (wx)/(yz) an integer?

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If w, x, y and z are positive, is the value of (wx)/(yz) an integer? [#permalink] New post   05 Jul 2017, 00:30
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If w, x, y and z are positive, is the value of \(\frac{(wx)}{(yz)}\) an integer?


(1) \(w = \frac{3}{4}*x = \frac{y}{2} = 3z\)

(2) \(w + x + y + z = 34\)
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Re: If w, x, y and z are positive, is the value of (wx)/(yz) an integer? [#permalink] New post   05 Jul 2017, 00:52
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Bunuel wrote:
If w, x, y and z are positive, is the value of \(\frac{(wx)}{(yz)}\) an integer?


(1) \(w = \frac{3}{4}*x = \frac{y}{2} = 3z\)

(2) \(w + x + y + z = 34\)



(1) gives us

x= 4/3w
y = 2w
z = w/3
On substituting in wx/yz we can get the answer (an integer).
Hence Sufficient

(2) gives us w + x + y + z = 34

Now consider w = 8, x=9 , y = 8 and z = 9 then we can get the integer so we can say Yes

However if we take w = 3/2, x=1/2, y = 16 and z=16 then we will not get an integer and the answer would be No

Hence A
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Re: If w, x, y and z are positive, is the value of (wx)/(yz) an integer? [#permalink] New post   05 Jul 2017, 01:08
st[1]

w = \(\frac{3x}{4}\) = \(\frac{y}{2}\) = 3z

multiply by 4

4w = 3x = 2y = 12z

now \(\frac{wx}{yz}\) = multiply by 12 in both denominator & numerator

\(\frac{4w * 3x}{y * 12 z}\)

\(\frac{2y * 2y}{y * 2y}\)

= \(\frac{4y^2}{2y^2}\)

= 2 ( an integer)

st[2] - does not tell us the relationship among numbers, can have n number of combinations.
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Re: If w, x, y and z are positive, is the value of (wx)/(yz) an integer? [#permalink] New post   08 Jan 2021, 08:47
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Bunuel wrote:
If w, x, y and z are positive, is the value of \(\frac{(wx)}{(yz)}\) an integer?


(1) \(w = \frac{3}{4}*x = \frac{y}{2} = 3z\)

(2) \(w + x + y + z = 34\)



(1) w= 3x/4

y= 6x/4
z=3x/12

Now putting the values of w, y, and z at \(\frac{(wx)}{(yz)}\) we get 2, which is an integer. Sufficient.

(2) This doesn't give us specific value for each variables.; Insufficient.

The answer is A
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Re: If w, x, y and z are positive, is the value of (wx)/(yz) an integer? [#permalink]
08 Jan 2021, 08:47
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Bunuel
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