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If w, x, y and z are integers such that w/x and y/z are [#permalink]
 01 Jun 2008, 05:41
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If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd? (1) wx + yz is odd (2) wz + yx is odd
Last edited by Bunuel on 13 Mar 2012, 14:00, edited 1 time in total.
Edited the question and added the OA
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Re: if w,x,y,and z are integers...DS [#permalink]
01 Jun 2008, 09:00
I think question is asking w/x + y/z odd and not w/x + w/z odd or not? If this is the case then here is my explanation.
Rephrased question is wz+xy/xz is odd or not?
Statement 1:
wx + yz is odd, this implies one pair is odd and other pair is even. As even + odd = odd. But we are not sure which pair is even or odd. So this is not sufficient and answer cannot be A or D.
Statement 2;
wz + xy is odd, this numerator of question is odd. As given in question w/x + y/z is integer so wz+xy/xz is not a fraction and this implies wz+xy is divisible by xz. Only way a odd number divisible by another number is that divisor has to be odd as well. So odd divided by odd will yield odd. So question is answered.
Answer B.
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Re: If w, x, y, and z are integers such that w/x and y/z are [#permalink]
13 Mar 2012, 12:06
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japped187 wrote: If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + w/z odd?
(1) wx + yz is odd
(2) wz + xy is odd IMO A is also satisfactory .... wx + yz is odd Case 1 wx is odd & yz is even wx is odd ==> w & x are odd (odd*odd = odd) ==> w/x is odd yz is even ==> There can be 3 cases y is even and z is odd = Not possible as we are given y/z is integer y is odd and z is even = Not possible as we are given y/z is integer y is even and z is even = Possible ==> y/z is even w/x (odd) + y/z (even) = Odd Case 2 wx is even & yz is odd can be proved in a similar manner. Please advice if i am wrong.
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Re: If w, x, y and z are integers such that w/x and y/z are [#permalink]
13 Mar 2012, 14:24
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If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd? Given: \frac{w}{x}=integer and \frac{y}{z}=integer. Hence, \frac{w}{x}+\frac{y}{z}=\frac{wz+yx}{xz}=integer and the question is whether this integer is odd. (1) wx + yz is odd --> if w=x=1 and y=z=2 then \frac{w}{x}+\frac{y}{z}=2=even but if w=x=1 and y=2, z=1 then \frac{w}{x}+\frac{y}{z}=3=odd. Not sufficient. (2) wz + yx is odd --> \frac{wz+yx}{xz}=\frac{odd}{xz}=integer --> odd=(xz)*integer --> all multiple must be odd in order the product to be odd, hence integer =odd. Sufficient. Answer: B. Hope it's clear.
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Re: If w, x, y and z are integers such that w/x and y/z are [#permalink]
14 Mar 2012, 01:02
Hi Bunuel,
I agree with ur exp .. but is there a problem with my algebraic method ?
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Re: If w, x, y and z are integers such that w/x and y/z are [#permalink]
20 Sep 2012, 06:33
Other way to look at the problem As w/x is integer we can say w=xa+0 , where a= any integer------> xa/x = a Same way y/z is integer we can say y=zb+0 , where b= any integer------->zb/z = b So the basically the question is, "Is a+b Odd"1) wx + yz ----> x^2a + z^2b = odd------> a+b may be or may not be odd ---> Insufficient 2) wz + yx -----> xza + xzb ----> xz(a+b) = odd--->it means that both xz & (a+b) are odd ---->Sufficient Answer B Hope it helps.
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Re: If w, x, y and z are integers such that w/x and y/z are [#permalink]
20 Sep 2012, 07:16
rohitgoel15 wrote: IMO A is also satisfactory ....
wx + yz is odd
Case 1
wx is odd & yz is even
wx is odd ==> w & x are odd (odd*odd = odd) ==> w/x is odd
yz is even ==> There can be 3 cases
y is even and z is odd = Not possible as we are given y/z is integer
y is odd and z is even = Not possible as we are given y/z is integer
y is even and z is even = Possible ==> y/z is even
w/x (odd) + y/z (even) = Odd
Case 2
wx is even & yz is odd can be proved in a similar manner.
Please advice if i am wrong.
rohitgoel15 wrote: Hi Bunuel,
I agree with ur exp .. but is there a problem with my algebraic method ? Yes there is a problem in statement: y is even and z is odd = Not possible as we are given y/z is integerEven/Odd can be integer, Consider eg Y=6 , z=3.. Hence that solution is incorrect.
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Re: If w, x, y and z are integers such that w/x and y/z are
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20 Sep 2012, 07:16
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