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09 Oct 2018, 02:56
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C
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Difficulty:
35%
(medium)
Question Stats:
70% (01:49) correct
30%
(01:39)
wrong
based on 104
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Not Attempted Yet
If x, y and z are positive integers, is y − x > 0?
(1) y/x = z/y
(2) z > x
(1) y/x = z/y
(2) z > x
09 Oct 2018, 03:16
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The answer is C.
1) let's use numbers to see the logic: say y=2. let's see if a "yes" answer is possible - that is, if y is larger than x: say x=1. This means 2/1=4/2 (z=4). definitely possible! now, is a "no" answer possible - can y-x<0? let's try: x=4. This means 2/4=1/2 (z=1). also possible!
we have found two contradicting answers, thus this data is insufficient - . eliminate answers A and D.
2) this tells us nothing about y, and thus nothing about the relationship between x and y, clearly insufficient - eliminate B
Combined: if z > x, then the second scenario we checked before (where y-x<o) is impossible, since it had z=1 and x=2. In fact, we can now see that any "no" answer will be impossible: if z>x, this means that z/x > 1, which means that the left side of the equation - y/x, must also be larger than 1: if y/x>1 ==> y - x >0 - sufficient! answer C.
1) let's use numbers to see the logic: say y=2. let's see if a "yes" answer is possible - that is, if y is larger than x: say x=1. This means 2/1=4/2 (z=4). definitely possible! now, is a "no" answer possible - can y-x<0? let's try: x=4. This means 2/4=1/2 (z=1). also possible!
we have found two contradicting answers, thus this data is insufficient - . eliminate answers A and D.
2) this tells us nothing about y, and thus nothing about the relationship between x and y, clearly insufficient - eliminate B
Combined: if z > x, then the second scenario we checked before (where y-x<o) is impossible, since it had z=1 and x=2. In fact, we can now see that any "no" answer will be impossible: if z>x, this means that z/x > 1, which means that the left side of the equation - y/x, must also be larger than 1: if y/x>1 ==> y - x >0 - sufficient! answer C.
09 Oct 2018, 03:18
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Bunuel
we are looking for the positive difference between y and x.
Statement 1: As we don't the order of these integers it is not possible to determine the difference. NOT sufficient.
Statement : z>x. but information about y. NOT sufficient.
Combining 1 and 2:
y/x = z/y
\(z= y^2 / x.\)
we already know,
z>x
\(y^2/x >x\)
\(y^2>x^2.\)
we already know all these are integers.
thus, y -x >0.
The best answer is C.
