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26 Nov 2017, 09:48
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:50) correct
36%
(01:40)
wrong
based on 309
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26 Nov 2017, 09:58
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Bunuel
Is x < y?
(1) 1/x < 1/y
(2) x/y < 0
(1) 1/x < 1/y
(2) x/y < 0
lovely Q
(1) \(\frac{1}{x} < \frac{1}{y}\)..
\(\frac{1}{x} - \frac{1}{y}<0........................\frac{y-x}{xy}<0\)
so xy and y-x have opposite signs..
case I: xy >0, y-x<0....y<x
case II : xy<0, y-x>0...y>x
insuff
(2) \(\frac{x}{y}< 0\)
Just tells us that one is positive and one is negative
any of the two x and y can be negative
so x<y or y<x
insuff
combined
case II is left..
both x and y are of opposite sign, so xy<0 and therefore y>x
suff
C
Updated on: 17 May 2021, 09:41
Originally posted by BrentGMATPrepNow on 16 Mar 2020, 06:57.
Last edited by BrentGMATPrepNow on 17 May 2021, 09:41, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 09:41, edited 1 time in total.
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Bunuel
Is x < y?
(1) 1/x < 1/y
(2) x/y < 0
(1) 1/x < 1/y
(2) x/y < 0
Target question: Is x < y?
Statement 1: 1/x < 1/y
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -1 and y = 1. In this case, the answer to the target question is YES, x is less than y
Case b: x = 2 and y = 1. In this case, the answer to the target question is NO, x is not less than y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x/y < 0
This tells us that x and y have OPPOSITE signs, but we don't have any information about which variable is positive and which variable is negative.
So, there's no way to tell whether x < y
Since we can't answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells us that x and y have OPPOSITE signs
Statement 1 tells us that 1/x < 1/y. If x and y have OPPOSITE signs, then we can be certain that x is NEGATIVE and y is POSITIVE.
Take: 1/x < 1/y
Multiply both sides by x to get: 1 > x/y [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]
Multiply both sides by y to get: y > x
Perfect! The answer to the target question is YES, x is less than y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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