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# If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y|

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y|  [#permalink]

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09 Aug 2017, 04:28
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:14) correct 36% (01:32) wrong based on 56 sessions

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If y≠0, is |x/y|=x/y?

1) |xy|=xy
2) |x/y|=|x|/|y|

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 06 Jul 2016 Posts: 358 Location: Singapore Concentration: Strategy, Finance Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink] ### Show Tags 09 Aug 2017, 04:51 MathRevolution wrote: If y≠0, is |x/y|=x/y? The question is basically asking if x & y have the same sign i.e. Are x,y > 0 OR x,y <0? Quote: 1) |xy|=xy 2) |x/y|=|x|/|y| 1) |xy| = xy => Both x and y have the same sign. x = 1, y = 1 |xy| = 1 xy = 1 They are the same. x = 1, y = -1 |xy| = 1 xy = -1 Not the same. Test Failed => x and y have the same sign. => |x/y| = $$\frac{x}{y}$$ So A is sufficient. 2) |x/y|=$$\frac{|x|}{|y|}$$ x = 1, y = 1 |x/y|=$$\frac{|x|}{|y|}$$ = 1 => |x/y| = $$\frac{x}{y}$$ = 1 => YES x = -1, y = 1 |x/y|=$$\frac{|x|}{|y|}$$ = 1 BUT |x/y| = 1 ≠ $$\frac{x}{y}$$ = -1 => NO. 2 answers, hence Insufficient. A is the answer. _________________ Put in the work, and that dream score is yours! Math Expert Joined: 02 Aug 2009 Posts: 7989 Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink] ### Show Tags 09 Aug 2017, 05:24 MathRevolution wrote: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| Hi.. $$\frac{x}{y}$$... Has to be EITHER 0 OR positive.... And for that any of conditions would be sufficient.. 1) x and y are of the same SIGN 2) x is 0.. Let's see the statements.. 1) |xy|=xy.. Clearly x*y is 0 or POSITIVE... Sufficient 2) |x/y|=|x|/|y| If x is zero ans is YES.. If x and y are of same sign, ans is YES But if x and y are of opposite sign ans is NO Insufficient A _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y| [#permalink] ### Show Tags 11 Aug 2017, 01:00 ==> If you modify the original condition and the question, in order to get |x/y|=x/y, you get x/y≥0?, and if you multiply y^2 on both sides, you get xy≥0?. Then, for con 1), to satisfy |xy|=xy, you get xy≥0, hence yes, it is sufficient. For con 2), if x=y=2, yes, but if x=2 and y=-1, no, hence it is not sufficient. The answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If y≠0, is |x/y|=x/y? 1) |xy|=xy 2) |x/y|=|x|/|y|   [#permalink] 11 Aug 2017, 01:00
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