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# M60-25

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
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11 Jun 2018, 07:03
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100% (00:11) correct 0% (00:00) wrong based on 1 sessions

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If $$x, y and z$$ are positive numbers, is $$xy+z > x+yz$$?

1) $$x>1$$

2) $$y>1$$

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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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re M60-25 [#permalink] ### Show Tags 11 Jun 2018, 07:03 Official Solution: Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 3 variables (x and y) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. Conditions 1) & 2): $$xy + z > x + yz$$ ⇔ $$xy - x - yz + z > 0$$ ⇔ $$x(y-1)-z(y-1) > 0$$ ⇔ $$(x-z)(y-1) > 0$$ ⇔ $$x - z > 0$$ since $$y > 1$$. If $$x = 2, y = 2$$, and $$z = 1$$, then $$xy + z = 5, x + yz = 4$$ and $$xy + z > x + yz$$. So, the answer is 'yes'. If $$x = 2, y = 2$$, and $$z = 3$$, then $$xy + z = 7$$, $$x + yz = 8$$ and $$xy + z < x + yz$$. So, the answer is 'no'. Since the question does not have a unique answer, both conditions together are not sufficient. Therefore, E is the answer. In cases where 3 or more additional equations are required, such as for original conditions with "3 variables", or "4 variables and 1 equation", or "5 variables and 2 equations", conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D. Answer: E _________________ 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$99 for 3 month Online Course"
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Joined: 11 Nov 2013
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10 Aug 2018, 02:59
I think the scenario "If x = 2, y = 2 and z = 3 ..." is incorrect.

Since x – z > 0, x > z.
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Joined: 01 Apr 2018
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14 Sep 2018, 07:30
Yes, the explanation is not Correct , if x - z >0 then how come x =2 and z=3? Please can someone help ?
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23 Sep 2018, 12:25
xy+z > x+yz
xy+z-x-yz>0
x(y-1)-z(y-1)>0
(x-z)(y-1)>0?

so for this statement to be true, (x-z) and (y-1) should have the same sign. We need to statements if they provide this info.

from 1: x>1, no info on y and z, so insuff
from 2: y>1, (y-1)>0, we don't have info on (x-z) so insuff

1+2 combined, x>1 and y-1>0, no info on x-z sp insuff. therefore E
Re: M60-25 &nbs [#permalink] 23 Sep 2018, 12:25
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# M60-25

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