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# Is |2x - 7| > y ?

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
Is |2x - 7| > y ?  [#permalink]

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05 Jul 2018, 07:30
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:05) correct 44% (02:02) wrong based on 44 sessions

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If x and y are real numbers,is |2x - 7| > y ?

(1) y^2 = 16.

(2) x is a negative number.

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Manager
Joined: 13 Feb 2018
Posts: 135
Re: Is |2x - 7| > y ?  [#permalink]

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05 Jul 2018, 08:14
my approach

1 stm: $$y^2$$=16 y=4 or y=-4 we know that modulus is always positive so we have to focus on y=4; nothing about x insuff.
2 stm: x is negative means that the modulus is >7; nothing about y. unsuff.

together we know that left side is >7 and the right side may take maximum value of 4. suff

In My Opinion
Ans: C
Math Expert
Joined: 02 Aug 2009
Posts: 7095
Re: Is |2x - 7| > y ?  [#permalink]

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05 Jul 2018, 08:16
If x and y are real numbers,is |2x - 7| > y ?

(1) y^2 = 16.
y can be 4 or -4
say x is 2 and y is 4....|2*2-7|>4.....3>4...NO
say x is 2 and y is -4......YES
insuff

(2) x is a negative number.

insuff

combined
|2x-7|>4, lets take the max possible value of y
if x is negative |2x-7| will always be >7
so 7>4
sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is |2x - 7| > y ? &nbs [#permalink] 05 Jul 2018, 08:16
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