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Is x > y? (1) |x| > |y| (2) x = |x|

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Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 04:21
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Is x > y?

(1) |x| > |y|
(2) x = |x|
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Re: Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 04:28
[quote="anushilaghosh"]Is x > y?

1. |x| > |y|
this tells us the numeric value of x is more than y..
so if x >0, ans is YES
but if x<0, ans is NO
insuff

2. x = |x|
tells us that is 0 or >0
insuff

combined
x>0 so ans is YES always
suff

C
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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 x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 04:32
chetan2u

Could you elaborate point 2.
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Re: Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 04:58
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anushilaghosh wrote:
chetan2u

Could you elaborate point 2.


x=|x|
Here modulus will always be positive or 0..
So |x|\(\geq{0}\), and thus x is also \(\geq{0}\)
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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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Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 07:42
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anushilaghosh wrote:
Is x > y?

(1) |x| > |y|
(2) x = |x|


(1) |x| > |y|
If x=1, y=0 --> Yes
If x=-1, y=0 --> No
--> Not sufficient.

(2) x = |x|
no info about y --> Not sufficient.

(1)+(2) x > |y|. As |y| \(>= y\), we can conclude that x > y --> Sufficient.

Answer C.
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Re: Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 10:29
anushilaghosh wrote:
Is x > y?

(1) |x| > |y|
(2) x = |x|


OA: C
(1)\(|x| > |y|\)
Taking \(x = 2\) and \(y = 1 ,|x| > |y|\) as \(|2| > |1|\)
Is x > y : Yes as \(2>1\)

Taking \(x = -2\) and \(y = -1 ,|x| > |y|\) as \(|-2| > |-1|\)
Is x > y : No as \(-2<-1\)

Statement \(1\) alone is insufficient.

(2) \(x = |x|\)
If we take \(x=-2\), then it will not satisfy the statement \(2\) as \({-2}\neq{|-2|}\)
Only non negative numbers can statisfy \(x = |x|\)
So Statement implies that \(x\geq{0}\), but \(y\) can take any value.

Statement \(2\) alone is insufficient.

Combining 1 and 2 , \(|x| > |y|\) and \(x\geq{0}\) leads to \(x > |y|\)
Is x>y : yes for all \(x > |y|\)
So Combining (1) and (2) will be sufficient.
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Re: Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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New post 27 Aug 2018, 11:38
1
anushilaghosh wrote:
Is x > y?

(1) |x| > |y|
(2) x = |x|
I have used the basic definition of module to solve this question. If you are fan of doing it on a number line, have a look at this approach

Answer is C
Attachment:
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1535398793939.jpg [ 61.18 KiB | Viewed 547 times ]


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Re: Is x > y? (1) |x| > |y| (2) x = |x| &nbs [#permalink] 27 Aug 2018, 11:38
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