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

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Intern
Joined: 31 Jan 2018
Posts: 5
Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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27 Aug 2018, 05:21
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Difficulty:

15% (low)

Question Stats:

73% (00:47) correct 27% (00:58) wrong based on 96 sessions

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Is x > y?

(1) |x| > |y|
(2) x = |x|
Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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27 Aug 2018, 05:28
[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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Re: Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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27 Aug 2018, 05:32
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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27 Aug 2018, 05:58
1
1
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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Is x > y? (1) |x| > |y| (2) x = |x|  [#permalink]

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27 Aug 2018, 08:42
3
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.

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

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27 Aug 2018, 11:29
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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27 Aug 2018, 12:38
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

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Re: Is x > y? (1) |x| > |y| (2) x = |x|   [#permalink] 27 Aug 2018, 12:38
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