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Is x > y ?

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Source: — Data Sufficiency |
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Re: Is x > y ?

by Stuart@KaplanGMAT » Sat May 03, 2008 10:52 am
amitansu wrote:Is x > y ?

1. [x] - absolute value of x = -8

2. y/absolute value of x = 1/2
I'm going to assume that [x] is just x.

(1) clearly insufficient, says nothing about y

(2) since y/|x| is positive, we know that y and |x| are the same sign. Since |x| is always positive, y must be positive.

However, x itself could be positive or negative. So, we could pick:

y = 1 and x = 2. Is 2 > 1? yes

y = 1 and x = -2. Is -2 > 1? no

Insufficient.

Now that we're combining, let's actually think about (1).

(1) x - |x| = -8

Let's rewrite as:

x + 8 = |x|

If x is positive, we'd get:

x + 8 = x (or 8 = 0), which of course is impossible. Therefore, x must be negative.

Do we care what the value is? No!

From statement (2) we know that y is definitely positive. So, if y is positive and x is negative, we know that the answer to "is x > y" is DEFINITELY NOT.

Together, statements (1) and (2) are sufficient: choose (c).
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by amitansu » Sun May 04, 2008 9:46 am
My choice was also c.
However i was a bit confused by the term [x].

So was confusing between c and e.

Does [x] has got any more interpretation other than just being 'x' in mathematics ?

Btw thanks, for your help ,Stuart.
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by maihuna » Tue Apr 14, 2009 10:10 am
any idea abt the source of this Q?
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by gmat740 » Tue Apr 14, 2009 8:16 pm
I'm going to assume that [x] is just x.
Does [x] has got any more interpretation other than just being 'x' in mathematics ?


[x] is a step function in Calculus

[] means the greatest integer term.

eg : [8.3] = 8

[] this function rounds up the number to its nearest integer(the integer has to be smaller or equal to the original number)

eg : [-9.2] = -10

Hope this helps

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by rohitd80 » Wed May 20, 2015 2:46 pm
Hi Kevin,
I've been struggling with similar DS questions this past week. I would appreciate if you can point me to some direction where I could solidify my fundamentals.

Re Statement [2] you explained:
(2) since y/|x| is positive, we know that y and |x| are the same sign. Since |x| is always positive, y must be positive.

However, x itself could be positive or negative. So, we could pick:

y = 1 and x = 2. Is 2 > 1? yes

y = 1 and x = -2. Is -2 > 1? no

Insufficient.

You are approaching this statement with the notion that albeit y/|x| is positive but x can actually be either +ve or -ve....which makes absolute sense!

Recently, I came across a similar question
If x ≠0, then what is the value of |x|/x?

(1) sqrt(x^2) = x
(2) |x−4|=x/3

My approach on condition 1) sqrt(x^2) = x
For +ve value of x...solving the condition will yield a +ve value of x
And, for a -ve value of x...solving the condition will still yield a +ve value of x
So I took the statement as a hint or guide! and said that x could still be -ve in value:
for +ve x --> |x|/x = 1
for -ve x --> |x|/x = -1
So we can't say whether |x|/x is +ve or -ve. Therefore. the condition/statement 1) is insufficient.

Are we supposed to treat these statements as absolute truth or just a hint/guiding statement?
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by j_shreyans » Fri May 22, 2015 8:59 am
Hi ,

I didn't get the solution , please explain the answer.

Thanks,

Shreyans
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by GMATGuruNY » Fri May 22, 2015 9:40 am
amitansu wrote:Is x > y ?

1. x - |x| = -8

2. y/|x| = 1/2
Statement 1: x - |x| = -8
No information about y.
INSUFFICIENT.

Statement 2: y/|x| = 1/2
If y=1 and x=2, then x>y.
If y=1 and x=-2, then x<y.
INSUFFICIENT.

Statements combine:.
Statement 1 implies the following:
x + 8 = |x|.

Case 1: Signs unchanged
x + 8 = x
8 = 0.
Not possible.

Case 2: Signs changed in the absolute value
x + 8 = -x
2x = -8
x = -4.

Since x=-4 and y/|x| = 1/2, we get:
y/|-4| = 1/2
y/4 = 1/2
y = 2.
Thus, x < y.
SUFFICIENT.

The correct answer is C.
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