Is |x|/|y| y^3 (2) y^5 y^4

Question

Is  \frac{|x|}{|y|} < |x|*|y| ?

(1)  x^3>y^3

(2)  y^5>y^4

GMATBusters · Accepted Answer

Is |x|/ |y| < |x|*|y| ?
Squaring both sides and cross multiplying, we get
or, x^2 < x^2 *y^4
or, x^2 (1-y^4)<0

This would be true if x is not equal to 0, and y >1 or y <-1
So, the question reduces to " Is x is not equal to 0, and y >1 or y <-1" ?

Statement 1: x^3 > y^3
Here x can be zero, and y any negative number. for which the answer can be NO
(x,y) can be (2,3), Answer is YES

NOT SUFFICIENT

Statement 2:
y^5 > y^4
or y^4(y-1) >0

here y >1, but x can be zero or non zero.
if y >1, x =0 , answer is NO
if y >1, x is non zero, ans is YES

NOT SUFFICIENT

Combing Both statements , we get y >1
and x^3 > y^3 , Hence x is NON zero,

So, We have y >1 ans X is NON ZERO.

Hence SUFFICIENT.
Answer is C

AsadAbu

Is \(\frac{|x|}{|y|} < |x|*|y|\)?

(1) \(x^3>y^3\)

(2) \(y^5>y^4\)

Shreshtha55 · Answer

If i wanted to solve this question with the help of numbers how can I solve it? Can anyone help me?

BelalHossain046 · Answer

I would go for C.

Statement 1: insufficient
Case 1: X=0 & y=-1 (thus, both sides are equal in main question. So, NO to main question)

Case 2: x=2 & y=3 (yes to main question)

Statement 2: insufficient
Case 1: X=0 & y=2 (thus, both sides are equal in main question. So, NO to main question)

Case 2: x=2 & y=3 (yes to main question)

Combining
From statement 2, it is clear that y is positive and greater than 1. 
So in statement 1, x must be positive.

In such situation, multiplication of same direction two number is greater than division of same numbers.

I.e. x=3 & y=2

Posted from my mobile device

strawberryjelly · Answer

Can people make sure that their answers are correct when posting questions? Makes it a lot harder to study when you are trying to work out whether the answer is actually the answer or not

TheUltimateWinner · Answer

Hi Bunuel and IanStewart , Can I rearrange the question stem in the following way? \frac{|x|}{|y|} < |x|×|y| ? ==> \frac{x^2}{y^2} x^2 y^4>1?

Bunuel · Answer

Yes. You could reduce by |x| directly (provided x is not 0). \frac{1}{|y|} < |y| --> |y|^2 > 1 --> y < -1 or y > 1. BTW, the correct answer is C, not B. (2) give y > 1. If x ≠ 0, then \frac{|x|}{|y|} > |x|×|y| (answer YES) but if x = 0, then \frac{|x|}{|y|} = |x|×|y| (answer NO). What is the source of the question?

TheUltimateWinner · Answer

Source: Wizako 
In this question, if we can determine that   y^2>1   then the data is sufficient.
Conversely, if we can determine that  y^2≤1  then the data is also sufficient.
Isn't it?
Statement 2 says:
(2)  y^5>y^4 
Here, y^4 is positive, so we can divide both part by  y^4 . We get from statement 2:
==>   y>1   
==>   y^2>1    
So, why not B sufficient?

Bunuel · Answer

Because we have one more variable in the question: |x| /|y|  <  |x| *|y|. From (2) we know that y > 1 but know nothing about x.  If x ≠ 0 , then  \frac{|x|}{|y|} > |x|×|y|  (answer YES) but  if x = 0 , then  \frac{|x|}{|y|} = |x|×|y|  (answer NO).

TheUltimateWinner · Answer

But i've deduced the question stem as   y^4>1   where there is no existence of x. 
Thanks__

Bunuel · Answer

Check my post above: You could reduce by |x| directly ( provided x is not 0 ). If x = 0, then we cannot reduce and thus only y^5 > y^4 will not be sufficient.

TheUltimateWinner · Answer

Thank you so much. Better if you edit the OA.

GMATGuruNY · Answer

Since division by 0 is not allowed, the prompt should indicate that \(y≠0\):

AsadAbu

If \(y≠0\), is \(\frac{|x|}{|y|} < |x|*|y|\)?

(1) \(x^3>y^3\)

(2) \(y^5>y^4\)

Since an absolute value cannot be negative. we can simplify the question stem by multiplying both sides by |y|:
\(\frac{|x|}{|y|}|y| < |x||y||y|\)
\(|x| < |x|y^2\)?

If \(x=0\), the answer to the question stem is NO.
If \(x≠0\), we can divide both sides by \(|x|\):
\(\frac{|x|}{|x|} < \frac{|x|y^2}{|x|}\)
\(1 < y^2\)?
Here, the answer will be YES if \(y>1\) or \(y<-1\).

Question stem, rephrased:
Is it true that \(x≠0\) and that \(y>1\) or \(y<-1\)?

Statement 1:
Case 1: x=3 and y=2
Since \(x≠0\) and \(y>1\), the answer to the question stem is YES.
Case 2: x=2 and y=1
Since \(y=1\), the answer to the question stem is NO.
INSUFFICIENT.

Statement 2:
Since the inequality implies that \(y≠0\), we can safely divide both sides by \(y^4\), which must be positive:
\(\frac{y^5}{y^4}>\frac{y^4}{y^4}\)
\(y > 1\)
No information about \(x\).
INSUFFICIENT.

Statements combined:
\(y>1\) implies that \(y^3>1\).
Thus:
\(x^3 > y^3 > 1\)
\(x^3 > 1\)
\(x > 1\)
Since \(x≠0\) and \(y>1\), the answer to the question stem is YES.
SUFFICIENT.

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C

.

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Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4

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