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If y 0 and y -1, which is greater, x/y or x/(y + 1) ?
[#permalink]
24 Feb 2011, 13:19
24 Feb 2011, 13:19
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If y ≠ 0 and y ≠ -1, which is greater, x/y or x/(y + 1) ?
(1) x ≠ 0.
(2) x > y.
_________________
(1) x ≠ 0.
(2) x > y.
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Re: If y 0 and y -1, which is greater, x/y or x/(y + 1) ?
[#permalink]
14 Jun 2012, 00:34
14 Jun 2012, 00:34
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If y is not equal to 0 and y is not equal to 1, which is greater, x/y or x/(y+1)
Is \(\frac{x}{y}>\frac{x}{y+1}\)? --> is \(\frac{x}{y}-\frac{x}{y+1}>0\)? --> is \(\frac{xy+x-xy}{y(y+1)}>0\)? --> is \(\frac{x}{y(y+1)}>0\)?
(1) x ≠ 0. Not sufficient.
(2) x > y. Not sufficient.
(1)+(2) Still not sufficient, for example: if x>0>(y=-1/2) answer is NO but if x>y>0 answer is YES.
Answer: E.
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Is \(\frac{x}{y}>\frac{x}{y+1}\)? --> is \(\frac{x}{y}-\frac{x}{y+1}>0\)? --> is \(\frac{xy+x-xy}{y(y+1)}>0\)? --> is \(\frac{x}{y(y+1)}>0\)?
(1) x ≠ 0. Not sufficient.
(2) x > y. Not sufficient.
(1)+(2) Still not sufficient, for example: if x>0>(y=-1/2) answer is NO but if x>y>0 answer is YES.
Answer: E.
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General Discussion
Re: If y 0 and y -1, which is greater, x/y or x/(y + 1) ?
[#permalink]
24 Feb 2011, 13:23
24 Feb 2011, 13:23
1
Bookmarks
If y≠0 and y≠-1, which is greater, x/y or x/(y+1)?
(1) x≠0
(2) x > y
Sol:
(1) x!=0 doesn't tell us anything.
x=10
y=1
\(\frac{x}{y}=10\)
\(\frac{x}{y+1}=\frac{10}{2}=5\)
\(\frac{x}{y}>\frac{x}{y+1}\)
x=-10
y=-2
\(\frac{x}{y}=\frac{-10}{-2}=5\)
\(\frac{x}{y+1}=\frac{-10}{-1}=10\)
\(\frac{x}{y}<\frac{x}{y+1}\)
(2) It tells us that x and y have same sign
x > y
x/y > 1 (same sign)
Use sample set from statement 1.
Not sufficient.
Combining both;
Use sample set from statement 1.
Not Sufficient.
Ans: "E"
(1) x≠0
(2) x > y
Sol:
(1) x!=0 doesn't tell us anything.
x=10
y=1
\(\frac{x}{y}=10\)
\(\frac{x}{y+1}=\frac{10}{2}=5\)
\(\frac{x}{y}>\frac{x}{y+1}\)
x=-10
y=-2
\(\frac{x}{y}=\frac{-10}{-2}=5\)
\(\frac{x}{y+1}=\frac{-10}{-1}=10\)
\(\frac{x}{y}<\frac{x}{y+1}\)
(2) It tells us that x and y have same sign
x > y
x/y > 1 (same sign)
Use sample set from statement 1.
Not sufficient.
Combining both;
Use sample set from statement 1.
Not Sufficient.
Ans: "E"
Re: If y 0 and y -1, which is greater, x/y or x/(y + 1) ?
[#permalink]
24 Feb 2011, 15:42
24 Feb 2011, 15:42
So the bottom line is that we need to know the sign of both x and y, to answer the question. And neither provides that.
Re: If y 0 and y -1, which is greater, x/y or x/(y + 1) ?
[#permalink]
24 Feb 2011, 15:52
24 Feb 2011, 15:52
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Expert Reply
bellcurve wrote:
So the bottom line is that we need to know the sign of both x and y, to answer the question. And neither provides that.
Just signs won't be enough.
\(\frac{x}{y(y+1)}>0\) holds true if:
A. \(x>0\) and \(y>0\) or \(y<-1\);
B. \(x<0\) and \(-1<y<0\).
Check the image below:
Attachment:
MSP4919ebfi83e60e30b700002i4ed3dd94aec949.gif [ 3.03 KiB | Viewed 12882 times ]
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Re: If y 0 and y -1, which is greater, x/y or x/(y + 1) ?
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20 Jul 2021, 06:32
20 Jul 2021, 06:32
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Re: If y 0 and y -1, which is greater, x/y or x/(y + 1) ? [#permalink]
20 Jul 2021, 06:32
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