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by akhilsuhag » Tue Apr 29, 2014 11:09 am
If x and y are positive integers, is (x/y)<(x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y
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Source: — Data Sufficiency |
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by akhilsuhag » Tue Apr 29, 2014 11:16 am
To Find:
(x/y)< (x+5)/(y+5). Solve this inequality. Cross Multiply------------------ (1)

x(y+5) < y(x+5) => xy + 5x < xy + 5y => 5x < 5y => x<y (this is what we need to find)

Statment 1:

y=5. Put this in (1)

this gives you x<5

so that makes it sufficient.

Statement 2:

x>y

So obviously sufficient.

Can someone point out my mistake.
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by Matt@VeritasPrep » Tue Apr 29, 2014 5:47 pm
akhilsuhag wrote:If x and y are positive integers, is (x/y)<(x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y
If we know x and y are positive, then we know that all our numerators and denominators are positive, so we know what happens when we multiply both sides by our variables.

Let's simplify the question first. Cross-multiplying gives us

"Is x * (y+5) < y * (x+5) ?"

or

"Is xy + 5x < xy + 5y ?"

or

"Is 5x < 5y ?"

or

"Is x < y ?"

The first statement isn't helpful -- what's the value of x? -- but the second statement answers our question definitively. ("Yes, x < y.")

The mistake you made is assuming that the answer is our question ("Is x < y?") is "yes". We don't KNOW that x < y ... we're trying to determine that! So we can't use that inequality when evaluating S1.
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by Brent@GMATPrepNow » Tue Sep 17, 2019 8:08 am
akhilsuhag wrote:If x and y are positive integers, is (x/y)<(x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y
Given: x and y are positive integers

Target question: Is x/y < (x+5)/(y+5)?
This is a good candidate for rephrasing the target question.

Since y is POSITIVE, we can safely take the inequality x/y < (x+5)/(y+5) and multiply both sides by y.
When we do this, we get: x < (y)(x+5)/(y+5)

Also, since y is POSITIVE, we also know that (y + 5) is POSITIVE
So, let's take the inequalityx < (y)(x+5)/(y+5) and multiply both sides by (y + 5).
We get: (x)(y+5) < (y)(x+5)
Expand both sides to get: xy + 5x < xy + 5y
Subtract xy from both sides to get: 5x < 5y
Divide both sides by 5 to get: x < y
We now have a very simple, REPHRASED target question. . . . .
REPHRASED target question: Is x < y?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: y = 5
Since we have no information about x, there's no way to determine whether x < y
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y
Perfect.
With information, we know (with certainty) that the answer to the REPHRASED target question is NO, x is NOT less than y
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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