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by akhilsuhag » Sat Jun 07, 2014 6:34 am

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If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y

OA Statement 2 is sufficient
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by sukriti2hats » Sat Jun 07, 2014 7:50 am

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akhilsuhag wrote:If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y

OA Statement 2 is sufficient
Hi akhilsuhag,

It is a YES/NO type question.

Statement 1: y=5
Substitute the value of y in x/y and x+5/y+5
You will get, x/5 and x+5/10
We cannot answer which one is greater without having any information regarding x. So statement 1 is INSUFFICIENT.

Statement 2: x>y
This is can be seen by taking examples in which x is greater than y. Let x=4 and y=2 so x/y=4/2=2
x+5/y+5=9/7=1.28 so x/y is not less than x+5/y+5. Thus we get a definite answer, NO.

So the correct answer is B

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Sukriti
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by Brent@GMATPrepNow » Sat Jun 07, 2014 8:45 am

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akhilsuhag wrote:If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5
Statement #2: x > y
Target question: Is x/y < (x+5)/(y+5)?

This is a great candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If y is a positive integer, then we can be certain that y and (y+5) are both POSITIVE. This allows us to safely multiply both sides of our inequality by y and (y+5).

Take x/y < (x+5)/(y+5) and multiply both sides by y to get: Is x < (y)(x+5)/(y+5)?
Then take x < (y)(x+5)/(y+5)? and multiply both sides by (y+5) to get: Is x(y+5) < (y)(x+5)?
Expand to get: Is xy + 5x < xy + 5y?
Subtract xy from both sides to get: Is 5x < 5y?
Divide both sides by 5 to get: Is x < y?

We now have a very simple, REPHRASED target question.....
REPHRASED target question: Is x < y?

Now onto the statements!

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

Statement 2: x > y
Perfect!
If x > y then we can answer our REPHRASED target question with certainty.
NO, x is definitely not less than y.
So, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by akhilsuhag » Sat Jun 07, 2014 9:37 am

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Hi Brent,

I actually solved the question by plugging in values, but it took some time doing that.

I posted it in hope to find a better way to do it- and you have blown me away. I am like- how could I not see that!!

Thank you so much!
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by [email protected] » Sat Jun 07, 2014 2:18 pm

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Hi akhilsuhag,

This DS question is great for TESTING Values, but there's also a hidden Number Property that makes dealing with Fact 2 easier than you might think.

We're told that X and Y are POSITIVE INTEGERS. We're asked if X/Y < (X+5)/(Y+5)? This is a YES/NO question.

*Brent's tactic to rewrite the question is quite useful, but not necessary to solve this problem*

Fact 1: Y = 5

With this information, we can rewrite the question as:

"Is X/5 < (X+5)/10?

Let's TEST Values...

If X = 1, is 1/5 < 6/10? The answer is YES.
If X = 5, is 5/5 < 10/10? The answer is NO.
Fact 1 is INSUFFICIENT

Fact 2: X > Y

Since both variables are POSITIVE INTEGERS and X > Y, we know that X+5 > Y+5 and we know that the numerator of both fractions is greater than the denominator.

Here's the Number Property I mentioned earlier: Since the numerator and denominator are both positive, ADDING the SAME value to both the numerator and the denominator will "push" the value of the fraction closer to 1.

eg 2/1 = 2

(2+1)/(1+1) = 3/2 = 1.5

(2+2)/(1+2) = 4/3 = 1.3333

(2+3)/(1+3) = 5/4 = 1.25

(2+4)/(1+4) = 6/5 = 1.2

Etc.

This ultimately means that, under these restrictions, X/Y will ALWAYS be greater than (X+5)/(Y+5), so the answer to the question will ALWAYS be NO.
Fact 2 is SUFFICIENT.

Final Answer: B

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by Brent@GMATPrepNow » Fri Jan 12, 2018 6:32 am

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akhilsuhag wrote:If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y
Target question: Is x/y < (x+5)/(y+5)?

This is a great candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If y is a positive integer, then we can be certain that y and (y+5) are both POSITIVE. This allows us to safely multiply both sides of our inequality by y and (y+5).

Take x/y < (x+5)/(y+5) and multiply both sides by y to get: Is x < (y)(x+5)/(y+5)?
Then take x < (y)(x+5)/(y+5) and multiply both sides by (y+5) to get: Is x(y+5) < (y)(x+5)?
Expand to get: Is xy + 5x < xy + 5y?
Subtract xy from both sides to get: Is 5x < 5y?
Divide both sides by 5 to get: Is x < y?

We now have a very simple, REPHRASED target question.....
REPHRASED target question: Is x < y?

Now onto the statements!

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

Statement 2: x > y
Perfect!
If x > y then we can answer our REPHRASED target question with certainty: NO, x is definitely not less than y.
So, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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