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

Simplify (we can cross multiply, since x and y are positive)

xy+5x<xy+5y
5x<5Y
So basically the question asks if x<y

st1. nothing about x-> insf.
st2. clear answer-> suff.

Answer B

MAGOOSH OFFICIAL SOLUTION:

We are adding the same number, 5, to both the numerator and the denominator, so the value of x/y will move closer to 1. All we need to determine is whether x/y is greater than 1 or less than 1.

Statement #1: y = 5. Here, we have a definite value for y, but zero information about x. If y = 5, some fractions (1/5) can be less than one, while others (7/5) will be greater than one. Either is possible. Since both are possible, we can’t give a definitive answer to the prompt. This statement, alone, by itself, is insufficient.

Statement #2: x>y. Dividing both sides of this inequality by y, we get (x/y) > 1. This means x/y must be a fraction greater than 1, which means the resultant fraction (x + 5)/(y + 5) must be closer to one, which means the resultant fraction must be smaller. Therefore, we can definitively say: the answer to the prompt question is, “No.” Because we can give a definite answer to the prompt, we have sufficient information. This statement, alone, by itself, is sufficient.
Statement #1 is insufficient and Statement #2 is sufficient.

Answer = B.

according to the solution
x>y
lets take x=2 y=1
2<7/6
its not valid
Can someone give the solution?

Hi ShravyaAlladi
See here the question is asking us whether x/y<x+5/y+5
There are two ways to solve this
First one => Using the concept of Fractions and decimals => Adding the same thing number to the numerator and the denominator just bring the number closer to one. Hence the question is really asking us if x/y is a proper fraction or an improper one.
Here if x>y => x/y will be an improper fraction
Hence x+5/y+5 will be less than the x/y so the answer is always a NO.
Second using the concept of inequality we can cross multiply to change the sides and the stem of the question reduces to is x/y<1

AS per your query you are absolutely right
The reason B is the answer is that no matter what be the values of x and y ; if x>y => x/y>1
so if x=2 y=1 => the answer is a NO
The answer to the question is always a NO

Refer to this to learn this concept => https://magoosh.com/gmat/2012/gmat-short ... nominator/

Hello!

I understand this concept, however, when I first went through this question, I answered D.

The reason is that for (1), I substituted y=5 into the equation, which lead me to x<5. And if x<5 then this statement is sufficient as that would make x<y.

Could someone please explain the flaw in my reasoning?

Thank you!

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


x/y < (x+5)/(y+5)

0 < (x+5)/(y+5) - x/y

0 < y(x+5) - [x(y+5)]/ y(y+5)....looks ugly but simplifying we get

0 < (5y-5x) / y(y+5)

0 < 5(y-x) / y(y+5)

As y & x are positive integers, the denominator is always positive.

teh question repharsed to be

is y-x> 0?? or is y>x

(1) y = 5

No info about x. We do not know sign of (y-x)

Insufficient

(2) x > y

Directly we can say: y-x<0 means it is ALWAYS negative. Answer is ALWAYS No

Sufficient

Answer: B

\(\frac{x}{y}<\frac{x+5}{y+5}\)
=> \(x<y?\)

1. y=5, no information about x. -> INSUFFICIENT.
2. x>y -> SUFFICIENT.

B.

1) Insufficient since we need the value of both x and y to determine x/y. So we can know if x/y is less than 1 or more than one.
2) sufficient
Answer: B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.