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# If x and y are positive integers, what is the value of x + y?

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GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4016
If x and y are positive integers, what is the value of x + y?  [#permalink]

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19 Feb 2019, 09:43
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1
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Difficulty:

65% (hard)

Question Stats:

54% (01:59) correct 46% (01:41) wrong based on 48 sessions

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If x and y are positive INTEGERS, what is the value of x + y?

1) x percent of 300 is equal to y percent of 125
2) y is 140 percent greater than x

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Re: If x and y are positive integers, what is the value of x + y?  [#permalink]

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19 Feb 2019, 13:20
3
Stmt 1 :
1.25y =3x

Cant determine (x+y) . Not Sufficient

Stmt 2 :
y = 2.4x

Cant determine (x+y) . Not Sufficient

Combining 1 and 2 .

1.25 (2.4x) = 3x

LHS = RHS

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Re: If x and y are positive integers, what is the value of x + y?  [#permalink]

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19 Feb 2019, 14:04
1
Both statements help us to get the value of one variable in terms of another. Since we don’t know the value of either of these variables, getting the sum using either of these statements alone is impossible.

Next, we try to use both these statements in tandem. A gives us (x = 0.4166y) while B gives us (y = 2.4x). Combining the give, we get x = x , a tautology which is clearly not useful.

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Re: If x and y are positive integers, what is the value of x + y?  [#permalink]

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12 Apr 2019, 08:35
Top Contributor
GMATPrepNow wrote:
If x and y are positive INTEGERS, what is the value of x + y?

1) x percent of 300 is equal to y percent of 125
2) y is 140 percent greater than x

Target question: What is the value of x + y?

Given: x and y are positive INTEGERS

Statement 1: x percent of 300 is equal to y percent of 125
We can write: (x/100)(300) = (y/100)(125)
Simplify: 3x = 1.25y
Divide both sides by 1.25 to get: 2.4x = y

There are several values of x and y that satisfy the equation 2.4x = y. Here are two:
Case a: x = 10 and y = 24. In this case, the answer to the target question is x + y = 10 + 24 = 34
Case b: x = 5 and y = 12. In this case, the answer to the target question is x + y = 5 + 12 = 17
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is 140 percent greater than x
We can write: y = x + 140% of x
In other words: y = x + 1.4x
Simplify: y = 2.4x
Divide both sides by 1.25 to get: 2.4x = y
At this point, we're finished.
This equation (2.4x = y) is the SAME equation we derived for statement 1.
Since statement 1 is not sufficient, we can conclude that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the statements, all we know is that 2.4x = y
We already know that this equation is not enough to answer the target question with certainty.
So, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: If x and y are positive integers, what is the value of x + y?   [#permalink] 12 Apr 2019, 08:35
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