If x and y are positive integers, is x a multiple of y?

Question

(1)  2y^2 + 5y = 3x 
(2) y is not a multiple of 3.

huongguyen · Answer

If x and y are positive integers, is x a multiple of y?

(1) \(2y^2 + 5y = 3x\)
<=> y(2y + 5) = 3x
<=> \(x = \frac{y}{3}(2y+5)\)
If y = 3k -> yes, x a multiple of y
If y = 1, 2, 4, 5... -> no, x is not a multiple of y
=> insufficient

(2) y is not a multiple of 3.
-> insuficient because no info of x

(1) (2): y is not a multiple of 3 => \(x = \frac{y}{3}(2y+5)\) not an integer
=> x is NOT a multiple of y
Sufficient
IMO: C

Victor19 · Answer

Answer is C.

Statement 1 : 2y2+5y=3x.
If y = 2, x=6. x is a multiple of y. 
If y = 3, x = 11. x is not a multiple of y.
We get different answers. So insufficient.

Statement 2 : y is not a multiple of 3.
No info on x. Insufficient.

Combining both, we get that x is a multiple of y.
So answer is C.

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

JerryAtDreamScore · Answer

Rephrase the question:

Is  x = i * y , where  i  is an integer?

Statement 1 Alone:

We have  x = \frac{2y^2 + 5y}{3} = \frac{2y + 5}{3}*y . We are concerned if  \frac{2y + 5}{3}  is an integer. If it is not, then y must be a multiple of 3 as we already know the result  x  is an integer. Currently we do not have enough information so this is insufficient.

Statement 2 Alone:

Insufficient.

Both Statements Combined:

Since y is not a multiple of 3, we need  \frac{2y + 5}{3}  to be an integer. Thus  x = i*y  is a multiple of 3.

Answer: C

Deska · Answer

I still get confused with this exercise.

The answer is supposed to be C (Both statements). However I have the following scenarios:
If Y = 5 (not a multiple of 3), then X = 25 and X is in fact a multiple of Y,
If Y = 7 (not a multiple of 3), then X = 133/3 and obviously X is not a multiple of Y.

That's why I chose answer E (not sufficient together).

Hope you could check my racionale.

harishramesh · Answer

when u insert 7 x would not be an integer. So that makes the statement invalid. We should try with values which makes x to become integer

pipet · Answer

i'm confused about the answer

we are asked to see if x/y is an integer

1) y(2y+5)=3x => (2y+5)/3=x/y
for y=1 we get 7/3 -> not an integer
for y=2 we get 9/3=3 -> integer
1 isn't sufficient

2) this doesn't explain anything about x so it isn't sufficient.

together) the numbers we inserted in 1) were already not multiples of 3 so we don't have any new information. not sufficient.

Bunuel · Answer

y cannot be 7 because we are told that x is an integer, and this value of y does not produce an integer value for x.

Bunuel · Answer

When we combine the statements, we get that x = (2y + 5)/3 * y and y is not a multiple of 3. Now, since y is not a multiple of 3 and we know that x is an integer, (2y + 5)/3 must itself be a multiple of 3, making it an integer. Therefore, x = integer * y, which means x is a multiple of y.

P.S. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question. 
 
Hope it helps.

If x and y are positive integers, is x a multiple of y?

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