If x and y are nonnegative integers, what is the value of y?

Question

(1) 3^x = 5^y
(2) |y| = −y

Bunuel · Accepted Answer

If x and y are nonnegative integers, what is the value of y?

(1) 3^x = 5^y. Since x and y are integers then x = y = 0. Sufficient.

(2) |y| = −y -->  y\leq{0} . From the stem we know that  y\geq{0} , therefore y = 0. Sufficient.

Answer: D.

2013gmat · Answer

1) x could be 0 or 3 as its a non negative number ( 0 or >0), so A is not sufficient.

2) this doesn't give us any specific value. Not sufficient.

1 + 2 -- No specific value.

E is answer.

Kudos please!

LighthousePrep · Answer

Please note, the original question changed since my post.

I disagree with the official answer. Here's why I think the answer is B (statement 2 alone is sufficient).

Statement 1:
3x = 5y

y has an infinite number of possibilities. For example...
x=0, y=0
x=5, y=3
x=10, y=6
x=15, y=9

Therefore, statement 1 is insufficient.

Eliminate answer choice A and D.

Statement 2:
|y| = -y

This statement requires an understanding of absolute value notation (that is what the vertical lines around y mean). Absolute value is by definition the magnitude of a number without regard to its sign. This means that the absolute value of any number cannot be negative, since negative is a sign, UNLESS you count absolute value of zero.

The only possible value of y in this case is y=0.

Eliminate C and E.

Correct answer is B.

intheend14 · Answer

Agree with lighthouse on this one... It's B.

A is not sufficient as there are many possibilities, but with B, y can only be zero.

aashu4uiit · Answer

Just corrected the question .

It's D , My doubt about statement 2 is clear now.

Thanks

aib4747 · Answer

Hi Bunuel,

I am unable to understand how you stated -

(1) 3^x = 5^y. Since x and y are integers then x = y = 0. Sufficient.

As per my understanding x & y can have multiple value combinations.
So answer should be (B). Please explain what am I misinterpreting.

Bunuel · Answer

The crucial point is that x and y are integers. 3^x cannot be a multiple of 5 and 5^y cannot be a multiple of 3. Thus for 3^x = 5^y to be true both x and y must be 0.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x and y are nonnegative integers, what is the value of y?

(1) 3^x = 5^y
(2) |y| = −y
 
There are 2 variables (x,y) and 2 equations are given by the 2 conditions, giving a high chance (C) will be our answer.
If we look at conditions together, x=y=0, making the answer seem like (C), but this is a commonly made mistake;

For condition 1, x=y=0. This is sufficient.
For condition 2, y<=0, this is non-negative so y=0. This is also sufficient.
The answer therefore become (D).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

ydmuley · Answer

x and y are non-negative integers - This means x & Y can be ZERO and Any POSITIVE integers.

y = ?

(1) 3^x = 5^y

As we can see that there is no value for x & y except ZERO which can satisfy this equation. So, we can write:

3^0 = 5^0

0 = 0

Or, we can write:  x + y = 0  or  x & y  are  Zero , Hence, we know  y = 0  =====>  Hence, Eq. (1) =====> SUFFICIENT

(2) |y| = −y

Considering y is non-negative integer, the only integer which can satisfy this equation is  y = 0

Hence, Eq. (2) =====> SUFFICIENT

Hence, the answer is D

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If x and y are nonnegative integers, what is the value of y?

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GMAT Data Sufficiency (DS) Questions

If x and y are nonnegative integers, what is the value of y?

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