Question: GCD of x and y

Comment on GCD of x and y

Please i dont understand the last part why both statements are sufficient
gmat-admin's picture

In statement 1, we found two possible cases:
case a: x = y, in which case the GCD = x = y
case b: x ≠ y, in which case the GCD = 1

In statement 2, we learned that one of the numbers (x or y) is odd and the other number is even.

So, when we combine the two statements, we can rule out case a (x = y) because one value is odd and the other value is even. So, there's no way the two values can be equal.

This leaves only case b (x ≠ y).

Since we can be certain that x and y are not equal AND x and y are prime numbers, then we can conclude that the GCD of x and y MUST be 1.

Dear Brent, I solve this problem and get the answer A. Why we can conclude that X and Y can be the same number (case 1)? In my interpretation, since X and Y was written in different symbol, then the number must be different. Is it the same interpretation that GMAT use in test?

Anyway thanks a lot for this wonderful lesson and practice test!
gmat-admin's picture

It's a common belief that, if two variables are different (e.g., x and y), then those variables cannot have the same value.

On the GMAT (and in any math class :-), two different variables can share the same value.

Sorry for being the devil's advocate and asking a terrible question, but .. if X and y can be same .. why then can we not add 7x and 4y say to 11x or 11y in algebra?
Is it because the variables "can" share same value but not "should"? Any analogy would be much appreciated!!
gmat-admin's picture

It all comes down to the strength of the word CAN.
This is a pretty weak word, and I'm not aware of any mathematical symbol that expresses the concept of CAN.

To use your example, we can write: 7x + 4y COULD POSSIBLY EQUAL 11x (if x = y)
But that's all we can say.
We certainly CANNOT conclude that 7x + 4y = 11x, because this boldly states that 7x + 4y MUST EQUAL 11x for all values of x and y.

On the other hand, we can write: 2k + 3k = 5k (for ALL values of k)

Another example is to examine the solutions to the equation x + y = 10.
One possible solution is x = 2 and y = 8
Another possible solution is x = -3 and y = 13
Another possible solution is x = 5 and y = 5

So, even though it's possible for x and y to both equal 5 (when x + y = 10), we must recognize that x and y are not necessarily equal.
As such, it would be mathematically incorrect to take the equation x + y = 10 and rewrite it as x + x = 10.

Does that help?


Thanks for this video, it was very helpful! I made the mistake by assuming that x and y can't be the same number, so for statement 1 I automatically assumed that they would be 2 different primes; eg 2 and 3, and therefor it would be certain that the GCD equals 1.

For the math I did back in high school, x and y were always used to represent DIFFERENT values. For the GMAT, should I assume that x and y can represent any values, including the same value, unless stated otherwise? And if it's stated, how would this be noted in the question text? Thanks for all your videos! MBA saver. :-)
gmat-admin's picture

You can safely assume that two different variables can have the same values, unless stated otherwise.

If the test-maker wanted to restrict two variables so they cannot be equal, there are a few ways to do so. Here are a couple of examples:

"If x and y are positive integers such that x ≠ y, then....."


"If x and y are DIFFERENT numbers, then....."


Thanks for the clarification and all the super helpful videos!

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