What is the value of xy?

[RP]

What is the value of xy?

(1) 3^x ∗5^y =75

(2) 3^{(x−1)(y−2)} =1

Is stmt 1 sufficient? Even if the Q does not say that x adn y are integers, can x and y have any other value other than 1 and 2 to satisfy the equation?

Thanks,
BC

[tim]

As per the forum rules, we need a verifiable source for the problem before we can deal with this question. If the question is not one of ours or one that is copyright-free, we will have to delete the question..

[RP]

It is one of the question from the GMAT Club tests. The question is in public domain in one of their threads. Its just that I did not find any of the reasoning convincing out there so I wanted to get some concept clarification from one of the experts here.

Thanks,
RP

[aditya8062]

i dont think st 1 is sufficient .as nothing is mentioned abt X and Y as in whether they r integer or not so we can have lot of values for which st 1 can hold true .if u put any random value of X ,lets say 1.232 then u will get some value of Y for which the eq will hlf true
i guess the answer of this prob sud be B

[tim]

give us a link to their thread so we can verify whether it is indeed "public domain". we certainly don't want to step on their toes by usurping their problem without adequate permission..

[brparajuli]

I could not find the exact thread for the question. "what is the value of xy" yields too many results.

What if the question is this?

Given: 2^m*7*n=42
Q: Do we know the unique values for m and n?

Can we really get the mathematically exact value of 42 by assigning values to m and n other than m=1, and n=3?

I tried that in excel and it gets very close to 42 but not exactly 42 (e.g. 42 and 10 zeros after that and some number after that and mathematically its not 42). I just want to know whether it is mathematically possible to do that.

Thanks,
RP

[RonPurewal]

I could not find the exact thread for the question. "what is the value of xy" yields too many results.

What if the question is this?

Given: 2^m*7*n=42
Q: Do we know the unique values for m and n?

Can we really get the mathematically exact value of 42 by assigning values to m and n other than m=1, and n=3?

yes, you can. to do so, though, you need "logarithms", which are not tested on the gmat exam.
if something like this were to show up on the gmat exam, there's no doubt that it would stipulate that x and y = integers.

excel, by the way, doesn't really use exact values for anything, unless the decimal actually terminates. e.g., excel will use 0.33333333 (i don't know exactly how many 3's, but some finite number) for 1/3. that's not exactly accurate either, but it's certainly accurate enough for any legitimate use of a spreadsheet.

[brparajuli]

Thank you Ron! That was all what I was trying to figure out.

Thanks Again!

[RonPurewal]

sure.