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STAT1 x is an integer If x = 0 then (4^x)^(5-3x) = (4^0)^(5-3*0) = 1 which is TRUE If x = 1 then (4^x)^(5-3x) = (4^1)^(5-3*1) = 16 not equal to 1 so FALSE So, INSUFFICIENT

STAT2 product of x and y is not x => x is NOT equal to 0 So, x can be 1, then (4^x)^(5-3x) != 1, So, FALSE Also, x can be fraction If x= 5/3 then (4^x)^(5-3x) = (4^5/3)^(5-3*5/3)) = (4^5/3)^0 = 1, So, TRUE So, INSUFFICIENT

STAT1 and STAT2 together We know that x is an integer and is not 0 For all values of x, (4^x)^(5-3x) will never be equal to 1 (substitute and check) So, SUFFICIENT

So, Answer will be C

Hope it helps!

goodyear2013 wrote:

Is (4^x)^(5-3x) = 1? (1) x is an integer. (2) The product of x and positive integer y is not x.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

Is (4 ^x )^ (5−3x) =1 ?

(1) x is an integer. (2) The product of x and positive integer y is not x.

If we modify the original condition and the question, we ultimately want to know whether 4^x(5-3x)=1=4^0, x(5-3x)=0, so whether x=0 or x=5/3. There is only one variable, so we only need one equation, when 2 equations are given from the 2 conditions; there is high chance (D) will be our answer. For condition 1, the answer becomes 'yes' for x=integer=0, but 'no' when x=1. This condition is insufficient. For condition 2, on the other hand, we get xy=/=x, x(y-1)=/=0, so likewise, the answer to the question becomes 'yes' for x=5/3 and y=2, but 'no' for x=3 and y=2. This is, again, insufficient. Combining the 2 conditions, the answer becomes 'no' for all x=1,2,3....... This is sufficient, so the answer becomes (C). This type of question is no longer asked in the test.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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(1) x is an integer. (2) The product of x and positive integer y is not x.

Required: \((4^x)^{(5-3x)}=1\) Or simply x*(5-3x) = 0 This can be simplified to x = 0 or 3/5 Hence simply we need to tell if x = 0 or 3/5

Statement 1: x is an integer We do not know any specific value of x from this statement INSUFFICIENT

Statement 2: The product of x and positive integer y is not x x*y ≠ x. Hence x ≠ 0 But we do not know anything else about x INSUFFICIENT

Combining Statement 1 and Statement 2: We know that x is an integer, but ≠ 0 Hence x ≠ 0 and x ≠ 3/5 Thus we can say that \((4^x)^{(5-3x)} ≠ 1\) SUFFICIENT

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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