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When x and y are integers, a3b4=c, a=?

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Math Revolution GMAT Instructor
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When x and y are integers, a3b4=c, a=?  [#permalink]

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New post 05 Jun 2016, 19:32
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:31) correct 36% (01:17) wrong based on 51 sessions

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When x and y are integers, a^3*b^4=c, a=?
1) c=5,000
2) b=5

*An answer will be posted in 2 days.

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Re: When x and y are integers, a3b4=c, a=?  [#permalink]

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New post 05 Jun 2016, 22:03
MathRevolution wrote:
When x and y are integers, a^3*b^4=c, a=?
1) c=5,000
2) b=5

*An answer will be posted in 2 days.


I am assuming that all a, b and c are integers. (not x, y, as given)

Then Statement 1 can be written as

5000 = 5 * \(10^3\) = 5*\(2^3\) * \(5^3\)

\(2^3\) * \(5^4\)

If we take 1 as an integer, we wont get correct one to one correspondence. So a has to be 2.

Sufficient.

Statement 2 is clearly insufficient.

A is the answer.
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When x and y are integers, a3b4=c, a=?  [#permalink]

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New post 07 Jun 2016, 18:47
There are three (a,b,c) variables and one equation (a^3b^4=c) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. There is, thus, high chance that C is the correct answer. Using the condition 1) and the condition 2), we get a=2. The answer is unique and the condition is sufficient. However, since this is one of key questions, integer question, we have to apply the common mistake type 4(A). From the condition 1), we get a^3b^4=5,000=2^35^4. The answer is a=2. The answer is unique and the condition is sufficient. Hence, the correct answer is A.

- 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.
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Re: When x and y are integers, a3b4=c, a=?  [#permalink]

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New post 19 Jul 2017, 10:16
Ans is A....

Kindly correct the question When x and y are integers should be When a and b are integers
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Re: When x and y are integers, a3b4=c, a=?   [#permalink] 19 Jul 2017, 10:16
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