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(a × b) ^(c × d) = n

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by sanju09 » Sat Feb 11, 2012 2:19 am
If a, b, c, and d are positive integers, and (a × b) ^(c × d) = n; then what is the unit's digit of n?
I. a^2 + b^2 = 41.
II. a × b = 20.




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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Feb 11, 2012 7:44 am
sanju09 wrote:If a, b, c, and d are positive integers, and (a × b) ^(c × d) = n; then what is the unit's digit of n?
I. a^2 + b^2 = 41.
II. a × b = 20.
I'm not sure why the "X's" are added here. They could be mistaken for variables.
How about . . .

If a, b, c, and d are positive integers, and (ab)^(cd) = n, then what is the unit's digit of n?
1)a^2 + b^2 = 41
2)ab = 20


Target question: What is the unit's digit of (ab)^(cd)?

Statement 1: a^2 + b^2 = 41
If a and b are positive integers, then it won't take long to check out the possible cases.
We need only consider the following squares: 1, 4, 9, 16, 25, 36
Given these squares, only 1 pair gives us a sum of 41 (16 and 25)
So, either a=4 and b=5 or a=5 and b=4
Either way, we now know that ab=20
If ab=20, then (ab)^(cd) = (20)^(cd)
If c and d are positive integers, then the units digit of (20)^(cd) must be 0
As such, statement 1 is SUFFICIENT

Statement 2:ab = 20
If ab=20, then (ab)^(cd) = (20)^(cd)
If c and d are positive integers, then the units digit of (20)^(cd) must be 0
As such, statement 2 is SUFFICIENT

The answer is D

Cheers,
Brent
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by ArunangsuSahu » Fri Feb 17, 2012 1:41 pm
(D)
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by [email protected] » Sat Feb 18, 2012 11:26 pm
Yes (D) is the correct answer.
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