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# If a, b and c are integers, what is the value of a?

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Senior Manager
Joined: 21 Oct 2013
Posts: 416
If a, b and c are integers, what is the value of a?  [#permalink]

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02 Aug 2014, 06:15
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Difficulty:

55% (hard)

Question Stats:

59% (01:35) correct 41% (01:32) wrong based on 137 sessions

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If a, b and c are integers, what is the value of a?

(1) 2^a+2^b=33
(2) a·c=5
Math Expert
Joined: 02 Sep 2009
Posts: 54376
If a, b and c are integers, what is the value of a?  [#permalink]

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02 Aug 2014, 09:30
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If a, b and c are integers, what is the value of a?

(1) 2^a+2^b=33. Here notice that neither a nor be can be a negative integer. For example, if a is negative, then 2^a will be a fraction from 0 to 1 and the sum of a fraction and an integer or the sum of two such fractions cannot equal to 33. Thus both of them must be nonnegative integers. So, we have that 33 is equal to the sum of powers of 2. By trial and error we can get that 33 can be broken in the sum of powers of 2 only in one way: 33 = 1 + 32 = 2^0 + 2^5. This implies that a = 0 and b = 5 or vise-versa. Not sufficient.

(2) a·c=5. 5 can be broken into the product of two integers in the following ways: 5 = 1*5 = (-1)*(-5). Thus a could be 1, -1, 5, or -5. Not sufficient.

(1)+(2) Intersection of values of a is only a = 5. Sufficient.

Hope it's clear.
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Re: If a, b and c are integers, what is the value of a?  [#permalink]

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03 Aug 2017, 07:59
goodyear2013 wrote:
If a, b and c are integers, what is the value of a?

(1) 2^a+2^b=33
(2) a·c=5

Given : a,b,c are integers
DS : Value of a

Statement 1: a and b can't be -ve as the value will become fraction and will not be equal to 33
So, there are 2 possible values of (a,b) : (0,5) or (5,0)
NOT SUFFICIENT

Statement 2 : There are 2 possible values of (a,b) : (1,5) or (5,1)
NOT SUFFICIENT

Combined : (a,b,c) = (5,0,1)..
SUFFICIENT

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Re: If a, b and c are integers, what is the value of a?   [#permalink] 03 Aug 2017, 07:59
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