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# If a and b are integers, Is b = 0? (1) a = ab – 1 (2) a is NOT equa

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If a and b are integers, Is b = 0? (1) a = ab – 1 (2) a is NOT equa  [#permalink]

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03 Oct 2017, 00:35
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Difficulty:

55% (hard)

Question Stats:

47% (01:53) correct 53% (01:31) wrong based on 23 sessions

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If a and b are integers, Is b = 0?

(1) a = ab – 1
(2) a is NOT equal to 1

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Re: If a and b are integers, Is b = 0? (1) a = ab – 1 (2) a is NOT equa  [#permalink]

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03 Oct 2017, 00:41
1
If a and b are integers, Is b = 0?

(1) a = ab – 1

ab - a = 1
a(b - 1) = 1
Since a and b are integers, then we can have two cases:
a = 1 and b - 1 = 1, which gives b = 2. Answer NO;
a = -1 and b - 1 = -1, which gives b = 0. Answer YES.

Not sufficient.

(2) a is NOT equal to 1. Not sufficient.

(1)+(2) Since from (2) a ≠ 1, then from (1) a = -1 and b = 0. Sufficient.

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Re: If a and b are integers, Is b = 0? (1) a = ab – 1 (2) a is NOT equa  [#permalink]

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03 Oct 2017, 00:52
If a and b are integers, Is b = 0?

(1) a = ab – 1
=> ab-a =1
=>a(b-1)=1
As a and b are integers
a(b-1) = 1* 1 or -1*-1
=> a=1 and b= 2 or a=-1 and b=0
as we have 2 values of b
Insufficient

(2) a is NOT equal to 1
Here given a is not equal to 1, this does not give any information about b
Insufficient

1+2
a = ab – 1 and a not equal to 1
=> by a=1 and b= 2 or a=-1 and b=0 and by statement 2 that a is not equal to 1,
we get => a=-1 and b=0
Sufficient

Re: If a and b are integers, Is b = 0? (1) a = ab – 1 (2) a is NOT equa &nbs [#permalink] 03 Oct 2017, 00:52
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# If a and b are integers, Is b = 0? (1) a = ab – 1 (2) a is NOT equa

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