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# Does a = 0? (1) a^3 = a^4 (2) ab ≠ b

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Math Expert
Joined: 02 Sep 2009
Posts: 49258
Does a = 0? (1) a^3 = a^4 (2) ab ≠ b  [#permalink]

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25 Sep 2017, 00:07
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Difficulty:

25% (medium)

Question Stats:

76% (00:42) correct 24% (00:35) wrong based on 41 sessions

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Does a = 0?

(1) a^3 = a^4
(2) ab ≠ b

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Joined: 30 Jan 2017
Posts: 85
Location: India
Schools: ISB '19
GMAT 1: 630 Q47 V29
GMAT 2: 660 Q47 V34
GMAT 3: 730 Q49 V40
GPA: 3.9
Re: Does a = 0? (1) a^3 = a^4 (2) ab ≠ b  [#permalink]

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25 Sep 2017, 02:04
Bunuel wrote:
Does a = 0?

(1) a^3 = a^4
(2) ab ≠ b

This is a yes/no answer type question. Hence, we need a definite answer whether a=0.

s1) DO NOT cancel out a^3 and arrive at a=1 because you DO NOT know the sign of the variable 'a'
The correct approach is to take all the terms on one side and get a^4 - a^3 = 0 ----> a^3(a-1) = 0
This implies that 'a' can be either 1 or 0.

Not sufficient

s2) Let's take some number for this one

a=0 & b=5 ----> 0 ≠ 5. Hence, 'a' CAN be zero
a=4 & b=2 ----> 8 ≠ 2. Hence, 'a' MIGHT NOT be zero

Not sufficient

s1) & s2)

From s1, you know that 'a' can be 0 or 1. Let's try out some numbers.

a=1 , b=4 ----> ab = b, which IS NOT permitted by s2.

Hence, 'a' cannot be 1 anymore.
Therefore, 'a' IS zero

Ans. C
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Joined: 12 Feb 2017
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Does a = 0? (1) a^3 = a^4 (2) ab ≠ b  [#permalink]

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25 Sep 2017, 02:58
(1) a^3 = a^4
a^4 - a^3 =0
this gives us two scenarios: a= 0 or a=1
clearly statement I is insufficient.

(2) ab ≠ b
ab-b ≠ 0
b(a-1) ≠ 0
that means b≠0 and a-1≠0 ----> a≠1
clearly Statement II is insufficient.

stmt I --- a=0,1
stmt II --- a≠1
from statement I and II,
a=0.
Hence both statements together are sufficient.

Kudos if it helps.
Does a = 0? (1) a^3 = a^4 (2) ab ≠ b &nbs [#permalink] 25 Sep 2017, 02:58
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