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25 Sep 2017, 00:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
62% (01:01) correct
38%
(01:04)
wrong
based on 68
sessions
History
Date
Time
Result
Not Attempted Yet
Does a = 0?
(1) a^3 = a^4
(2) ab ≠ b
(1) a^3 = a^4
(2) ab ≠ b
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
25 Sep 2017, 02:04
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Bunuel
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
25 Sep 2017, 02:58
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(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.
Hence answer is option C.
Kudos if it helps.
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.
Hence answer is option C.
Kudos if it helps.
