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Is a^2 = a?
i.e a(a-1)=0
a=0 or a=1

Statement (1) a^2 = 2a
a^2-2a=0
a=0 or a=2
Not sufficient

Statement (2) a ≠ 2
Not sufficient

Combined
a= 0

C is the answer
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Is a^2 = a?
a^2 -a =0
a(a-1)=0
a=0,a=1

(1) a^2 = 2a
a^2-2a=0
a(a-2)=0
a=0 ,a=2
Two different values for a. Putting it in above equation will give different values.
Not sufficient

(2) a ≠ 2
a could take any values hence clearly not sufficient.

Combining the two statement we have one value of a=0
Sufficient

IMO C.

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Is, a^2 = a?

Stat1: \(a^2\) = 2a or, a(a-2) =0, if a =0 then a^2 = a, and if a= 2, a^2 not equal to a. Not sufficient

Stat2: a ≠ 2. Not sufficient.

Combining both, a = 0, then a^2 = a Sufficient.

So, I think C. :)
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given
a^2-a=0
a ( a-1) = 0
a= 1 or =0
#1
a^2 = 2a
a^2-2a=0
a(a-2) = 0
a= 0 or a= 2
insufficient
#2
a≠ 2
insufficient
from 1 &2
a= 0 sufficient
option C


Bunuel
Is a^2 = a?

(1) a^2 = 2a

(2) a ≠ 2


Project DS Butler Data Sufficiency (DS3)


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Bunuel
Is a^2 = a?

(1) a^2 = 2a

(2) a ≠ 2


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here

Is a^2 = a?

(1) a^2 = 2a --> a^2 - 2a = 0 --> a(a - 2) = 0 --> a = 0 or a = 2. If a = 0, then the answer is YES but if a =2 then the answer is NO. Not sufficient.

(2) a ≠ 2. Not sufficient.

(1)+(2) Since from (2) a ≠ 2, then from (1) a = 0 and the answer to the question is YES. Sufficient.

Answer: C.
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