GMAT Club Around The World!!! Does a^2 = ab? (1) Cubic root of b^3 = a

Question

Does  a^2 = ab ?

(1)  \sqrt {b^3} = a

(2)  b = |a|

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rocky620 · Answer

Lets simplify the ques:

Is  a^2  = a*b, which simplifies to,
Is a=b

(1) Third root of  b^3  = a

Since, a is an odd root of a cube, it will be equal to the number.
So, a=b.

Sufficient

(2) b=|a|

If a=1, b=1, so its yes.
If a=-1, b=1, so its a no.

Insufficient

IMO Option A

MHIKER · Answer

(1)  a^2=a.a=a^2 : Sufficient.

(2)  a^2=a*-a=-a^2 \ or \ a^2=a*a=a^2 ;Insufficient.

The answer is  A

Deepakjhamb · Answer

stem says a^2 - ab = 0 means either a= 0 or a =b then we have yes otherwise no

statement 1 |b|= a so we can have a= -b if b < 0 or a =b if b>0 or a=b=0 also we have yes and no both

statement 2 : b = |a| so we have b = -a if a < 0 or b= a if a > 0 or b=a=0 if a =0 we have yes and no both

combining statement 1 and 2 we get a and b both have to be positive so a =b or either a=b=0 so in either case we have yes so both combined are sufficient

so answer is c)

TestPrepUnlimited · Answer

Happy New Year Brunei, People's Republic of China, Hong Kong, Indonesia, Macau, Malaysia, Mongolia, Philippines, Singapore and Taiwan !

We want to write the question as does  a^2 - ab = a(a - b) = 0 ? So we want to know if a = 0 or if a = b.

Statement 1:

\sqrt {b^3} = b  no matter what b is since 3 is odd, so we have  b = a . Sufficient.

Statement 2: 
If we have b = -a we do not necessarily have  a*(a - b)= 0 . If we have b = a then  a*(a - b)= 0  is true. Insufficient.

Ans: A

ananya3 · Answer

IMO A

Que:  a^2 =ab ?
=> a (a - b) =
=> a=0? or a=b?

(1)  3√b^3=a 
 b^\frac{3}{3}  = a
=> b = a 
 SUFFICIENT

(2) b=|a|
=> b = a or b = -a
 NOT SUFFIECIENT

BIDJI23 · Answer

Question is : a(a-b)=0--> a=o and/or (a-b)=0 or a=b

1->Sufficient
2->Not sufficent. b=-a ou b=a

Push A

Aks111 · Answer

Does  a^2=ab?  In short, the question asks if a = b, i.e. a and b are equal and have same sign.

1)  \sqrt {b^3}= a 
Cube and cube root of a number do not change the sign of the result. So, cube root of  b^3  will be 'b'. 
As b = a Statement 1 is sufficient.

(2) b=|a|
Here, b could be equal to a or -a. 
Statement 2 alone is not sufficient.

Answer: A

TarunKumar1234 · Answer

Given, a^2=ab, a*(a-b)= ? Stat1: b^3=a^3, which means a=b, so we have, a*(a-b)= 0, sufficient. Stat2: b=|a|, b= +-a, not sufficient. So, I think A.

bidskamikaze · Answer

Does  a^2 =ab?

(1)  \sqrt {b^3}  = a

This implies that a and b have same absolute value AND same sign.
In this case,  a^2 = ab.
Sufficient.

(2) b=|a| 
b is positive. However, a could be negative.
So a^2 may be different from ab, even though the absolute value of the two terms may be equal.
Insufficient.

Answer A.

ShankSouljaBoi · Answer

cube root - can be cubed without introducing extraneous roots
rephrasing - Is a(a-b) = 0 ?

1. b = a suff
2. b = a or b = -a ... not suff. 
A

Green2k1 · Answer

Correct Answer A

Does a^2=ab?
 
a^2-ab =0
a(a-b)=0, a=0 or a=b

(1) (b^3)^(1/3)=a
 a=b 
- Sufficient

(2) b=|a|
 b>=0
b = a or b= -a
- Not sufficient

manasi05 · Answer

a^2 = ab?
As a^2 can be either positive or 0 so we have to find if a = b and if they are of the same sign or if a=0

Statement 1
Cube root of b^3 = a
Since the sign doesn’t change for odd exponent power so the value of cube root of b^3 will b
a = b
a and b are equal and of the same sign hence Sufficient

Statement 2
b = |a|
b = +a, -a
when b = +a then a^2 = ab = a*a = a^2 —— yes
when b = -a then a^2 = ab = a*-a = -a^2 —— No
Hence Insufficient

The answer will be A

MakSha · Answer

Firstly, lets simplify the expression a^2 = ab. for the expression to be true, 
a(a-b)=0, which implies a=0 or a=b.

From the first statement, b=a (since power is odd, b takes the same sign as b^3).  Sufficient .

From the second statement, b can be equal to a or -a. Thus,  insufficient to conclude .

Thus,  IMO option A is the answer .

MaryKaaviya · Answer

Answer is A

1) sufficient as cube root of the cubed value will also contain the sign.
2) insuff - No information on the sign of a

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GMAT Club Around The World!!! Does a^2 = ab? (1) Cubic root of b^3 = a

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