Is a an integer?

Question

Is a an integer?

(1) a^3 is an integer.
(2) The cube root of a is an integer.

JusTLucK04 · Answer

From Statement 1, a could definitely be an integer since any integer cubed will remain an integer. However, a could also be a cube root. If we cube the cube root of 2, the result is 2. Insufficient. Statement 2, however, guarantees that a must be an integer. a = cubert(a) * cubert(a) * cubert(a). If cubert(a) is an integer, then a must be an integer as well. Thus, the correct answer is B

thalcantero · Answer

I still don't get why the first statement is insufficient, could someone explain a little further please?

Bunuel · Answer

Is a an integer?

(1) a^3 is an integer -->  a  will be an integer if a^3 is a perfect cube, for example, if a^3 is 0, 1, 8, 27, ... but  a  can also be the cube root from an integer (which is not a perfect cube), for example if  a  is  \sqrt {2} ,  \sqrt {3} ,  \sqrt {4} , ... Not sufficient.

(2) The cube root of a is an integer.  \sqrt {a}=integer  -->  a=integer^3=integer . Sufficient.

Answer: B.

Hope it's clear.

thalcantero · Answer

Thanks a lot for the explanation, it is pretty clear now.

narendran1990 · Answer

Bunuel  : I am not able to understand this part of your explanation ''but a can also be the cube root from an integer (which is not a perfect cube), for example if a is 2√3, 3√3''.

Bunuel · Answer

Not sure what to explain... If  a  is  \sqrt {2} ,  \sqrt {3} , or  \sqrt {4} , then a^3 will be 2, 3, or 4 respectively.

narendran1990 · Answer

I am not good with some basics of exponents, so I couldn't understand your explanation. It is clear now.

Thank you.

JanGMAC · Answer

Only this made me understand the problem Thanks!

arvind910619 · Answer

The answer is B

From Statement 1 it is clear that cube of an integer is always an integer but when we take cube of root(2) then also the result will be integer hence insufficient 
Statement 2 on the other hand clearly tells us that the cube root of the number is always an integer .Therefore the number a must be an integer hence sufficient .

chesstitans · Answer

hello, it seems that practice is the only way to ensure that we will not make any mistakes in thinking, is that so?
it is because I have not worked on any math problems for a long time. When I try to find the answer, I always worry that I will miss something.

KanishkM · Answer

From 1 
We dont know the orientation of a, what if it was

a = 3^1/3, we satisfy 1, but answer to the question will be a No
a = 3, we satisfy 1, and answer the question a Yes

From 2 
The cube root of a is an integer.

This will always be true, a^1/3 = 3^ (3*1/3) = Yes

B

ScottTargetTestPrep · Answer

Solution:

Statement One Only:

a^3 is an integer.

If a^3 is an integer, a may or may not be an integer. For example, if a^3 = 8, then a = 2 is an integer. However, if a^3 = 9, then a = 3^√9 is not an integer. Statement one alone is not sufficient.

Statement Two Only:

The cube root of a is an integer.

If the cube root of a is an integer, then a itself must be an integer. Since a is the cube of the cube root of a, a is the cube of an integer, and the cube of any integer is an integer. Statement two alone is sufficient.

Answer: B

Basshead · Answer

(1) If a^3 is an integer, a could or could not be an integer.

If  a^3 = 2 ; a = not an integer.
If  a^3 = 8 ; a = integer

INSUFFICIENT.

(2) If the cube root of a is an integer, we can conclude a = integer. SUFFICIENT.

For example,  \sqrt {8} = 2 ; therefore 8 must be an integer.

Answer is B.

kittle · Answer

This is a high-quality question.

Ashish632 · Answer

narendran1990

I am not sure if you still have this doubt, but to whomsoever having doubts with the statement 1

Is a an integer?

(1) a^3 is an integer.
(2) The cube root of a is an integer.

So the question is, is a an integer and the first statement is 1) a^3 is an integer

lets dive in

so hmm, a^3 is an integer, okey let me put that in an equation then 
so say a^3=11 , this does satisfy the criterion does it not, but is a an integer,certainly no 
and say a^3=8, satisfies the condition, and here a=2 and a is an integer

So no and yes .

Does this help ??

Hoozan · Answer

Similar Question: https://gmatclub.com/forum/is-a-3-3-an- ... 85747.html

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Is a an integer?

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