*n*are there such that

*n*is less than 1,000 and at the same time

*n*is a perfect square and a perfect cube?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers *n* are there such that *n *is less than 1,000 and at the same time *n* is a perfect square and a perfect cube?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

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- Ariel Goldberg
- My name is Ariel Goldberg and I have been a GMAT tutor for eight years. I have taken the GMAT more than twenty times and scored into the 99th percentile; I like to share my GMAT knowledge with everybody. One of the things I like is to write GMAT quant questions that do reflect the changes in the test. The questions sold by some prep services are outdated in that they reflect the GMAT of three or four years ago, before Pearson took over. So that is where I come in, I provide people with good, real-looking GMAT questions.

Find all n such that 0 < n^6 < 1000

ReplyDelete10^3 = (greater than 3)^3

1,2, 3 are the possible ones.

(B)

I think the answer should be A because between 1 and 1000 we only have two integers which are perfect square and perfect cube at the same time.

ReplyDeleteThose integers are: 1 - sqrt(1) =cubert(1) =1 integer

second integer is 64 - sqrt(64) =8 cubert(64) = 4 they both are integers.

Hence A.

If you look closely you can generalize the numbers as

ReplyDelete1 and

(2k)^2 x (2k)^2 x (2k)^2= 64K^6 and

(3k)^2 x (3k)^2 x (3k)^2 = 729k^6

answer is 3. Or as Blaoism suggested:

0 < n^6 < 10^3 or

n^2 < 10 (valid for 1,2,3)

Hence answer is 3.

Why have you not considered 0? I think including 0, the answer should be C) or 4.

ReplyDeletethe question asks positive integers zero is nether positive nor negative

ReplyDeletethe number are 1, 64 and 729.