If positive integer m is a multiple of 8 and of 9, is the

Question

If positive integer m is a multiple of 8 and of 9, is the positive square root of m between two consecutive integers?

(1) m is not a multiple of 48.
(2) m is not a multiple of 27.

maratikus · Answer

A is the answer.

m = k*(2^3)*(3^2)

1) 48 = (2^4)*3

since m is not a multiple of 48, then k is an odd number -> sqrt(m) is not an integer -> it's between two integers -> sufficient
2) 27 = 3^3 -> k is not a multiple of 3 -> insufficient

k = 2 -> sqrt(m) = 4*3 = 12 -> not between integers
k = 5 -> sqrt(m) = 6*sqrt(5*2) = 6*sqrt(10) -> between integers

terp26 · Answer

When a question says between, is that inclusive?

maratikus · Answer

inclusive wouldn't make much sense because otherwise any number would work

terp26 · Answer

I mean for example the question states

is the positive square root of m between two consecutive integers?

so if the positive squareroot was 12

What does that mean? Is 12 between 2 consecutive integers?

GMATBLACKBELT · Answer

I believe this is A. Not sure if I understand the question correctly, but I take it as is the sqare root of m not an integer? Hence btwn two integers.

1: the only way for M to be an integer is if m has even exponents ex/ 2^4*3^2

currently the lowest number m can be is 72. 48 is 2^4*3. M can never have an even exponent on the 2, thus 1 is suff.

2: this is no help. we could have 2^4*3^2 or 2^3*3^2

vshaunak@gmail.com · Answer

m is a multiple of 8 and 9.
this means m = 2*2*2*3*3 or it's multiples
Stmt 1: m is not a multiple of 48. It means that there will never be  four  2s among the factors of m. But for m to be a perfect square, there should be even number of 2s and 3s. This means m can never be a perfect square. So the sqaure root of m will always lie between two consecutive integers. Hence suff.

Stmt 2: m is not a multiple of 27. There i no restriction on 2s. We can have even/odd number of 2s. This leads m to be a perfect square in some cases and not a square in other cases. Hence Insuff

answer is 'A'

If positive integer m is a multiple of 8 and of 9, is the

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