If n = 66 and n^4 = m x 6 x 22 x 33 x 198, what is the value of m?

Question

A) 11
B) 22
C) 33
D) 44
E) 66

SChatrg · Answer

(11 * 6 )^4 = m * 6 * 22 * 33 * 11 * 18

we need 4 11's and 6's on the RHS

we have 3 11's hence m is a multiple of 11

we have 3 6's and an extra 3, so we need to multiply 2 to get another 6

Hence,  m = 11 * 2 = 22

Abhishek009 · Answer

\frac{n^3 = m * 6 * 22 * 33 * 198}{66}

Or,  n^3 = m * 22 * 3 * 198

Or,  n^3 = m * 22 * 3 * (22*3^2)

Or,  n^3 = m * 22^2 * 3^3

Or,  m = 22  , to make n a perfect Cube, Answer must be (B)

Hunter2021 · Answer

Another way to solve this question would be to rearrange and shorten.

66x66x66x66 / 6x22x33x11x18 = m

Shorten and you will get 2x11=m

Lowpoint · Answer

We can use units digits to solve the problem.

66^4 will have units digits of 6.

RHS has a units digit of 8.

So 8 needs to be multiplied by a number that results in the unit digit of 6.

Only answer choice B fits.

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