GMAT Quantitative Reasoning Practice Test 1

Question : 9 of 100

Marks: +1, -0

X

is a positive integer and

(405)^4

is a multiple of

3^x

, what is the largest possible value of

X

Solution:

Find the factors of

(405)^4

and see what the largest value of

X

can be.

\;405=81 × 5=9 × 9 × 5=3 × 3 × 3 × 3 × 5(405)^4

\;=(3 × 3 × 3 × 3 × 5)^4=3^{16} × 5^4 .

The largest possible value of

3^x

that is still a factor of

(405)^4

is the largest possible value of

X

and that is

3^{16}

x=16 \;\text ". "\;

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