GATE2017-1-GA-4

Question

Find the smallest number $y$ such that $y \times 162$ is a perfect cube.

• A. $24$
• B. $27$
• C. $32$
• D. $36$

Answer 1

$y \times 162 = y \times 3^4 \times 2$

So, for perfect cube we need to add two $3s$ and two $2s.$

Answer is: $3^2 \times 2^2= 36.$

Correct Answer: $D$

Answer 2

162 = 2 * 3³ * 3

hence we can see the value which have two 2's and 2 3's wil be minimum value = 4 * 9 = 36 so option 4

Answer 3

Ans. 36

Factorization of 162 = 2*9*9

So, multiply by 2*2*9 to make perfect cube

Answer 4

very easy just putting the options as the value of Y we get 36

so D is the correct answer i guess

Comments

putting option is time consuming , just factorize everything is clear.