Question : What is the least number that can be multiplied by 69120 to make it a perfect cube?
Option 1: 10
Option 2: 50
Option 3: 25
Option 4: 5
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Correct Answer: 25
Solution : Prime factorization of $69120 = 2^9 × 3^3 × 5$ For the number to be a perfect cube, all the exponents must be multiples of 3, thus the above number must be multiplied by $5^2=25$ Hence, the correct answer is 25.
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Question : The least number that should be subtracted from the number 32146 to make it a perfect square is:
Option 1: 305
Option 2: 105
Option 3: 205
Option 4: 405
Option 3: 605
Option 4: 205
Question : Two numbers are 35% and 50% less than a third number. By what percentage must the second number be increased to make it equal to the first number?
Option 1: 23.08%
Option 2: 15%
Option 3: 25%
Option 4: 30%
Question : The quotient when $10^{100}$ is divided by $5^{75}$ is:
Option 1: $2^{25}×10^{75}$
Option 2: $10^{25}$
Option 3: $2^{75}$
Option 4: $2^{75}×10^{25}$
Question : Find the least value for * in the number 3*7440 such that it is divisible by 12.
Option 1: 0
Option 2: 2
Option 3: 1
Option 4: 4
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