Quantitative Reasoning

Number System

Easy

Which of the following numbers is both a perfect square and a perfect cube?

128

200

✅ Correct Option: 1

A number that is both a perfect square and a perfect cube must be a perfect sixth power.

$64 = 2^6$ , so $64 = 8^2 = 4^3$ .

The others fail: $72 = 2^3 \times 3^2$ , $128 = 2^7$ which is a cube-free exponent for squares, and $200 = 2^3 \times 5^2$ .

2022: 6 Oct Shift 1

The value of $\frac{(2 \cdot 7)^3 - (2 \cdot 2)^3}{(2 \cdot 7)^2 + 2 \cdot 7 \times 2 \cdot 2 + (2 \cdot 2)^2}$ is

2026: 14 May Shift 2

The difference between the two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the reminder is 15. Find the smallest number?

2026: 29 May Shift 2

Find the sum of the first n positive integers.

2026: 12 May Shift 2

The sum of the natural numbers which are divisors of 100, is:

2022: 6 Aug Shift 1

Ratio $5^{8.14} : 5^{5.14}$ is equal to:

2026: 22 May Shift 2

Match List-I with List-II

List-I (Statements/Expressions etc.)	List-II (Values, etc.)
(A) Find the sum of the first 20 odd natural numbers.	(I) 285
(B) How many prime numbers are there between 100 and 200?	(II) 0
(C) Find the sum of the squares of the digits from 1 to 9.	(III) 400
(D) Find the unit's digit in the product $81 \times 82 \times 83 \times ... ... ... \times 89$ ?	(IV) 21

Choose the correct answer from the options given below:

Which of the following numbers is both a perfect square and a perfect cube?

Solution

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