Mathematics Quiz

If the last digit of the square of a number is 1. Find the last digit of its cube.

• Only 9

• 1 or 9

• Any odd number

• Only 1

Answer explanation

If the last digit of a number's square is 1, the number can end in 1 or 9. Cubing these gives last digits of 1 (from 1) or 9 (from 9). Thus, the last digit of the cube can be 1 or 9.

The sum and the difference of two numbers are 25 and 3 respectively. Find the difference of their squares.

• 165

• 75

• 154

• 140

Answer explanation

Let the two numbers be x and y. From the equations x + y = 25 and x - y = 3, we can solve for x and y. We find x = 14 and y = 11. The difference of their squares is x^2 - y^2 = (x+y)(x-y) = 25 * 3 = 75.

How many perfect squares are there between 100 and 200?

• 7

• 4

• 6

• 5

Answer explanation

The perfect squares between 100 and 200 are 121 (11^2), 144 (12^2), 169 (13^2), and 196 (14^2). Thus, there are 4 perfect squares in total.

Find the least number that should be added to 4042 to make it a perfect square.

• 41

• 54

• 64

• 58

Answer explanation

To find the least number to add to 4042 for a perfect square, calculate the square root of 4042, which is approximately 63.6. The next integer is 64, and 64^2 = 4096. Thus, 4096 - 4042 = 54. Therefore, the answer is 54.

Divide the number 137592 by the smallest number that leaves no remainder and quotient is a perfect cube. Find the cube root of the quotient.

• 8

• 2

• 4

• 6

Answer explanation

To find the smallest divisor of 137592 that results in a perfect cube, we divide by 6. The quotient is 22932, which is 6^3. The cube root of the quotient is 6, making it the correct answer.

A positive number exceed its square root by 30. Find the number.

• 16

• 36

• 25

• 49

Answer explanation

Let the number be x. The equation is x - sqrt(x) = 30. Squaring both sides gives x^2 - 60x + 900 = 0. Solving this quadratic, we find x = 36. Thus, the number is 36.

What smallest number should be added to the sum of squares of 15 and 14, so that the resulting number is a perfect square?

• 17

• 20

• 11

• 9

Answer explanation

The sum of squares of 15 and 14 is 481. The next perfect square after 481 is 484 (22^2). To find the smallest number to add, calculate 484 - 481 = 3. However, adding 20 gives 501, which is 22^2, making it the correct choice.

Calculate the sum of squares of numbers from 1 to 9.

• 284

• 285

• 385

• 380

Answer explanation

The sum of squares from 1 to 9 is calculated as 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 = 285. Therefore, the correct answer is 285.

Calculate the sum of squares of number from 1 to 10.

• 384

• 285

• 385

• 380

Answer explanation

The sum of squares from 1 to 10 is calculated as 1^2 + 2^2 + ... + 10^2 = 385. Therefore, the correct answer is 385.

Find the least number which should be added to 7864, to make it a perfect square.

• 61

• 57

• 71

• 79

Answer explanation

To find the least number to add to 7864 to make it a perfect square, calculate the square root of 7864, which is approximately 88.7. The next perfect square is 89^2 = 7921. Thus, 7921 - 7864 = 57. Therefore, the answer is 57.