Mathematics Quiz

The ratio of five numbers are 1:2:3:4:5 and their sum is 30. Find the sum of second and fifth number?

• 15

• 14

• 13

• 12

Answer explanation

The numbers can be represented as 1x, 2x, 3x, 4x, 5x. Their sum is 15x = 30, so x = 2. The second number is 4 and the fifth number is 10. Their sum is 4 + 10 = 14, which is the correct answer.

There are 2401 students in a school. The PT teacher wants all of them to stand in rows and columns. Find the number of rows, if the number of rows is equal to the number of columns.

• 29

• 39

• 49

• 19

Answer explanation

To find the number of rows and columns, we need to calculate the square root of 2401. Since the number of rows equals the number of columns, we find that 49 x 49 = 2401. Thus, the number of rows is 49.

The sum of two numbers is 27 and the difference of their squares is 243. What is the difference between the numbers?

• 42

• 9

• 72

• 3

Answer explanation

Let the numbers be x and y. We have x + y = 27 and x^2 - y^2 = 243. The difference of squares can be factored: (x - y)(x + y) = 243. Substituting x + y = 27 gives (x - y)(27) = 243, so x - y = 9.

What is the sum of the squares of the numbers from 1 to 12?

• 655

• 660

• 650

• 665

Answer explanation

To find the sum of the squares from 1 to 12, calculate 1² + 2² + ... + 12². This equals 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121 + 144 = 650. Thus, the correct answer is 650.

Find the least number which must be added to the number 6412 to get a perfect square.

• 149

• 129

• 181

• 150

Answer explanation

To find the least number to add to 6412 for a perfect square, we check the next perfect square after 6412, which is 6561 (81^2). The difference is 149. Thus, adding 149 to 6412 gives us 6561, confirming that 149 is the correct answer.

Out of four consecutive numbers, the sum of the first two numbers is equal to the fourth number. What is half of the sum of the four numbers?

• 14

• 7

• 9

• 2

Answer explanation

Let the four consecutive numbers be x, x+1, x+2, x+3. The equation x + (x+1) = x+3 simplifies to 2x + 1 = x + 3, leading to x = 2. The numbers are 2, 3, 4, 5. Their sum is 14, and half of that is 7.

24 mango trees, 56 apple trees and 72 orange trees have to be planted in rows such that each row contains the same number of trees of one variety only. Find the minimum number of rows in which the above mentioned trees may be planted.

• 15

• 18

• 17

• 19

Answer explanation

To find the minimum number of rows, we calculate the GCD of 24, 56, and 72, which is 8. Dividing each by 8 gives us 3, 7, and 9 rows respectively. Adding these together results in 19 rows, which is the correct answer.

What is the sum of the cubes of the first four natural numbers?

• 96

• 84

• 100

• 1000

Answer explanation

The sum of the cubes of the first four natural numbers (1^3 + 2^3 + 3^3 + 4^3) is 1 + 8 + 27 + 64 = 100. Therefore, the correct answer is 100.