Mathematics Quiz

If each packet contains the same number of pencils and there are 96 pencils in all in 12 packets, how many packets will one have to purchase if one requires 304 pencils?

• 39

• 38

• 33

• 36

Answer explanation

Each packet contains 8 pencils (96 pencils / 12 packets). To get 304 pencils, divide 304 by 8, which equals 38 packets. Therefore, one needs to purchase 38 packets.

From 3/4 of a number P, Ramakrishna subtracts 2/3 of another number Q and obtain 5/8 as the difference. What is the answer Ramakrishna should obtain if he subtracts eight times of Q from nine times of P?

• 15 2

• 25 4

• 20 3

• 25 3

Answer explanation

Let P = 15 and Q = 2. From the equation, (3/4)P - (2/3)Q = 5/8, substituting gives (3/4)*15 - (2/3)*2 = 5/8. Now, 9P - 8Q = 9*15 - 8*2 = 135 - 16 = 119. Thus, the answer is 15 2.

In a class of 80 students 1/10 of the class likes chocolate D and 1/20 of the class likes chocolate E. What is the difference between the number of students who like chocolate D and the number of students who like chocolate E?

• 2

• 9

• 5

• 4

Answer explanation

In a class of 80 students, 1/10 like chocolate D, which is 8 students, and 1/20 like chocolate E, which is 4 students. The difference is 8 - 4 = 4. Thus, the correct answer is 4.

Sunita won 3/5 of the marbles that were there in the beginning of the game. Ravi won 2/3 of the remaining marbles while Sunny won the remaining 60 marbles. How many marbles did Sunita Win?

• 255

• 240

• 285

• 270

Answer explanation

Let the total marbles be x. Sunita won 3/5 of x, Ravi won 2/3 of the remaining (2/5 x), and Sunny got 60. Setting up the equation: 3/5 x + 2/3(2/5 x) + 60 = x. Solving gives x = 450, so Sunita won 270 marbles.

The difference between two numbers is 18. If the difference between their squares is 360, find the larger number.

• 18

• 15

• 19

• 16

Answer explanation

Let the two numbers be x and y, with x > y. We have x - y = 18 and x^2 - y^2 = 360. Using the identity x^2 - y^2 = (x - y)(x + y), we get 18(x + y) = 360, leading to x + y = 20. Solving these gives x = 19.

A 91 cm long wire is cut into two pieces so that the length of one piece is three-fourth of the other. Find the length of the shorter piece.

• 36.23 m

• 39 cm

• 42.17 cm

• 38 cm

Answer explanation

Let the lengths of the pieces be x and (3/4)x. Then, x + (3/4)x = 91 cm. Solving gives x = 52 cm and (3/4)x = 39 cm. Thus, the shorter piece is 39 cm.

A 3 digit number is such that the ratio of its units digit, tens digit and hundreds digit is 1 : 2 : 3. The sum of this number and the reversed number obtained by reversing the order of its digits is 1332. Find the number.

• 246

• 414

• 123

• 369

Answer explanation

Let the digits be 3x, 2x, and x. The number is 321x. The reversed number is x23. The equation 321x + x23 = 1332 leads to x = 3, giving the number 369, which satisfies the ratio and sum condition.

A man plants 21,025 mango trees in his garden in such a way that there are as many rows as there are mango trees in each row. Find the number of rows.

• 135

• 125

• 145

• 130

Answer explanation

To find the number of rows, we need to determine the square root of 21,025. The square root is 145, meaning there are 145 rows with 145 trees in each row. Thus, the correct answer is 145.

The sum of two numbers is 27. Five times one number is equal to 4 times the other. The smaller of the two numbers is:

• 12

• 11

• 13

• 15

Answer explanation

Let the numbers be x and y. From the equations x + y = 27 and 5x = 4y, we can solve for x and y. Substituting y = 27 - x into the second equation gives 5x = 4(27 - x). Solving this yields x = 12, the smaller number.

There are two consecutive natural numbers such that the sum of their squares is 313. Find smaller of these two numbers.

• 12

• 14

• 15

• 13

Answer explanation

Let the two consecutive numbers be n and n+1. The equation is n^2 + (n+1)^2 = 313. Simplifying gives 2n^2 + 2n - 312 = 0, or n^2 + n - 156 = 0. Solving this, we find n = 12. Thus, the smaller number is 12.