Question 1

80 /? =? / 20

Accepted Answer

Let 80/y = y/20 Then, y 2 = 80 x 20 = 1600 ∴ y = √1600 = 40.

Question 2

Which number should replace both the asterisks in (* /21) x (*/189) = 1?

Accepted Answer

Let (y/21) x (y/189) = 1 Then , y2 = 21 x 189 = 21 x 21 x 9 ∴ y = (21 x 3) = 63 .

Question 3

What least number must be subtracted from 13601 to get a number exactly divisible by 87?

Accepted Answer

On dividing 13601 by 86, we get 29 as remainder ∴ Required number to be subtracted = 29.

Question 4

392/√ ? = 28

Accepted Answer

Let 392/√x = 28 Then √x = 392/28 =14 ⇒ x = 142 = 196

Question 5

The sum of first four prime numbers is?

Accepted Answer

First four prime numbers are 2,3,5,7, Their sum = (2 + 3 + 5 + 7) = 17.

Question 6

The first prime number is?

Accepted Answer

The first prime number is 2.

Question 7

10 / 11 =110 /?

Accepted Answer

Let 10/11 = 110/N, Then, 10N = 11 x 110 ∴ N = (11 x 110) /10 = 121.

Question 8

The largest natural number by which the product of three consecutive even naturals is always divisible, is?

Accepted Answer

Required number is 2 x 4 x 6 = 48.

Question 9

In a division sum, the divisor is 12 times the quotient and 5 times the remainder . If the remainder be 48 then the dividend is?

Accepted Answer

Let quotient = Q and remainder = R Then, Divisor = 12 Q =5 R Now, R = 48 ⇒ 12Q = 5 x 48 ⇒ Q = 20 Dividend = Divisor x Quotient + Remainder ∴ dividend = ( 20 x 240 + 48 ) = 4848

Question 10

If a number is multiplied by three-forth of itself. The value thus obtained is 10800. What is that number?

Accepted Answer

Let the number be N According to the question N x ( N x 3)/4 = 10800 ⇒ 3N2 / 4 = 10800 ⇒ N2 = (10800 x 4) / 3= 14400 N = √14400 = 120

Question 11

The product of two consecutive odd numbers is 19043. Which is the smaller one?

Accepted Answer

Let the two consecutive numbers are N and N+2 According to the question N (N + 2) = 19043 ⇒ N2 + 2N - 19043 = 0 ⇒ N2 + 139N - 137N - 19043= 0 ⇒ N( N + 139) - 137 ( N - 137 ) = 0 ⇒ N( N + 139) ( N - 137) = 0 ⇒ N = 137 and N = - 139 ∴ N = 137

Question 12

If the three- fourth of number is subtracted from the number, the value so obtained is 163. What is that number?

Accepted Answer

Let the number be N According to the question N - 3N/4 = 163 ⇒ N/4 = 163 ∴ N = 652

Question 13

A positive number, when increased by 10 equal 200 times its reciprocal . What is the number?

Accepted Answer

Let the positive number be N. According to the question, N + 10 = 200/N ⇒ N2 + 10N = 200 ⇒ N2 + 10N - 200 = 0 ⇒ ( N - 10) ( N + 20) = 0 &ythere4; N = 10 and N = -20 But N ≠ -20, since N is a positive number. So, the required number is 10.

Question 14

The sum of two numbers is 10. Their product is 20. Find the sum of the reciprocals of the two numbers.

Accepted Answer

Here, M + N = 10 and MN = 20 According to the question, (1/M) + (1/N) = (M + N) / MN = 10/20 = 1/2

Question 15

Five time of a positive integer is equal to 3 less than twice the square of that number. Find the number?

Accepted Answer

Let the number be N. According to the question, ⇒ 5N = 2N2 - 3 ⇒ 2N2 - 5N - 3 = 0 ⇒ (N - 3) ( 2N + 1 ) = 0 N = 3 and N = -1/2 Thus, the required number is 3.

Question 16

A man has given one-fourth part of his property to his daughter, half part to his sons and one-fifth part given as charity. How much part of his property he has given?

Accepted Answer

Total share given by a person = (1/4) + (1/2) + (1/5) = (5 + 10 + 4)/20 = 19/20

Question 17

A chocolate has 12 equal piece. Monju gave 1/4 th of it to Anju, 1/3 rd of it to Sujata and 1/6 th of it to Fiza. The number of piece of chocolate left with Manju is?

Accepted Answer

The number of pieces of chocolate left with Manju = 1- [(1/4) + (1/3) + (1/6) = 1 - (3 + 4 + 2)/12 = 1 - 9/12 = (12 - 9) / 12 = 3/12

Question 18

A students was asked to multiply a number by 3/2 but he divided that number by 3/2. His result was therefore 10 less than the correct answer. Find the number?

Accepted Answer

Let the number be N. According to the question, (N x 3)/2 - N / (3/2) = 10 ⇒ 3N/2 - 2N/3 = 10 ⇒ (9N - 4N) / 6 = 10 ⇒ 5N / 6 = 10 ∴ N = (10 x 6)/5 = 12

Question 19

What value should come in place of the question mark(?) in the following question? √ ? /19 = 4?

Accepted Answer

Let √N/19 = 4 Then √N = 19 x 4 = 76 ∴ N = 76 x 76 = 5776.

Question 20

4050/√ ? = 450?

Accepted Answer

Let 4050/√N = 450 Then √N = 4050/450 = 9 ∴ N = (9 x 9) = 81.

Number System Questions