Question 1

The face value of 8 in the numeral 458926 is?

Accepted Answer

The face value of 8 in 458926 is 8

Question 2

The local value of 7 in the numeral 5679032 is?

Accepted Answer

The local value of 7 in 5679032 is 70000.

Question 3

What value should come in place of the question mark(?) in the following question? ? x 48 = 173 x 240

Accepted Answer

Let y x 48 = 173 x 240 Then y = (173 x 240) / 48 =173 x 5 = 865 .

Question 4

160 x 106 + 94 x 94 =?

Accepted Answer

106 x 106 + 94 x 94 =(106)2 + (94)2 =1/2 [2(a2 + b2)] =1/2 [(a+b)2 + (a-b)2] =1/2 [(106 + 94)2 + (106 -94 )2] =1/2 [ (200)2 + (12)2] = 1/2 x [ 40000 + 144 ] = 40144/2 = 20072 .

Question 5

5358 x 51 =?

Accepted Answer

5358 x 51 = 5358 x (50 +1 ) 5358 x 50 + 5358 x 1 =267900 + 5358 = 273258

Question 6

1307 x 1307 =?

Accepted Answer

1307 x 1307 = (1307)2 = (1300 + 7 )2 = (1300)2 + (7)2 + 2 x 1300 x 7 = 1690000 + 49 +18200 = 1708249

Question 7

1299 x 1299 =?

Accepted Answer

1299 x 1299 = (1299)2 = (1300 - 1)2 = (1300)2 + (1)2 - 2 x 1300 x 1 = 1690000 + 1 - 2600 = 1687401

Question 8

1014 x 986 =?

Accepted Answer

1014 x 986 = (1000 + 14 ) x (1000 -14) = (1000)2 - (14)2 = (1000000 - 196) = 999804 .

Question 9

387 x 387 + 114 x 114 + 2 x 387 x 114 =?

Accepted Answer

Given expression = a2+b2+2ab = (a+b)2 where a = 387 and b = 114 = (387 + 114 )2 = (501)2 =(500 +1 )2 =(500)2 + (1)2+ 2 x 500 x 1 = 250000 + 1 +1000 = 251001.

Question 10

11 Times a number gives 132. The number is?

Accepted Answer

Let the number be x. Then, 11x =132 ⇒ x = 12

Question 11

A number is as much greater than 31 is less than 55. The number is?

Accepted Answer

Let the number be x. Then, x - 31 = 55 - x ⇒ 2x = 55 + 31= 86 ⇒ 2x = 86 ∴ x = 43

Question 12

1/4 of a number subtracted from 1/3 of the same number gives 12. The number is?

Accepted Answer

Let the required number is N. Then, N/3 - N/4 = 12. ⇒ 4N - 3N = 144 ∴ N = 144

Question 13

3/4 of a number is 19 less than the original number. The number is?

Accepted Answer

Let the original number be N. So from question N - 3N/4 = 19 ⇒ 4N - 3N = 76 ∴ N = 76

Question 14

If one-fifth of a number decreased by 5 is 5, then the number is?

Accepted Answer

Let the number be N. Then, N/5 - 5 = 5 ⇒ N - 25 = 25 ∴ N = 50

Question 15

A number is 25 more than its two-fifth. The number is?

Accepted Answer

Let the number be N. So from question 2N/5 + 25 = N ⇒ 2N + 125 = 5N ⇒ 3N = 125 ∴ N = 125/3

Question 16

Three fourth of one-fifth of a number is 60. The number is?

Accepted Answer

Let the required number be N. So 3/4 x 1/5 x N = 60 ⇒ 3N / 20 = 60 ∴ N = 400

Question 17

The difference between the squares of two consecutive number is 35. The number are?

Accepted Answer

Let the two number be x and (x + 1) Then, (x+1)2 - x2 = 35 ⇒ 2x = 34 ⇒ x = 17 So, the number are 17 and 18

Question 18

The ratio between two numbers is 3:4 and their sum is 420. The greater of two number is?

Accepted Answer

Let the number be 3N and 4N. Then, 3N + 4N = 420 ⇒ 7N = 420 ⇒ N = 60 ∴ Greater number = 4 x 60 = 240

Question 19

The sum of two number is 100 and their difference is 37. The difference of their squares is?

Accepted Answer

Let the numbers be a and b. Then, a + b = 100 and a - b = 37 ∴ a2 - b2 = (a+b) (a-b) = 100 x 37 = 3700

Question 20

The difference of two number is 8 and 1/8th of their sum is 35. The number are?

Accepted Answer

Let the number be x and (x + 8) Then, 1/8[x + (x + 8)] = 35 ⇒ 2x + 8 = 280 ⇒ 2x = 270 ∴ x = 136 So, the number are 136 and 144.

Number System Questions