Problems on Numbers for Exam
Q71. Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is
(a) 5
(b) 7
(c) 11
(d) 12
Answer: (a) 5
Let the number be x
A/Q, 3x2 - 4x = x + 50
⇒ 3x2 - 5x - 50 = 0
⇒ 3x2 - 15x + 10x - 50 = 0
⇒ 3x (x - 5) + 10 (x - 5) = 0
⇒ (x - 5) (3x + 10) = 0
∴ x - 5 = 0
x = 5
Q72. Two fifth of two - seventh of one - third of a number is 12. What is the number ?
(a) 150
(b) 275
(c) 280
(d) 315
Answer: (d) 315
Let the number be x
A/Q, (2/5) X (2/7) X (1/3) X x = 12
⇒ 4x/105 = 12
⇒ x = 315
Q73. The difference between two positive numbers is 5. If the sum of the squares of these numbers is 325, then the sum of the numbers is
(a) 20
(b) 25
(c) 30
(d) 35
Answer: (b) 25
Let the number be x and y
A/Q x - y = 5 ------> (1)
and x2 + y2 = 325 -------> (2)
(1) ⇒ x - y = 5
⇒ (x - y)2 = 52
⇒ x2 + y2 - 2xy = 25
⇒ 325 - 2xy = 25
⇒ 2xy = 300
⇒ xy = 150
Now (x + y)2 = (x - y)2 + 4xy = 52 + 4 X 150 = 25 + 600 = 625
∴ x + y = √ 625 = 25
Q74. The number that should be added to both the numerator and denominator of 42/92 so that the fraction becomes 4/9 is
(a) 28
(b) 36
(c) 42
(d) 56
Answer: (b) 36
Let the number be x
| A/Q | 42 + x | = | 4 |
| 92 + x | 9 |
| ⇒ | 16 + x | = | 4 |
| 81 + x | 9 |
⇒ 144 + 9x = 324 + 4x
⇒ 5x = 180
⇒ x = 36
Q75. A two digit number is such that the product of its digits is 3. When 18 is added to the number the digits are reversed. The number is
(a) 9
(b) 12
(c) 13
(d) 15
Answer: (c) 13
Let the unit digit number be x and ten's digit number be y
∴ The number = 10y + x
A/Q xy = 3 ------> (1)
And 10y + x + 18 = 10x + y
⇒ 9y + 18 = 9x
⇒ 9x - 9y = 18
⇒ x - y = 2 -----> (2)
Now (x + y)2 = (x - y)2 + 4xy
= 22 + 4 X 3 = 16
∴ x + y = √ 16 = 4 ------> (3)
(2) + (3) ⇒ 2x = 6 ⇒ x = 3
(2) ⇒ y = x - 2 = 3 - 2 = 1
∴ Number = 10 X 1 + 3 = 13
Q76. Three numbers are in the ratio 3 : 4 : 6 and their product is 1944. The smallest of these number is
(a) 5
(b) 7
(c) 8
(d) 9
Answer: (d) 9
Let the numbers be 3x, 4x, 6x
A/Q 3x X 4x X 6x = 1944
⇒ 72x3 = 1944
⇒ x3 = 27
⇒ x3 = 33
⇒ x = 3
∴ Smallest number = 3 X 3 = 9
Q77. Which of the following numbers is not a square of any natural number ?
(a) 34602
(b) 4096
(c) 15309
(d) 10000
Answer: (a) 34602
The square of a number never ends by 2, i.e at unit place by 2
Q78. The ratio of two numbers is 5 : 6. If sum of the numbers be 121, then the biggest number is
(a) 52
(b) 55
(c) 66
(d) 71
Answer: (c) 66
Let the numbers be 5x and 6x
A/Q 5x + 6x = 121
⇒ 11x = 121
⇒ x = 11
∴ the biggest number = 6 X 11 = 66
Q79. The ratio of two numbers is 9 : 10. If the difference between them is 5 then the smallest number is
(a) 45
(b) 47
(c) 51
(d) 55
Answer: (a) 45
Let the numbers be 9x and 10x
A/Q 10x - 9x = 5
⇒ x = 5
∴ the smallest number = 9 X 5 = 45
Q80. If 3 is added to the denominator of a fraction it becomes 1/3 and if 4 is added to its numerator, it becomes 3/4. The fraction is
(a) 5/17
(b) 3/11
(c) 5/12
(d) 3/17
Answer: (c) 5/12
Let the fraction be x/y
| A/Q | x | = | 1 |
| y + 3 | 3 |
⇒ 3x = y + 3
⇒ 3x - y = 3
⇒ y = 3x - 3 ----- (1)
| And | x + 4 | = | 3 |
| y | 4 |
⇒ 4x + 16 = 3y
⇒ 4x + 16 = 3 (3x - 3) from (1)
⇒ 4x + 16 = 9x - 9
⇒ 5x = 25
⇒ x = 5
(1) ⇒ y = 3 X 5 - 3 = 15 - 3 = 12
∴ The Fraction is 5/12
Practice Test Exam