1 | The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number. A. 69 B. 70 C. 71 D. 72 Answer : D. 72 Explanation: Let the numbers be x and (184 - x). Then, \({X \over3 }- {184-x \over7} = 8\) => 7x – 3(184 – x) = 168 => 10x = 720 => x = 72. So, the numbers are 72 and 112. Hence, smaller number = 72. |
2 | The ratio between a two-digit number and the sum of the digits of that number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what is the number? A. 34 B. 35 C. 36 D. 37 Answer : C. 36 Explanation: Let the ten's digit be x. Then, unit's digit = (x + 3). Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3. \({{11x+3} \over {2x + 3 } }= {4 \over 1 }\) => \(11x + 3 = 4 (2x + 3)\) => 3x = 9 => x = 3. Hence, required number = 11x + 3 = 36. |
3 | The sum of two numbers is 15 and the sum of their squares is 113. Find the numbers. A. 6 and 9 B. 7 and 8 C. 4 and 11 D. 10 and 5 Answer : B. 7 and 8 Explanation: Let the numbers be x and (15 - x). Then,\( x^2 + (15 - x)^2 = 113?\) => \(x^2 + 225 + x^2 - 30x = 113\) => \(2x^2 - 30x + 112 = 0 \) => \(x^2 - 15x + 56 = 0\) => (x - 7) (x - 8) = 0 => x = 7 or x = 8. So, the numbers are 7 and 8. |
4 | If three numbers are added in pairs, the sums equal 10, 19 and 21. Find the numbers A. 6, 4 and 15 B. 7, 4 and 14 C. 6, 2 and 17 D. 6, 5 and 13 Answer : A. 6, 4 and 15 Explanation: Let the numbers be x, y and z. Then, x+ y = 10 ...(i) y + z = 19 ...(ii) x + z = 21 …(iii) Adding (i) ,(ii) and (iii), we get: 2 (x + y + z ) = 50 or (x + y + z) = 25. Thus, x= (25 - 19) = 6; y = (25 - 21) = 4; z = (25 - 10) = 15. Hence, the required numbers are 6, 4 and 15. |
5 | 50 is divided into two parts such that the sum of their reciprocals is \(1\over 12\).Find the two parts. A. 10 and 40 B. 15 and 35 C. 45 and 5 D. 30 and 20 Answer : D. 30 and 20 Explanation: Let the two parts be x and (50 - x). Then, 1 / x + 1 / (50 – x) = \(1 \over 12\) => (50 – x + x) / x ( 50 – x) = \(1 \over 12\) => x2 – 50x + 600 = 0 => (x – 30) ( x – 20) = 0 => x = 30 or x = 20. So, the parts are 30 and 20. |
6 | The average of four consecutive even numbers is 27. Find the largest of these numbers. A. 29 B. 30 C. 31 D. 32 Answer : B. 30 Explanation: Let the four consecutive even numbers be x, x + 2, x + 4 and x + 6. Then, sum of these numbers = (27 x 4) = 108. So, x + (x + 2) + (x + 4) + (x + 6) = 108 or 4x = 96 or x = 24. \(\dot{..}\)Largest number = (x + 6) = 30. |
7 | A number is as much greater than 36 as is less than 86. Find the number. A. 71 B. 61 C. 51 D. 41 Answer : B. 61 Explanation: Let the number be x. Then, x - 36 = 86 - x => 2x = 86 + 36 = 122 => x = 61. Hence, the required number is 61. |
8 | Find a number such that when 15 is subtracted from 7 times the number, the Result is 10 more than twice the number. A. 5 B. 6 C. 7 D. 8 Answer : A. 5 Explanation: Let the number be x. Then, 7x - 15 = 2x + 10 => 5x = 25 =>x = 5. Hence, the required number is 5. |