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PROBLEMS ON NUMBERS

Aptitude

PROBLEMS ON NUMBERS -> DESCRIPTION

Types of Numbers:
Natural Numbers : Counting numbers 1,2,3,4,5,..... are called natural numbers.
Whole Numbers : All counting numbers together with zero from the set of whole numbers. Thus,
(i). 0 is the only whole number which is not a natural number.
(ii). Every natural number is a whole number.
Even Numbers : A number divisible by 2 is called an even number. e.g. 2,4,6,7,10,etc.
Odd Numbers : A number is not divisible by 2 is called an odd number. e.g. 1,3,5,6,7,9,11, etc.

PROBLEMS ON NUMBERS -> SOLVED EXAMPLES

1. 50 is divided into tow parts such that the sum of their reciprocals is 1/12 Find the two parts.
  Sol. Let the two parts be x and (50 - x)
Then, 1/x + 1/50-x = 1/12 ⇔ 50 - x + x/ x(50-x)
= 1/12 ⇒ x² - 50x + 600 = 0
⇒ (x - 30) (x - 20) = 0 ⇒ x = 30 or x = 20.
So, the parts are 30 and 20.
2. A number is as much greater than 36 as is less than 86. Find the number.
  Sol. Let the number be x. Then, x - 36 = 86 - x ⇔ 2x = 86 + 36 = 122 ⇔ x = 61.
Hence, the required number is 61.
3. Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
  Sol.
Let the number be x. Then, 7x - 15 = 2x + 10 ⇔ 5x = 25 ⇔ x = 5.
Hence, the required number is 5.
4. 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.
  Sol.
Let the numbers be x and (184 - x). Then,
x / 3 - (184-x)/7 = 8 ⇔ 7

PROBLEMS ON NUMBERS -> Exercise

7. If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is
 
  • A. 40
  • B. 44
  • C. 80
  • D. 88
Ans: A.
Sol.
Let the numbers be x and y.
Then, (x+y) = 22 and x2 + y2 = 404.
Now, 2xy = (x+y)2 - (x2 + y2)
= (22)2 - 404 = 484 - 404 = 80
xy = 40.
 
8. Of the three numbers, the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. The third number is
 
  • A. 15
  • B. 20
  • C. 25
  • D. 30
Ans: D.
Sol.
Let the numbers be x,y and z.
Then, x + y = 45
y+z = 55 and
3x+z = 90
⇒ y = 45 - x, z = 55 - y = 55 - (45 - x) = 10 + x.
∴ 3x + 10 + x = 90 or x = 20.
y = (45 - 20) = 25 and z = (10 + 20) = 30.
∴ Third number = 30.
 
 
9. The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is
 
  • A. 10
  • B. 12
  • C. 16
  • D. 22
Ans: B.
Sol.
Let the numbers be x and (22 - x).
Then, 5x = 6(22 - x)
⇔ 11x = 132⇔ x = 12.
So, the numbers are 12 and 10.