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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

4. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
 
  • A. 4
  • B. 5
  • C. 6
  • D. 8
Ans: A.
Sol.
Let the ten’s digit be x and unit’s digit be y,
Then, (10x + y) - (10y + x) = 36 ⇔ 9 (x - y) = 36
⇔ x - y = 4.
 
5. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by :
 
  • A. 5
  • B. 7
  • C. 9
  • D. 11
Ans: D.
Sol.
Let the ten’s digit be x and unit’s digit be y. Then, number = 10x + y
Number obtained by interchanging the digits = 10y + x.
∴ (10x+y) + (10y + x) = 11 (x + y), which is divisible by 11.
 
 
6. A two-digit number exceeds the sum of the digits of that number by 18. If the digit at the unit’s place is double the digit in the ten’s place, what is the number?
 
  • A. 20
  • B. 22
  • C. 24
  • D. 40
Ans: C.
Sol.
Let the ten’s digit be x. Then, unit’s digit = 2x.
Number = 10x + 2x = 12x; Sum of digits = x = x + 2x = 3x.
∴ 12x - 3x = 18 ⇔ 9x = 18 ⇔ x = 2.
Hence, required number =12x = 24.