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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

10. If the number obtained on interchanging the digits of a two digit number is 18 more than the original number and the sum of the digits is 8, then what is the original number?
 
  • A. 25
  • B. 30
  • C. 35
  • D. 40
Ans: C.
Sol.
Let ten's digit = x.
Then, unit's digit = (8-x).
∴ [10 (8-x)+x] - [10x + (8-x)] = 18
⇔ 18x = 54
⇔x = 3
So, ten's digit = 3 and units digit = 5.
Hence, original number = 35.
 
11. The difference between a number and its three fifth is 50. What is the number?
 
  • A. 75
  • B. 100
  • C. 125
  • D. 165
Ans: C.
Sol.
Let the numbers be x.
Then, x-3/5x = 50
⇔2/5x = 50⇔ x = (50x5/2) = 125.
 
 
12. The sum of the digits of a two digit number is 9 less than the number. Which of the following digits is at units place of the number?
 
  • A. 1
  • B. 2
  • C. 3
  • D. Data inadequate
Ans: D.
Sol.
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (x + y) = 9 or x = 1.
From the data, we cannot find y, the units digit.
So, the data is inadequate.