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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

22. What is the sum of two consecutive even numbers, the difference of whose squares is 84?
 
  • A. 42
  • B. 44
  • C. 48
  • D. 56
Ans: A.
Sol.
Let the numbers be x and x + 2.
then, (x + 2)² - x² = 84 ⇔ 4x + 4 = 84 ⇔ 4x = 80 ⇔ x=20.
∴ Required sum = x + (x + 2) = 2x + 2 = 42.
 
23. A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is
 
  • A. 3
  • B. 5
  • C. 7
  • D. 9
Ans: C.
Sol.
Let the numbers be x.
Then, x - 4 = 21/x
⇔ x2 - 4x - 21 = 0
⇔ (x-7)(x+3) = 0
⇔ x = 7.
 
 
24. In a two digit number, if it is known that its units digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
 
  • A. 42
  • B. 46
  • C. 22
  • D. 24
Ans: D.
Sol.
Let the ten's digit be x.
Then, units digit = x + 2.
Number = 10x + (x+2) = 11x + 2;
Sum of digits = x + (x+2) = 2x +2.
∴ (11x +2)(2x+2) = 144
⇔ 22x2 + 26x - 140 = 0
⇔ 11x2 + 13x - 70 = 0
⇔ (x - 2)(11x+35) = 0 ⇔ x =2.
Hence, required number = 11x + 2 = 24.