FeedBack Form

Your Name :
Your Email :
Your Location :
Your Message :
   
FeedBack

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

25. If the sum of a number and its square is 182, what is the number?
 
  • A. 13
  • B. 15
  • C. 17
  • D. 19
Ans: A.
Sol.
Let the numbers be x.
Then, x + x2 = 182
⇔ x2 + x - 182 = 0
⇔ (x+14)(x-13) = 0
⇔ x = 13.
 
26. The difference between a two digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?
 
  • A. 4
  • B. 8
  • C. 12
  • D. 16
Ans: B.
Sol.
Since the number is greater than the number obtained on reversing the digits, so the ten's is greater than the unit's digit.
Let the ten's and units digit be 2x and x respectively.
Then, (10× 2x + x) - (10x + 2x) = 36
⇔ 9x = 36
⇔ x = 4.
∴ Required difference = (2x+x)-(2x-x) = 2x = 8.
 
 
27. There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is
 
  • A. 6
  • B. 9
  • C. 12
  • D. 15
Ans: B.
Sol.
Let the numbers be x and y.
Then, 2x + 3y = 39 ................(i)
3x + 2y = 36 .................(ii)
On solving (i) and (ii), we get : x = 6 and y = 9.
∴ Larger number = 9.