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

28. If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is
 
  • A. 2
  • B. 3
  • C. 4
  • D. 5
Ans: C.
Sol.
Let the number be x.
Then, 2x + 20 = 8x - 4
⇔ 6x = 24
⇔ x = 4.
 
29. The sum of two numbers is 25 and their difference is 13. Find their product.
 
  • A. 104
  • B. 108
  • C. 114
  • D. 325
Ans: C.
Sol.
Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x+y)2 - (x-y)2
= (25)2 - (13)2 = 625 - 169 = 456
⇒ xy = 114.
 
 
30. Two numbers differ by 5. If their product is 336, then the sum of the two numbers is
 
  • A. 21
  • B. 28
  • C. 37
  • D. 51
Ans: C.
Sol.
Let the number be x and y.
Then, x - y = 5 and xy = 336.
⇔ (x+y)2 = (x-y)2 + 4xy = 25 + 4 x 336 = 1369
⇒ x+y = √1369 = 37.