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PROBLEMS ON NUMBERS

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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

1. The sum of three consecutive multiples of 3 is 72. What is the larget number?
 
  • A. 26
  • B. 27
  • C. 46
  • D. 57
Ans: B.
Sol.
Let the numbers be 3x, 3x + 3 and 3x + 6.
Then, 3x + (3x + 3) + (3x + 6) = 72 ⇔ 9x = 63 ⇔ x = 7.
∴ Largest number = 3x +6 = 27.
 
2. The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number?
 
  • A. 3
  • B. 6
  • C. 9
  • D. 12
Ans: C.
Sol.
Let the numbers be x, x + 2 and x + 4.
Then, x + (x + 2) + (x + 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
 
 
3. The sum of four consecutive even integers is 1284. The greatest of them is:
 
  • A. 324
  • B. 342
  • C. 364
  • D. 382
Ans: A.
Sol.
Let the four integers be x, x + 2, x + 4 and x + 6
Then, x + (x + 2) + (x + 4) + (x + 6) = 1284 ⇔ 4x = 1272 ⇔ x = 318
∴ Greatest integer = x + 6 = 324.