Number System Model 4

Examples on Number System:

17.The difference between two numbers is 4 and the difference between their squares is 128. What is the larger number?

1) 14 2)16 3)12 4) 18 5) None of these

18.The difference between two numbers is 3 and the difference between their squares is 63. What is the larger number?

1) 12 2)9 3)15 4) Cannot be determined 5) None of these

19.On a school’s sports day sweets are to be equally distributed amongst 112 students. But on that particular day, 32 students were absent. Thus the remaining students got 6 extra sweets. How many sweets was each student originally supposed to get?

1)24 2)18 3)15 4) Cannot be determined 5) None of these

20.There are two numbers such that the sum of twice the first number and thrice the second number is 300 and the sum of thrice the first number and twice the second number is 265. Which number is the larger ?

1) 24 2)39 3)85 4)74 5) None of these

Example 17:

Explanation:

We assume the numbers are 'x' and 'y'.

The difference between 'x' and 'y' is 4.  i.e.   x - y = 4

The difference between 'x' and 'y' squares is128. i.e. x² - y² = 128

Now We build the relation between  x - y &  x² - y² 

x + y = ( x² - y² ) / (x - y)   where x² - y²  = (x + y) (x - y)

x + y =  128 / 4 = 32

Now solve x + y && x - y

x  +  y =  32
x  -  y =    4

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2x  = 36 ⇒ x = 18 then y = 14.
∴The Large Number is 18

Number System Model 1

Number System Model 2

Number System Model 3

Number System Model 5

Number System Model 6