Numbers Questions

The Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 upto 40. Mutiples of 4 means which can be divided by 4 leaving remainder '0'.

Common Multiples of 4 & 6 are 12, 24, 36, 48, 60 upto 60.

In the given options,

12/49 can be written as 1/(49/12) = 1/4.083

7/30 can be written as 1/(30/7) = 1/4.285

13/56 can be written as 1/(56/13) = 1/4.307

11/46 can be written as 1/(46/11) = 1/4.1818

Here in the above,

1/4.083 has the smallest denominator and so 12/49 is the largest number or fraction.

Given, difference of the squares of two numbers is 180.

= k² - l² - 180

Also, square of the smaller number is 8 times the larger.

= l² = 8k

Thus, k² - 8a - 180 = 0

k² – 18k + 10k - 180 = 0

→  k(k - 18) + 10(k – 18) = 0

= (k + 10)(k – 18) = 0

→  k = -10, 18

Thus, the other number is

324 - 180 = l² 

→ Numbers are 12, 18 or -12, 18.