Question

A shopkeeper has 5 red pens. x green pens and
8 black pens. If range of the data is a multiple of 7
and x is a two-digit prime number, then the sum of
digits of maximum possible value of x is
(1) 17
(2) 12
(3) 16
(4) 15​

Answer 1

the sum of other two 7+5=12

Answer 2

Given:

Number of red pens = 5

Number of black pens = 8

Number of green pens = x

To Find:

Sum of  digits of maximum possible value of x is

Solution:

Two digit prime numbers are - 11, 13, 17, 19, 23, upto 93, 97,

Since x is a two digit prime number, therefore -

= 5 + 8 + x is divisible by 7 ( Multiple of 7 given)

As the maximum value of x is to be found,

Let x = 97,

Therefore,

5 + 8 + 97 = 110 ( It is not divisible by 7

Let x = 93,

5 + 8 + 93 = 106 ( It is not divisible by 7 )

If x = 89,

5 + 8 + 89 = 102 ( It is divisible by 7 )

Therefore, the maximum value of x is 89,

Sum of digits -

8 + 9

= 17

Answer: The sum of digits of maximum possible value of x is 17.