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

Answer:

17

Step-by-step explanation:

simple

it clearly mentions that X is a two digit prime number

from the given options apart from 17 remaining all are non primes

Answer 2

Answer:

17

Step-by-step explanation:

Range of the data is

Highest number - Lowest number

The data we have is 5, 8 and x

As x is a two digit number hence highest number is x and the lowest number is 5

So,

Range = x - 5

Now as range is a multiple of 7 hence we can say

7n = x - 5.

Now listing out all the two digit prime numbers, we have

11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

Maximum possible value of x such that x - 5 is a multiple of 7 is 89.

Hence the value is 8+9 = 17.

People seem to be misunderstanding the question. They are thinking that question is asking for x and choosing 17 because it is a prime number but the question is asking for the sum of the digits of x rather than x itself.