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​

Answer 1

if we add 5 and 7 then their sum will be 13

Now,out of the four options if we add 15 to it, it becomes 28 which is a multiple of 7

hence, option 4 is the answer

Answer 2

Answer:

The maximum possible value of x is 17

Step-by-step explanation:

Range of the data is Highest value - Lowest value

Since x is a two digit prime number

Therefore, x is the greatest number

Range will be x-5

x-5 should be divisible by 7

i.e. x when divided by 7 should give remainder 5

Two digit numbers divisible by 7 are

14, 21, 28, 35, 42, 49, 56,63, 70, 77, 84, 91, 98

Thus, x can be

14+5 = 19 (Prime)

21+5 =26 (Not prime)

28 + 5 = 33 (Not prime)

35 + 5 = 40 (Not Prime)

42 + 5 = 47 (Prime)

49 + 5 = 54 (Not prime)

56 + 5 = 61 (Prime)

63 + 5 = 67 (Prime)

70 + 5 = 75 (Not prime)

77 + 5 = 82 (Not prime)

84 + 5 = 89 (prime)

91 + 5 = 96 (Not prime)

Therefore, the highest value of x can be 89

The sum of the digits = 8 + 9 = 17

Hope this helps.