GRE Quiz | GRE Quantitative 2 | Question 17

How many 2 digit numbers which are composite numbers?

(A) 2
(B) 20
(C) 60
(D) 74
(E) 70

Answer: (E)
Explanation: There are 25 prime numbers between 1 and 100. They are,

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 
 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 

1 is neither prime nor composite number and single digit composite numbers are 4, 6, 8, 9. Integer 100 has three digit so, it will not counted.

Therefore, two digit numbers which are composite numbers are,

= 75 - 1 - 4
= 70 

They are,

10 12 14 15 16 18 20 21 22 24 25 26 27 28 30
32 33 34 35 36 38 39 40 42 44 45 46 48 49 50 
51 52 54 55 56 57 58 60 62 63 64 65 66 68 69 70 
71 72 74 75 76 77 78 80 81 82 84 85 86 87 88 90 
91 92 93 94 95 96 98 99 

So, option (E) is correct.

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