How many ODD integers n, where 100

Question

How many ODD integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?

(A) 37
(B) 38
(C) 39
(D) 40
(E) 46

GMATinsight · Answer

Total Integers from 100 to 200 inclusive = 101 (51 even and 50 odd)
 Total Odd Integers from 100 to 200 = 50

Total No. that are multiple of 7 from 1-200 = 200/7 = 28 (i.e. 14 even and 14 odd)
Total No. that are multiple of 7 from 1-100 = 100/7 = 14 (i.e. 7 even and 7 odd)
 Total No. that are ODD multiple of 7 from 100-200 = 14-7 = 7

Total No. that are multiple of 9 from 1-200 = 200/9 = 22 (i.e. 11 even and 11 odd)
Total No. that are multiple of 9 from 1-100 = 100/9 = 11 (i.e. 5 even and 6 odd)
 Total No. that are ODD multiple of 9 from 100-200 = 11-6 = 5

Total No. that are odd multiple of 7 and 9 will be multiple of 63 and count of such numbers from 100-200 = 1

So Total No. that are odd multiple of 7 and/or 9 from 100-200 = 7+5-1 = 11

So Total No. that are NOT odd multiple of 7 and/or 9 from 100-200 = 50-11 = 39

Answer: Option C

Drealnapster · Answer

Very clear. Thanks so much

Sent from my KFGIWI using Tapatalk

bumpbot · Answer

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How many ODD integers n, where 100 <= n <= 200, are divisible neither

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