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What is the number of 2 digits positive integers which are r

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by Max@Math Revolution » Sun Sep 15, 2019 11:26 pm

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[GMAT math practice question]

What is the number of 2 digits positive integers which are relatively prime to 100?

A. 24
B. 36
C. 48
D. 51
E. 63
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by Max@Math Revolution » Tue Sep 17, 2019 11:05 pm
=>

Remind that the number of terms of an arithmetic sequence with its first term F, its last term L and its difference d is (L-F)/d + 1.
We have 90 of 2 digits positive integers from 10 to 99.
The number of multiples of 2 is 45 = (98-10)/2 + 1 since they are 10, 12, ..., 98.
The number of multiples of 5 is 18 = (95-10)/5 + 1 since they are 10, 15, ..., 95.
The number of multiples of both 2 and 5 is 9 = (90-10)/10 + 1 since they are 10, 20, ..., 90.

Thus, the number of2 digits positive intergers which are relatively prime is 90 - (45 + 18 - 9) = 36.

Therefore, B is the answer.
Answer: B
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