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Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5?

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by Max@Math Revolution » Sun Jan 19, 2020 11:07 pm
[GMAT math practice question]

Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5?

A. 14
B. 16
C. 18
D. 20
E. 22
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Re: Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5?

by jbryant62 » Tue Jan 21, 2020 7:17 am
Max@Math Revolution wrote: ↑
Sun Jan 19, 2020 11:07 pm
 [GMAT math practice question]

Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5?

A. 14
B. 16
C. 18
D. 20
E. 22
To find the multiples of 4 divide 50 by4 = 12.5. keep the integer 12

To find the multiples of 5 divide 50 by 5 =10.

12+10=22. But this includes counting multiples of 20 (4*5) twice. Therefore we need to find the multiples of 20. Divide 50 by 20 = 2.5. Keep the 2

Now subtract 22-2=20. Answer D
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Re: Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5?

by Max@Math Revolution » Wed Jan 22, 2020 5:14 pm
=>

The number of multiples of 4 is 12 = (48 – 4)/4 + 1 = 11 + 1, since 4, 8, …, 48 are the multiples of 4 between 1 and 50, inclusive.
The number of multiples of 5 is 10 = (50 – 5)/5 + 1 = 9 + 1, since 5, 10, …, 50 are the multiples of 5 between 1 and 50, inclusive.
Multiples of 20 are double-counted, and the number of multiples of 20 is 2 since 20 and 40 are multiples of 20 between 1 and 50, inclusive.
Then we have 12 + 10 - 2 = 20.

Therefore, D is the answer.
Answer: D
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