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How many integers from 100 through 150 are neither a multiple of 3 nor

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How many integers from 100 through 150 are neither a multiple of 3 nor [#permalink] New post   15 Jul 2024, 23:58
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How many integers from 100 through 150 are neither a multiple of 3 nor a multiple of 5?

A. 25

B. 26

C. 27

D. 28

E. 29


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C
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Re: How many integers from 100 through 150 are neither a multiple of 3 nor [#permalink] New post   22 Jul 2024, 01:51
Explanation please?
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Re: How many integers from 100 through 150 are neither a multiple of 3 nor [#permalink] New post   22 Jul 2024, 02:36
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You need to find the multiple of 3 from 100 to 150 minus those from 1 to 99

150/3-99/3=50-33=17

Same with those of 5

150/5-99/5=30-19=11

Multiple of 15 (3 and 5)= 150/15-99/15=10-6=4

Took out the overlapping

17+11-4=24

Total numbers from 100 to 150 are 51

51-24=27

C is the answer
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Re: How many integers from 100 through 150 are neither a multiple of 3 nor [#permalink] New post   01 Aug 2024, 14:52
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Number of integers from 100 through 150 = 51

We can then subtract those that are multiples of 3 or 5 in other words 3 union 5


If A = 51

B = Multiples of 3 = 17

C = Multiples of 5 = 11

x = BnC = Multiples of 15 within range.


Therefore

A - AnB - AnC + x

51-28 + 4

= 27

Answer C

Adewale Fasipe quant instructor Lagos Nigeria.
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Re: How many integers from 100 through 150 are neither a multiple of 3 nor [#permalink] New post   01 Aug 2024, 15:16
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Re: How many integers from 100 through 150 are neither a multiple of 3 nor [#permalink]
01 Aug 2024, 15:16
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