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How many multiples of 3 are there among the integers 15 through 105 in

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Bunuel
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How many multiples of 3 are there among the integers 15 through 105 in [#permalink] New post   27 Mar 2024, 01:30
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­How many multiples of 3 are there among the integers 15 through 105 inclusive?

A) 30
B) 31
C) 32
D) 33
E) 34


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B
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Nidzo
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Re: How many multiples of 3 are there among the integers 15 through 105 in [#permalink] New post   27 Mar 2024, 02:02
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­15 is the 5th positive multiple of 3: \(\frac{15}{3}=5\)

105 is the 35th positive multiple of 3: \(\frac{105}{3}= 35\)

How many multiples of 3 are there among the integers 15 through 105 inclusive: 

\(35 - 5 = 30\), however, as the question stem specified "15 through 105 inclusive" we need to add 1 so the answer is 31.

ANSWER B

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Re: How many multiples of 3 are there among the integers 15 through 105 in [#permalink] New post   27 Mar 2024, 04:42
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IMO B

Multiples of 3

3*5 =15
3*6=18
.
.
.
.
3*35=105

so Total numbers = 35-5+1 = 31
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Re: How many multiples of 3 are there among the integers 15 through 105 in [#permalink] New post   27 Mar 2024, 08:26
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Bunuel wrote:
­How many multiples of 3 are there among the integers 15 through 105 inclusive?

A) 30
B) 31
C) 32
D) 33
E) 34­

\(\frac{­(105 - 15)}{3} +1 = 31\), Answer must be (B)
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Re: How many multiples of 3 are there among the integers 15 through 105 in [#permalink]
27 Mar 2024, 08:26
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