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How many integers from 1 to 200, inclusive, are divisib

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banksy
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How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   14 Feb 2011, 15:52
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How many integers from 1 to 200, inclusive, are divisible by 3 but not divisible by 7?

(A) 38
(B) 57
(C) 58
(D) 60
(E) 66
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B
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   14 Feb 2011, 16:14
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banksy wrote:
How many integers from 1 to 200, inclusive, are divisible by 3 but not divisible by 7?
(A) 38
(B) 57
(C) 58
(D) 60
(E) 66


We should find # of integers divisible by 3 but not by 3*7=21.

# of multiples of 3 in the range from 1 to 200, inclusive is (198-3)/3+1=66 (check this: totally-basic-94862.html);
# of multiples of 21 in the range from 1 to 200, inclusive is (189-21)/21+1=9;

66-9=57.

Answer: B.
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jlgdr
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   25 Nov 2013, 08:18
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banksy wrote:
How many integers from 1 to 200, inclusive, are divisible by 3 but not divisible by 7?

(A) 38
(B) 57
(C) 58
(D) 60
(E) 66


We need to find the multiples of 3 and subtract the multiples of 21.

So in 21 numbers we have 7 multiples of 3 - 1 multiple of 21 = 6 total

In the selected range we have 9 sets of 21 = 198 and three more multiples of three none of which is a multiple of 7 (192, 195 and 198)

So in total we have (9*6) + 3 = 57

Answer is B

Hope it helps
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J :)
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How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   27 Jun 2015, 10:02
The toughest part of the question for me is how to extrapolate the number of 21s in 200, quickly, I might add. What if the question were to ask the number of 21s between some obsure numbers like 698,743 and 796,453, are there any strategies without involving long division?
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   24 Jan 2017, 19:32
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1) The number of integers that are divisible by 3 but not divisible by 7 is equal to the number of integers that are divisible by 3 minus the number of integers that are divisible by the product of 3 and 7 (21)
2) 200/3=66
3) 200/21=9
4)66-9=57

The correct answer is B
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   02 May 2018, 14:18
banksy wrote:
How many integers from 1 to 200, inclusive, are divisible by 3 but not divisible by 7?

(A) 38
(B) 57
(C) 58
(D) 60
(E) 66


198/3=66
63/7=9
66-9=57
B
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   03 May 2018, 10:48
Expert Reply
banksy wrote:
How many integers from 1 to 200, inclusive, are divisible by 3 but not divisible by 7?

(A) 38
(B) 57
(C) 58
(D) 60
(E) 66


First let’s determine the number of multiples of 3. We use the formula: number of multiples of 3 = (largest multiple of 3 - smallest multiple of 3)/3 + 1

(198 - 3)/3 + 1 = 66 multiples of 3

Since multiples of 21 are multiples of both 3 and 7, we need to exclude them from our list.

(189 - 21)/21 + 1 = 9 multiples of 21

So there are 66 - 9 = 57 numbers that are divisible by 3 but not divisible by 7.

Answer: B
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink] New post   11 Jan 2023, 08:04
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Re: How many integers from 1 to 200, inclusive, are divisib [#permalink]
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