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Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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15 Apr 2007, 01:42

kevincan wrote:

How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?

(A) 114 (B) 121 (C) 122 (D) 129 (E) 136

There are 1000/5=200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000.

multiples of 20=1000/20=50 multiples. and multiples of 35= 1000/35 =28.5 so 28 multiples of 35.

So multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200-78 = 122 multiples.
So the answere is C.

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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15 Apr 2007, 06:49

Javed's method seems to be straight forward and correct.

Although in a counting problem such as this, B is tempting because it's very close to C and it might make you think that you forgot to subtract 1 from somewhere...

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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15 Apr 2007, 12:12

multiples of 5: 5(1,2,3,4,5......, 199), 199 in total < 1000
multiples of 4 and 5: 20(1,2,3,4,5,....,49) 49 in total < 1000
multiples of 5 and 7: 35(1,2,3,4,5,....,28) 28 in total < 1000

199 - 49 - 28 = 122

The double counts include multiples of 20,35 (2*2*5, 7*5)
70,140,350,700,770,910,980

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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15 Apr 2007, 13:51

alfyG wrote:

multiples of 5: 5(1,2,3,4,5......, 199), 199 in total < 1000 multiples of 4 and 5: 20(1,2,3,4,5,....,49) 49 in total < 1000 multiples of 5 and 7: 35(1,2,3,4,5,....,28) 28 in total < 1000

199 - 49 - 28 = 122

The double counts include multiples of 20,35 (2*2*5, 7*5) 70,140,350,700,770,910,980

122 + 7(doubles) =129

I think the double counts given by you are incorrect. 70, for example, is not a multiple of 4 and 5.

Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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29 Apr 2015, 10:27

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Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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11 May 2016, 12:07

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Re: How many positive integers less than 1000 are multiples of 5 [#permalink]

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15 Jun 2016, 23:50

1

This post was BOOKMARKED

Did I understand the concept correctly?

To find multiples of a number X less that Y, we divide Y/X. If Y/X has no remainder then no. of multiples if Y/X - 1. If Y/X has remainder then no. of multiples is quotient of Y/X. Eg

no. of multiples of 5 less than 1000 = 1000/5 - 1=199. (If 1000 was included then we wouldnt have subtracted 1) No. of multiples of 3 less than 1000 = 1000/3 = 333

To find common multiples of two nos U and V up to some no. W (eg common multiples of 20 and 35 less than 1000), we find the first common multiple (in this case 140). No all multiples of 140 less than 1000 would be common multiples of 20 and 35 less than 1000 (140, 280, 420, 560, 700, 840, 980, total 7)

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