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GMAT Instructor
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How many positive integers less than 1000 are multiples of 5 [#permalink]
 14 Apr 2007, 23:34
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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
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Senior Manager
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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.
Javed.
Cheers!
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Manager
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It's 129 (D)
There are 199 multiples of 5 that are less than 1000.
Now we have to exclude the multiples of 4 and 7 from these 199 numbers.
Let's first find out the numbers below 1000 that are multiples of 5 as well as 4. (that is, multiples of 20). There are 49 such numbers.
Ditto for 5 as well as 7. There are 28 such numbers.
Subtracting these numbers from 199, we get, 199-49-28=122.
However, there will be some numbers which are multiples of both 4 and 7 which have been subtracted twice in the above calculation.
There are 7 such numbers (multiples of 20 as well as 35, that is multiples of 140).
Thus the required number is 122+7 = 129.
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Senior Manager
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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...
What is the OA?
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Senior Manager
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rakesh.id wrote: It's 129 (D)
There are 199 multiples of 5 that are less than 1000.
Now we have to exclude the multiples of 4 and 7 from these 199 numbers.
Let's first find out the numbers below 1000 that are multiples of 5 as well as 4. (that is, multiples of 20). There are 49 such numbers.
Ditto for 5 as well as 7. There are 28 such numbers.
Subtracting these numbers from 199, we get, 199-49-28=122.
However, there will be some numbers which are multiples of both 4 and 7 which have been subtracted twice in the above calculation.
There are 7 such numbers (multiples of 20 as well as 35, that is multiples of 140).
Thus the required number is 122+7 = 129.
I agree with your explanation. Answere is 129.
Javed
Cheers!
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Manager
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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
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Manager
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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.
The double counts are: 140, 280, 420, 560, 700, 840, 980
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Manager
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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
D. I thought of putting my explanation but rakesh.id's is the better one
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