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# how many of the integers between 1 and 400

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Intern
Joined: 20 Aug 2010
Posts: 38
how many of the integers between 1 and 400 [#permalink]

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26 Nov 2011, 07:16
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how many of the integers between 1 and 400 are not divisible by 4 and do not contain 4 as a digit?
Manager
Joined: 16 Dec 2009
Posts: 75
GMAT 1: 680 Q49 V33
WE: Information Technology (Commercial Banking)
Re: how many of the integers between 1 and 400 [#permalink]

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26 Nov 2011, 13:13
I think the answer is 252.

I approached it in a very simple way . Consider the range of 0-100 only. Here the numbers which are out of contention to be the potential values are
(i) multiples of 4 = 25
(ii) whose unit's digit is 4 but the number is not divisible by 4 = 5 (14,34,54,74,94)
(iii) whose ten's digit is 4 but the number is not multiple of 4 = 7 (41,42,43,45,46,47,49)

Total (i) + (ii) + (iii) = 37 . The pattern will repeat for ranges 100-200 , 200-300 , 300-400. So total number of values which are not potential answers is 37*4=148.

So the total number of potential answer values is 400-148=252.
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Re: how many of the integers between 1 and 400   [#permalink] 26 Nov 2011, 13:13
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