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Integers

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by highlydetermined » Thu Jul 16, 2009 11:00 am
Is there a quick way of figuring out how many integers there are between 250 and 300, inclusive, that can be evenly divided by NEITHER 3 NOR 5?

Listing all the numbers are time consuming and not advisable for the GMAT.
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by mike22629 » Thu Jul 16, 2009 11:45 am
Number of total integers = 300 - 250 + 1 = 51

Total Divisible by 3 = (300 - 252)/3 = 16

Total Divisible by 5 = (300 - 250)/5 = 10

Total Divisible by both = 255, 270, 290
(first first one divisble by both and add 15 to each one)

16 + 10 - 3 = 23 ( are divisible by either)

51 - 23 = 28 (not divisible)

IMO 28

Looks long when you write it out, but only took me about 1 min to solve.
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by highlydetermined » Thu Jul 16, 2009 12:21 pm
Thanks for the short cut, but the book has an answer of 27. There are 11 integers divisible by 5 and 13 integers divisible by 3, for a total of 24.

51-24=27
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by tohellandback » Thu Jul 16, 2009 4:46 pm
mike's method is Ok but his counting is wrong
total number of integers=51
total divisible by 3=(300-252)/3+1=17
total divisible by 5=(350-250)/5+1=11
divisible by both=(300-250)/15 (take the quotient)+1 i.e. 4 and the numbers are 255,270,285 and 300
17+11-4=24

so numbers not divisible=51-24=27
The powers of two are bloody impolite!!
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