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SETS & FACTORS

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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SETS & FACTORS

by wingsoffire » Mon Oct 03, 2011 5:10 am
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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by rajanjindal27 » Wed Oct 05, 2011 11:10 pm
129
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by razorback » Fri Oct 07, 2011 4:46 pm
129.

20 multiples of 5 in each 100 number set (5,10,15...90,95,100)
= 20(10)

subtract 5 from each set that are multiples of 4 (20,40,60,80,100) <-- takes care of 1000 since its "less than 1000"

so now its 15(10).

subtract 21 for all the multiples of 7 (manually crunched it, didn't double count the multiples of 4 already subtracted).

=150 - 21 = 129

Took about 3 minutes with the manual number crunching of multiples of 7 that didnt double dip the fours.
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