SETS & FACTORS

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wingsoffire: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Tue Aug 02, 2011 2:50 am

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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Source: Beat The GMAT — Quantitative Reasoning | Mon Oct 03, 2011 5:10 am

rajanjindal27: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Sep 13, 2011 10:48 pm

by rajanjindal27 » Wed Oct 05, 2011 11:10 pm

129

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razorback: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Aug 29, 2011 6:43 pm; Thanked: 1 times

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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