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factors

by GmatTakerNo.1 » Sun Apr 25, 2010 4:39 am
Hey, can you help me out with this one:

How many positive integers less than 1000 have no factors (other than 1) in common with 1000?
a) 400
b) 410
c) 411
d) 412
e) None of the above

What is the approach to solve this under two minutes?
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by akhpad » Sun Apr 25, 2010 5:02 am
Total no divisible by 2
2, 4, 6, 8 ... 1000 = 500

Total no divisible by 5
5,10,15,20 ... 1000 = 200

Total no divisible by both 2 and 5
10,20,40 ... 1000 = 100

Total no divisible by either 2 or 5
500+200-100 = 600

Total no not divisible by either 2 or 5
1000 - 600 = 400

Since 1 is not included, required number = 399

Is answer E?
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by Stuart@KaplanGMAT » Sun Apr 25, 2010 2:00 pm
akhp77 wrote:Total no divisible by 2
2, 4, 6, 8 ... 1000 = 500

Total no divisible by 5
5,10,15,20 ... 1000 = 200

Total no divisible by both 2 and 5
10,20,40 ... 1000 = 100

Total no divisible by either 2 or 5
500+200-100 = 600

Total no not divisible by either 2 or 5
1000 - 600 = 400

Since 1 is not included, required number = 399

Is answer E?
Excellent work right up until the last step!

The question doesn't say that we shouldn't include 1 as a potential answer, it says we shouldn't consider 1 as a "factor in common".

So, the correct answer is (A) 400.
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