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If the above Venn diagram were filled with all integers

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If the above Venn diagram were filled with all integers

by Brent@GMATPrepNow » Fri Mar 06, 2020 6:10 am

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If the above Venn diagram were filled with all integers greater than 1, how many of the regions marked with a letter (from a to h) would be empty?

A) 0
B) 1
C) 2
D) 3
E) 4

Answer: B
Source: www.gmatprepow.com
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If the above Venn diagram were filled with all integers

by Brent@GMATPrepNow » Mon Mar 09, 2020 6:10 am
Brent@GMATPrepNow wrote: ↑
Fri Mar 06, 2020 6:10 am
 Image

If the above Venn diagram were filled with all integers greater than 1, how many of the regions marked with a letter (from a to h) would be empty?

A) 0
B) 1
C) 2
D) 3
E) 4

Answer: B
Source: www.gmatprepow.com
Let's start filling in each region, starting with a

a) 3 works here, since it's a prime number, but it's neither even nor divisible by 5
b) 5 works here (it's prime AND it's divisible by 5)
c) 15 (divisible by 5, but neither even nor prime)
d) EMPTY. In order for a number to be in this region, it must be prime AND divisible by both 2 and 5. There is no such number.
e) 2 is is both prime and even
f) 10 is even and divisible by 5 (but not prime)
g) 4 is even, but neither prime nor divisible by 5
h) 9 works here

So, only one region is left empty

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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