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05 Mar 2020, 06:57
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B
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Difficulty:
45%
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Question Stats:
63% (01:31) correct
37%
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wrong
based on 204
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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
firas92
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Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
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05 Mar 2020, 07:44
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a can be any prime, lets say a=13
b must be a prime divisible by 5, b=5 is the only option
c can be any integer divisible by 5, lets say c=15
d must be an even prime which is divisible by 5. We know that 2 is the only even prime but 2 is not divisible by 5
So d must be empty
e is an even prime so e=2
f is an even integer divisible by 5, lets say f=10
g is any even number, lets say g=4
h is a non prime odd number which is not divisible by 5, lets say h=9
So we can fill all areas except d
Answer is (B)
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b must be a prime divisible by 5, b=5 is the only option
c can be any integer divisible by 5, lets say c=15
d must be an even prime which is divisible by 5. We know that 2 is the only even prime but 2 is not divisible by 5
So d must be empty
e is an even prime so e=2
f is an even integer divisible by 5, lets say f=10
g is any even number, lets say g=4
h is a non prime odd number which is not divisible by 5, lets say h=9
So we can fill all areas except d
Answer is (B)
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06 Mar 2020, 07:11
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GMATPrepNow
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
