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13 Jul 2021, 05:00
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E
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Difficulty:
5%
(low)
Question Stats:
86% (01:23) correct
14%
(01:40)
wrong
based on 111
sessions
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If a + b + c + d + e is odd, and a, b, c, d, and e are integers, which of the following could be the number of integers among a, b, c, d, and e that are even?
I. 0
II. 2
III. 4
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
I. 0
II. 2
III. 4
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
13 Jul 2021, 05:08
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Bunuel
a + b + c + d + e = odd
even+even = even
Odd + odd = Even
therefore, Either there should be one odd and 4 even e.g. e+e+e+e+o = o
OR there should be three odd and 2 even e.g. e+e+o+o+o = o
OR there should be five odd and 0 even e.g. o+o+o+o+o = o
Answer: Option E
13 Jul 2021, 05:40
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E.
Small recap about Even & ODD :
#1 O+O= E (Whenever there are an even number of odd integers, the sum of the corresponding integers is Even- Always)
#2 O+O+O=O (Whenever there are an odd number of odd integers, the sum of the corresponding integers is ODD- Always)
#3 E+E= E
E+E+E= E
(Whenever there are even/odd numbers of even integers, the sum of the corresponding integers is Even- Always)
Approach :
What we can infer from above? If we have an odd number of integers as odd, then the sum of those integers definitely be ODD.
1. 0 even integers=> 5 odd integers=> sum of a,b,c,d,e = ODD. Possibility
2. 2 even integers=> 3 odd integers=> sum of 3 odd integers (refer #2 above) + sum of 2 even integers( refer #3 above) = ODD. Possibility
3. 4 even integers=> 1 odd integer=> sum of 1 odd integer (refer #2 above) + sum of 4 even integers( refer #3 above) = ODD. Possibility
Thus, all three are possible. Hence E.
Hit Kudos, If you love logic and like simple approaches
Small recap about Even & ODD :
#1 O+O= E (Whenever there are an even number of odd integers, the sum of the corresponding integers is Even- Always)
#2 O+O+O=O (Whenever there are an odd number of odd integers, the sum of the corresponding integers is ODD- Always)
#3 E+E= E
E+E+E= E
(Whenever there are even/odd numbers of even integers, the sum of the corresponding integers is Even- Always)
Approach :
What we can infer from above? If we have an odd number of integers as odd, then the sum of those integers definitely be ODD.
1. 0 even integers=> 5 odd integers=> sum of a,b,c,d,e = ODD. Possibility
2. 2 even integers=> 3 odd integers=> sum of 3 odd integers (refer #2 above) + sum of 2 even integers( refer #3 above) = ODD. Possibility
3. 4 even integers=> 1 odd integer=> sum of 1 odd integer (refer #2 above) + sum of 4 even integers( refer #3 above) = ODD. Possibility
Thus, all three are possible. Hence E.
Hit Kudos, If you love logic and like simple approaches
