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12 Nov 2009, 15:32
Kudos
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D
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Difficulty:
35%
(medium)
Question Stats:
79% (01:13) correct
21%
(01:00)
wrong
based on 33
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If both the products and sum of four integers are even, which of the following could be the number of even integers in the group?
I. 0
II. 2
III. 4
A. I only
B. II only
C. III only
D. II and III
E. I, II, III
I. 0
II. 2
III. 4
A. I only
B. II only
C. III only
D. II and III
E. I, II, III
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12 Nov 2009, 15:55
Kudos
Bookmarks
Welcome to the forum Marcos4.
Edited your post. Added the original question as I had it in my database. Also moved the topic to the Problem Solving forum from DS forum.
As for the question:
If both the products and sum of four integers are even, which of the following could be the number of even integers in the group?
I. 0
II. 2
III. 4
A. I only
B. II only
C. III only
D. II and III
E. I, II, III
a+b+c+d=even and a*b*c*d=even.
For the sum of 4 integers to be even, group should contain 0, 2 or 4 even numbers. So possible scenarios are 0, 2, or 4 even numbers among 4.
For the product of the integers to be even at least one of them should be even. So 1, 2, 3, or all 4 numbers from a,b,c,d should be even. If there is 0 even number among them, it means that all 4 integers are odd, the product of four odd integers is odd. Hence there can not be 0 even number. So possible scenarios are 1, 2, 3 or 4 even numbers among 4.
Both conditions to be met: there can be 2 or 4 even numbers among 4.
So the answer is D.
Edited your post. Added the original question as I had it in my database. Also moved the topic to the Problem Solving forum from DS forum.
As for the question:
If both the products and sum of four integers are even, which of the following could be the number of even integers in the group?
I. 0
II. 2
III. 4
A. I only
B. II only
C. III only
D. II and III
E. I, II, III
a+b+c+d=even and a*b*c*d=even.
For the sum of 4 integers to be even, group should contain 0, 2 or 4 even numbers. So possible scenarios are 0, 2, or 4 even numbers among 4.
For the product of the integers to be even at least one of them should be even. So 1, 2, 3, or all 4 numbers from a,b,c,d should be even. If there is 0 even number among them, it means that all 4 integers are odd, the product of four odd integers is odd. Hence there can not be 0 even number. So possible scenarios are 1, 2, 3 or 4 even numbers among 4.
Both conditions to be met: there can be 2 or 4 even numbers among 4.
So the answer is D.
