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# If both the products and sum of four integers are even, whic

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Joined: 06 Nov 2009
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If both the products and sum of four integers are even, whic [#permalink]

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12 Nov 2009, 15:32
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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
[Reveal] Spoiler: OA
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 258 [0], given: 31

Re: odd number/kaplan [#permalink]

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12 Nov 2009, 15:42
marcos4 wrote:
Dear All,
Here is the question :
"If both the product and sum of four integers are even, which of the following could be the number of even integers in the group ?"
Among the answers is "0", but it's a bad answer. I don't understand why and the explanation from the Kaplan is quite confusing for me.
Please S.M.S (Save My Soul) !
Thanks !
Marc

post the question and answers..
Math Expert
Joined: 02 Sep 2009
Posts: 35235
Followers: 6618

Kudos [?]: 85278 [1] , given: 10236

Re: odd number/kaplan [#permalink]

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12 Nov 2009, 15:55
1
KUDOS
Expert's post
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.
_________________
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Joined: 05 Mar 2008
Posts: 1473
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Kudos [?]: 258 [0], given: 31

Re: odd number/kaplan [#permalink]

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12 Nov 2009, 16:15
Bunuel wrote:
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:

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.

thanks bunuel...yes, definitely d
Intern
Joined: 06 Nov 2009
Posts: 4
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Kudos [?]: 1 [0], given: 2

Re: odd number/kaplan [#permalink]

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12 Nov 2009, 18:28
lagomez wrote:
marcos4 wrote:
Dear All,
Here is the question :
"If both the product and sum of four integers are even, which of the following could be the number of even integers in the group ?"
Among the answers is "0", but it's a bad answer. I don't understand why and the explanation from the Kaplan is quite confusing for me.
Please S.M.S (Save My Soul) !
Thanks !
Marc

post the question and answers..

I think I should have asked first, actually I don't know how editors like Kaplan react if you write the full question with the full answers from their book.

So I tried to copy only part of it as a "sample" but it wasn't enough to be understood.

Sorry !
Marc
Re: odd number/kaplan   [#permalink] 12 Nov 2009, 18:28
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# If both the products and sum of four integers are even, whic

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