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Re: If both the product and sum of four integers are even, which of the [#permalink]
Even if one number in the series is even, the product of the numbers become even.
e.g. 2*3*3*1= 18

For the sum to be even, the odd numbers must be even. For example: 3+3=6 (two 3's)
2+2+3+3= 10
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Re: If both the product and sum of four integers are even, which of the [#permalink]
Expert Reply
Bunuel wrote:
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?

I. 0
II. 2
III. 4

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III


Let’s test each Roman numeral.

I. 0

Since we need at least 1 even integer in the set for the product of 4 integers to be even, there could not be 0 even integers in the set.

II. 2

If there are 2 even numbers in the set, there also would be 2 odd numbers. Furthermore, the sum of 2 even integers and 2 odd integers is even, and the product of 2 even integers and 2 odd integers is even. There could be 2 even integers in the set.

III. 4

Since the sum of 4 even integers is even and the product of 4 even integers is even, there could be 4 even integers in the set.

Answer: D
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Re: If both the product and sum of four integers are even, which of the [#permalink]
Expert Reply
Bunuel wrote:
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?

I. 0
II. 2
III. 4

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III


Given: 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.

Answer: D.
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Re: If both the product and sum of four integers are even, which of the [#permalink]
Expert Reply
Bunuel wrote:
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?

I. 0
II. 2
III. 4

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III


If there are 0 even integers in the group, the product would be odd.

If there are 2 even and 2 odd integers in the group, both the product and sum will be even.

If there are 4 even integers in the group, both the product and sum will be even.

Answer: D
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Re: If both the product and sum of four integers are even, which of the [#permalink]
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Re: If both the product and sum of four integers are even, which of the [#permalink]
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