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If both the product and sum of four integers are even, which of the

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Bunuel
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If both the product and sum of four integers are even, which of the [#permalink] New post   04 Dec 2015, 00:46
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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
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D
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Re: If both the product and sum of four integers are even, which of the [#permalink] New post   04 Dec 2015, 02:11
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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


hi,
i)for the product of any number of integers to be even, only one number requires to be even...
ii) for any set numbers to have their sum to be even, the number ofodd numbers should be even...

with these two properties in mind..
for four int to have their product and sum as even..
2 and 4 are ok..
but 0 even number will result in an odd integer as product..
D
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Re: If both the product and sum of four integers are even, which of the [#permalink] New post   16 Jan 2017, 00:34
Nice Question.
Here is what i did in this one =>
Since the product is even => At-least one of them must be even.
Since the sum is even => Number of odd numbers must be even

Cases ->
E,E,E,E
E,E,O,O

Either all are even
or exactly 2 are even


Hence D.
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Re: If both the product and sum of four integers are even, which of the [#permalink] New post   03 Apr 2017, 22:19
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] New post   06 Apr 2017, 09:42
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] New post   12 Oct 2017, 23:46
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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] New post   25 Aug 2019, 18:52
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] New post   11 Sep 2021, 01:45
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Re: If both the product and sum of four integers are even, which of the [#permalink]
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