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# If the sum of three integers is even, is the product of the three

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Math Expert
Joined: 02 Sep 2009
Posts: 47033
If the sum of three integers is even, is the product of the three [#permalink]

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10 Aug 2017, 04:39
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55% (hard)

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56% (00:47) correct 44% (01:05) wrong based on 125 sessions

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If the sum of three integers is even, is the product of the three integers a multiple of 4 ?

(1) All three integers are equal.

(2) All three integers are even.

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Joined: 09 Jul 2017
Posts: 3
Re: If the sum of three integers is even, is the product of the three [#permalink]

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10 Aug 2017, 05:14
E
Because 0 is an even integer
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Joined: 18 May 2017
Posts: 54
If the sum of three integers is even, is the product of the three [#permalink]

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Updated on: 10 Aug 2017, 23:07

Statement 1: as the the sum of the three integers is even, and as all three integers are equal to each other, we can conclude that all numbers are even integers (even + even + even = even while odd + odd + odd = odd). In this case the multiplication is necessarily a multiple of 4: If one of the number is zero the multiplication also equal to zero and thus a multiple of 4 (zero is a multiple of all integers) and If non of the numbers is equal to zero the multiplication has at least 3 two's (because each of the numbers is even) and thus the product is necessarily a multiple of 4. Sufficient.

Statement 2: this statement state explicitly the conclusion we inferred from the first statement. Thus the analysis is the same. Sufficient.

Originally posted by oryahalom on 10 Aug 2017, 06:26.
Last edited by oryahalom on 10 Aug 2017, 23:07, edited 1 time in total.
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Re: If the sum of three integers is even, is the product of the three [#permalink]

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10 Aug 2017, 06:30
oryahalom wrote:

Statement 1: as the the sum of the three integers is even, and as all three integers are equal to each other, we can conclude that all numbers are even integers (even + even + even = even while odd + odd + odd = odd). In this case the multiplication is necessarily a multiple of 4: If one of the number is zero the multiplication also equal to zero and thus a multiple of 4 (zero is a multiple of all integers) and If non of the numbers is equal to zero the multiplication has at least 3 two's (because each of the numbers is even) and thus the product is necessarily a multiple of 4. Sufficient.

Statement 2: this statement state explicitly the conclusion we infer from the first statement. Thus the analysis is the same. Sufficient.

You are right. I looked it up, 0 is also a multiple of 4
Math Expert
Joined: 02 Aug 2009
Posts: 6217
Re: If the sum of three integers is even, is the product of the three [#permalink]

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10 Aug 2017, 07:05
Bunuel wrote:
If the sum of three integers is even, is the product of the three integers a multiple of 4 ?

(1) All three integers are equal.

(2) All three integers are even.

Ways SUM of three integers can be even..
1) O+O+E....
2) E+E+E

Now let's see the two cases..
1) O+O+E...
Here the product will surely be Even but will depend onvalue of E to know if PRODUCT is multiple of 4..
If E is MULTIPLE of 4, product is otherwise not
2) E+E+E..
In all cases and will be YES..

Let's see the statements..
1) All three integers are EQUAL..
Only possibility is that all are even and case (2) above follows..
Sufficient
2) All three integers are even..
Again case (2) ..
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If the sum of three integers is even, is the product of the three [#permalink]

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10 Aug 2017, 11:34
Bunuel wrote:
If the sum of three integers is even, is the product of the three integers a multiple of 4 ?

(1) All three integers are equal.

(2) All three integers are even.

x+y+z = even
xyz = 4n ?

1) x = y = z
and x + y + z = even
=> x = y = z = even
xyz = 4n (3 even numbers will have at least 3 pairs of 2)
Sufficient.

2) x = y = z = even
Same as 1. Sufficient.

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Joined: 13 Mar 2013
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Re: If the sum of three integers is even, is the product of the three [#permalink]

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12 Aug 2017, 01:45
If the sum of three integers is even, is the product of the three integers a multiple of 4 ?

(1) All three integers are equal.

(2) All three integers are even.

As per the question :
SUM of three integers can be even..
1) O+O+E....
2) E+E+E
As per the statement

1) All three integers are EQUAL..
Only possibility is that all are even and case (2) above follows..
Sufficient
2) All three integers are even..
Again case (2) ..
Sufficient

D
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Intern
Joined: 09 Mar 2017
Posts: 4
Re: If the sum of three integers is even, is the product of the three [#permalink]

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11 Oct 2017, 08:45
Bunuel wrote:
If the sum of three integers is even, is the product of the three integers a multiple of 4 ?

(1) All three integers are equal.

(2) All three integers are even.

Why we're not considering 0 as an even number here ?
Math Expert
Joined: 02 Sep 2009
Posts: 47033
Re: If the sum of three integers is even, is the product of the three [#permalink]

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11 Oct 2017, 09:08
priyanknema wrote:
Bunuel wrote:
If the sum of three integers is even, is the product of the three integers a multiple of 4 ?

(1) All three integers are equal.

(2) All three integers are even.

Why we're not considering 0 as an even number here ?

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check below for more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: If the sum of three integers is even, is the product of the three   [#permalink] 11 Oct 2017, 09:08
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