If A,B,C are three integers and AB+C is even . . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If A,B,C are three integers and AB+C is even . . . .

by VJesus12 » Sat Jan 06, 2018 4:15 am

If A, B, C are three integers and AB+C is even; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even

1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them

The OA is the option E.

I don't know how to solve this PS question. Experts I need your help. I'd be thankful.

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Source: Beat The GMAT — Problem Solving | Sat Jan 06, 2018 4:15 am

elias.latour.apex: Master | Next Rank: 500 Posts; Posts: 228; Joined: Thu Apr 20, 2017 1:02 am; Location: Global; Thanked: 32 times; Followed by:3 members; GMAT Score:770

by elias.latour.apex » Sat Jan 06, 2018 10:35 am

To make things easy, let us assume that our odd numbers are 1 and that our even numbers are 2.

AB+C is even.
So what if C is 1? Then AB must also be odd. In other words, all three numbers must be 1 (odd).
What if C is 2? Then AB must also be even. So AB must equal 2 or 4.

So these are our options:

1) 1,1,1
2) 2,1,2
3) 1,2,2
4) 2,2,2

The first answer suggests that A+C must be even. But this is proved false by scenario 3.
The second answer suggests that B+C must be even. But this is proved false by scenario 2.
The third answer suggests that ABC must be even. But this is proved false by scenario 1.

Thus, (E) must be the best answer.

Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Jan 06, 2018 11:24 am

Hi VJesus12,

We're told that A, B, C are all integers and (A)(B)+C is EVEN. We're asked which of the following MUST be true (meaning "which of these things is ALWAYS TRUE no matter how many different examples we come up with?"). This question can be answered by TESTing VALUES or using Number Property Rules.

To start, since (A)(B) + C = an EVEN, there are a limited number of possible 'combinations' of Odds and Evens that will 'fit' here:

(Even)(Even) + (Even) = Even
(Even)(Odd) + (Even) = Even
(Odd)(Even) + (Even) = Even
(Odd)(Odd) + (Odd) = Even

A)A+C is even

In the 3rd example, this is NOT true. Eliminate Answer B and Answer D.

B)B+C is even

In the 2nd example, this is NOT true. Eliminate Answer C.

C)ABC is even

In the 4th example, this is NOT true. Eliminate Answer A.

There's only one answer remaining...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Aug 11, 2019 6:35 pm

VJesus12 wrote:If A, B, C are three integers and AB+C is even; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even

1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them

Since AB + C is even, we can have:

Case 1: A, B, and C are all odd,

or

Case 2: A, B, and C are all even,

or

Case 3: A is odd and B and C are even,

or

Case 4: B is odd and A and C are even.

Now let's analyze the three given statements.

If it's case 3, A + C is odd and thus it's not even.

If it's case 4, B + C is odd and thus it's not even.

If it's case 1, ABC is odd and thus it's not even.

Thus, none of the scenarios have to be true.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]