Integer Properties

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 13, 2008 11:09 am

If x is an integer, and k= (x –1)(x +2) –(x –1)(x –2), then which of the following must be true?

(A) k is odd only when x is odd.
(B) k is odd only when x is even.
(C) k is even only when x is even.
(D) k is even only when x is odd.
(E) None of the above.

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Source: Beat The GMAT — Problem Solving | Sat Dec 13, 2008 11:09 am

tdadic84: Master | Next Rank: 500 Posts; Posts: 111; Joined: Sat Sep 27, 2008 12:41 pm; Thanked: 1 times

by tdadic84 » Sat Dec 13, 2008 11:16 am

plug in numbers to test it

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 13, 2008 11:19 am

That's one method.
There are at least three methods that can be used.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Dec 13, 2008 12:55 pm

Please post official answers using spoiler function when posting questions!

Eg: OA : WHATEVER THE OA IS

I am getting none of the above.

x-1 (x+2-x+2) = k
4 * x-1 = k

Always even....

What is the answer by the way??

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 13, 2008 5:22 pm

Sorry about not supplying the OA. I'm pretty new to the site.

The answer is E.

One way is to treat the question generically and ask what would happen if: 1) x is odd and 2) x is even

1) x is odd --> k =(odd-1)(odd+2)-(odd-1)(odd-2)
= (even)(odd)-(even)(odd)
= (even)-(even)
= even

2) x is even --> k =(even-1)(even+2)-(even-1)(even-2)
= (odd)(even)-(odd)(even)\
= (even)-(even)
= even

k is always even so the correct answer is E
-------------------------

Another method is to simplify (x –1)(x +2) –(x –1)(x –2)
When we do that we get k = 4(x-1)
We can see here that k will always be even for any integer x.
So the answer is still E.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Sat Dec 13, 2008 5:25 pm

Brent Hanneson wrote:Sorry about not supplying the OA. I'm pretty new to the site.

The answer is E. .

Don't feel bad Brent. Cramya is a software. Beat the Gmat installed it on math forums to help people solving problems and warn people about using the spoiler function. If you dont want to see its messages simply press:

CTRL+ALT+C

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Dec 13, 2008 6:27 pm

Sorry about not supplying the OA. I'm pretty new to the site.

Brent,
Not a problem ;welcome to this forum!

Cramya is a software

If you dont want to see its messages simply press:

CTRL+ALT+C

By the way think of me either as a software or a fictional character (like Robin in Batman) and I also do one other thing in addition to what Logitech mentioned.

Protect this forum as much as possible from JOKER (guess who that is its my buddy Logitech - should have seen the other icon picture that he posted; seriously for a while I thought the Joker character from batman movies came out to take the GMAT) Jus kidding!:-) Logitech is awesome too as I have seem some excellent posts from him on this forum

Sometimes he does slip from my watchful eyes and posts funny sh.. t (or should I say stuff...) like above. I got to watch him like a hawk to make sure he is on track...

Dont take any of this seriously as we just like taking humurous jabs at each other for fun sake and that gets us going....

Again good luck with ur preps. We are all here to help each other. Keep posting the good questions.

Regards,
Cramya

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 13, 2008 8:16 pm

Thanks cramya and logitech.
Great site!

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