Integer

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govind_raj_76: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Apr 20, 2010 7:16 pm; Location: Newark, DE

by govind_raj_76 » Sun Jun 13, 2010 1:23 pm

If a and b are odd inetegers, which of the following is necessarily true ?

a) ab is even.

b) ab(a-1)(b-1) is divisible by 8.

c) ab(a+1)(b+1) is divisible by 8.

d) a^2 - B^2 is divisible by 8.

e) a^2b is divisible by 3.

Govind

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Source: Beat The GMAT — Problem Solving | Sun Jun 13, 2010 1:23 pm

tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Sun Jun 13, 2010 1:58 pm

This about number properties - specifically even/odd which is often best tested by pluggin in numbers when you don't knwo the rule. But this question is badly written because if you plug in 1 for each of the answers you see that none of them have to be true. Even if you assume the question says if a and b are distinct odd integers then you have to make them different and you see that if you plug in 1 and -1 they are all false - can you give me the source of the question?

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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sogmat: Master | Next Rank: 500 Posts; Posts: 113; Joined: Tue Oct 21, 2008 9:43 pm; Location: Mumbai; Thanked: 1 times

by sogmat » Sun Jun 13, 2010 4:52 pm

I think the question should state if If a and b are positive odd integers, then only c holds true, try plugging in 1 for all choices then only c holds true

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Sun Jun 13, 2010 5:12 pm

c doesn't work if they are both 1 becuase 1(2)(2) - is not divisible by 8.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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sandy_online: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Apr 25, 2009 11:40 am; Thanked: 2 times

by sandy_online » Mon Jun 14, 2010 1:01 am

problems says which option is necessarily true.
so if we look at answer choices then except D other may or may not be true.
So i think option D is correct one.
options:
A) is false as ab will always be odd
B) in ab(a-1)(b-1), there are two even numbers and to be divisible by 8 there has to be at
least 3 even nmbers( three 2's), so this may or may not be correct
C) similar reasoning as B , this may or may not be correct.
D) is correct, always divisible by 8
E) similar reasoning as B & C.

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