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# M03#35

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Manager
Joined: 23 Oct 2009
Posts: 84
Location: New Delhi, India
Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia

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03 Jan 2011, 01:09
Official Explanation:
Statement (1) by itself is sufficient. All the variables equal zero, and the product of the variables is zero; therefore their product is even.
My issue here is: is 0 an even number? I thought it was neither even nor odd. I've made flashcards where I put in this statement, but I don't remember the source. So I'm confused about 0 now. Help?!

Statement (2) by itself is insufficient. The variables can be either odd or even. If all the variables are even, their product is even; if they are odd, their product is odd.
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Math Expert
Joined: 02 Sep 2009
Posts: 39723

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03 Jan 2011, 04:16
gmatdelhi wrote:
Official Explanation:
Statement (1) by itself is sufficient. All the variables equal zero, and the product of the variables is zero; therefore their product is even.
My issue here is: is 0 an even number? I thought it was neither even nor odd. I've made flashcards where I put in this statement, but I don't remember the source. So I'm confused about 0 now. Help?!

Statement (2) by itself is insufficient. The variables can be either odd or even. If all the variables are even, their product is even; if they are odd, their product is odd.

Zero is an even integer.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form $$n=2k$$, where $$k$$ is an integer.

So for $$k=0$$ --> $$n=2*0=0$$.

For more on number properties check: math-number-theory-88376.html

As for the question:

Is the product abcd even?

(1) a^2+b^2+c^2+d^2=0 --> number squared is always non-negative (zero or positive), so the sum of 4 non-negative values to be 0 then each must be zero, so abcd=0=even. Sufficient.

(2) a=b=c=d. Clearly insufficient.

Hope it's clear.
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03 Jan 2011, 10:32
Thank you so much Bunuel! Explanation's great!
_________________

1st Feb '11 -- Actual GMAT : 730 (Q48 V42) AWA 6.0

My Practice GMAT Scores
29th Jan '11 -- GMATPrep#2 : 700 (Q47 V38)
23rd Jan '11 -- MGMAT Practice Test #3 : 670 (Q45 V36)
19th Jan '11 -- GMATPrep#1 v.1 : 710 (Q49 V37)
15th Jan '11 -- GMATPrep#1 : 720 (Q47 V42)
11th Jan '11 -- MGMAT Practice Test #2 : 740 (Q47 V44)
6th Jan '11 -- Kaplan#2 : 620 (Q40 V35)
28th Dec '10 -- PowerPrep#1 : 670 (Q47 V35)
30th Oct '10 -- MGMAT Practice Test #1 : 660 (Q45 V35)
12th Sept '10 -- Kaplan Free Test : 610 (Q39 V37)
6th Dec '09 -- PR CAT #1 : 650 (Q44 V37)
25th Oct '09 -- GMATPrep#1 : 620 (Q44 V34)

If you feel like you're under control, you're just not going fast enough.
A goal without a plan is just a wish.
You can go higher, you can go deeper, there are no boundaries above or beneath you.

Re: M03#35   [#permalink] 03 Jan 2011, 10:32
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# M03#35

Moderator: Bunuel

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