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If x is an integer, then x(x + 2)(x + 3) is a) odd

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Manager
Joined: 09 Jan 2007
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If x is an integer, then x(x + 2)(x + 3) is a) odd [#permalink]  09 Mar 2007, 09:53
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If x is an integer, then x(x + 2)(x + 3) is

a) odd whenever x is odd
b) even only when x is even
c) even only when x is odd
d) divisible by 3 when x is odd
e) divisible by 2
SVP
Joined: 01 May 2006
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x(x + 2)(x + 3)

We can analize 1 by 1 the answer choices

A) x is odd implies that y is odd ?

A fast way is to plug value... So, x=1
1*(1 + 2)*(1+3) = 12 = even

Wrong.

B) even only when x is even ?

We saw just before that if x is 1, we have an even. So no.

Wrong.

C) even only when x is odd ?

If x=0, then 0*(0+2)*(0+3) = 0 = even

Wrong.

D) divisible by 3 when x is odd ?

If x=5, 5*(5 + 2)*(5 + 3) = 5*7*2*2*2.... Not divisible by 3

Wrong.

E) divisible by 2 ?

Yes... By POE ... but, why not try to solve it?

Case 1 : x is odd and so x = 2*k+1 where k is an integer.

(2*k+1) * (2*k+1 + 2) * (2*k+1 + 3)
= (2*k+1) * (2*k+3) * (2*k+4)
= (2*k+1) * (2*k+3) * 2*(k+2)
= 2 * [(2*k+1) * (2*k+3) * (k+2)] ..... Divisible by 2 >>> OK

Case 2 : x is even and so x = 2*k where k is an integer.

(2*k) * (2*k + 2) * (2*k + 3)
= 2 * [(k) * 2 * (k+1) * (2*k+3)] ..... Divisible by 2 >>> OK
Senior Manager
Joined: 20 Feb 2007
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It is E!

By the way, I would like to share how I remember this odd-even-calculations-results. It may help in reducing long-time calculations. Of course, it helps me a lot.

Just remeber these keywords: e = even, o = odd, i = into (multiplication), p = plus, m = minus

1. eipmee (even *, +, - even = even)

2. opmoe (odd +, - odd = even)

3. opmeo (odd +, - even = odd)

4. oioo (odd * odd = odd)

5. oiee (odd * even = even)

It looks ridiculous but really a great help! You just remember these 5 silly words and pretty easy to go. Earlier I had difficulty to remember odd-even stuff and alsways used numbers to check but now it saves my time.

Thanks!
Manager
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DATA SUFFICIENCY [#permalink]  24 Mar 2007, 11:38
How will this apply to division?

IF M is an integer, is m odd?

1) m/2 is not an even integer.

2) m-3 is an even integer.

I can understand 2) 2. opmoe (odd +, - odd = even). Is 1 above sufficient, I'm actualy not even sure how you could divide an odd integer by 2 and come up with an odd integer.
Director
Joined: 14 Jan 2007
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the product x(x+2)(x+3) will always be even.
Why?
if x even, product will be even
if x odd, product will be odd*odd*even. hence even
hence will always be divisible by 2.
Senior Manager
Joined: 20 Feb 2007
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nfa1rhp wrote:

Quote:
How will this apply to division?

IF M is an integer, is m odd?

1) m/2 is not an even integer.

2) m-3 is an even integer.

I can understand 2) 2. opmoe (odd +, - odd = even). Is 1 above sufficient

I think if a statement has this term NOT something something...it might be a trap.

So for (1) not an even integer = odd int or fraction

Now we can read this question like this:

If m is an integer, is m odd?
(1) m/2 = odd int or fraction so m can be 10, 11, 14 (odd or even) since m/2 can be 5 (odd int) or 5.5 (fraction) INSUFF

(2) m-3 = even integer. SUFF

What is OA for this question?

Last edited by Summer3 on 28 Mar 2007, 15:54, edited 1 time in total.
Senior Manager
Joined: 11 Feb 2007
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E.

x(x + 2)(x + 3)

plug in an odd number for x, (x + 3) will make it even for you~

plug in an even number for x, (x + 2) (or x itself!) will make it even for you~

either way you get an even number so is divisible by two~~

"An 800 test taker, rather than attempting to prove every other answer choices wrong, gets to the right choice using mathematical reasoning."
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