Two Elementary Questions about GMAT Math

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boysangur: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Aug 14, 2010 2:57 pm

by boysangur » Tue Sep 07, 2010 3:42 pm

These are probably pretty dumb questions but I must finally clarify these.

1) As far as GMAT concerned, is 0 an even number? Princeton Review tells me it is NOT. Kaplan tells me it IS. Could someone clarify this for me once and for all? Is 0 an even number or not?

2) This one is a little longer but should be as easy for most of you to answer. I can't think of a non-confusing way to ask this so I will do it with an example of an OG problem. It gave the following equation: sqrt(3-2x) = sqrt(2x)+1, and asked for 4x^2.

What I did immediately was square both sides and I got: 3-2x=2x+1 but that was wrong because OG got: (sqrt(3-2x))^2 = (sqrt(2x)+1))^2. My mistake was that I squared each individual element instead of putting each side in parentheses and squaring that. However, after a few operations, OG divided equation 2-4x = 2sgrt(2x) by 2 and this time they divided each individual element by 2 and got 1-2x = sqrt(2x) instead of putting each side in parentheses and dividing them by 2. My question is why. Why did we have to put them in parentheses before squaring but not before dividing each side. And how would we go about multiplying each side?

Thank you for any help

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Source: Beat The GMAT — Quantitative Reasoning | Tue Sep 07, 2010 3:42 pm

KapTeacherEli: GMAT Instructor; Posts: 578; Joined: Tue Aug 25, 2009 6:00 pmFollowed by: 62 members; Thanked: 136 times

by KapTeacherEli » Tue Sep 07, 2010 10:57 pm

0/2 = 0, with no remainder. Thus 0 is even.

Playing with numbers will answer your second question. Try 4 + 2, for instance. Square it, and you get (4 + 2)^2 = 36; this does NOT equal 4^2 + 2^2 = 20. On the other hand, (4 + 2)/2 = 4/2 + 2/2 = 3. I'm sure there is a name for this property, but as a GMAT teacher, I've learned that memorizing math terms doesn't help to bubble in the correct answer

Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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Tani: Legendary Member; Posts: 1255; Joined: Fri Nov 07, 2008 2:08 pmFollowed by: 90 members; Location: St. Louis; Thanked: 312 times

by Tani » Fri Sep 10, 2010 8:32 pm

Zero is even because you do not get a remainder when you divide by 2. (The definition of even.)

To see why you have to put parentheses around those expressions before squaring them, simply substitute a number for x and try it both ways. You will see that you get different numbers. For example:

to square a + b

x = (a+b)^2 = a^2 + 2ab + b^2
NOT a^2 + b^2

so if a = 2 and b = 3

x = 2 + 3

x = 5
x^2 = 25

x^2 does not = 2^2 + 3^2 - that would give you 4 + 9 = 13

Tani Wolff

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