Help with advanced question

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leswm: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri May 04, 2007 10:58 pm

by leswm » Thu May 17, 2007 7:31 pm

I found the manhattan gmat question of the week:

If abc is not 0, what is the value of ? (a^3 + b^3 + c^3) / abc
( a^3 is a-cubed, b^3 is b-cubed...)

(1) |a|=1, |b|=2, |c|=3

(2) a + b + c = 0

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements together are sufficient, but NEITHER statement alone is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

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My answer was B, but it was after I plugged in and that took a while. Is there some property of numbers that can help me solve this one quick?

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Source: Beat The GMAT — Data Sufficiency | Thu May 17, 2007 7:31 pm

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

Re: Help with advanced question

by jayhawk2001 » Thu May 17, 2007 9:39 pm

leswm wrote:I found the manhattan gmat question of the week:

If abc is not 0, what is the value of ? (a^3 + b^3 + c^3) / abc
( a^3 is a-cubed, b^3 is b-cubed...)

(1) |a|=1, |b|=2, |c|=3

(2) a + b + c = 0

(a+b+c)^3 = a^3 + b^3 + c^3 +3ab(a+b+c) + 3bc(a+b+c) + 3ac(a+b+c) - 3abc

2 tells us that a+b+c = 0. So, a^3+b^3+c^3 = 3abc

So, (a^3+b^3+c^3) / abc = 3 always

Hence B

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Fri May 18, 2007 5:38 am

I found the manhattan gmat question of the week:

If abc is not 0, what is the value of ? (a^3 + b^3 + c^3) / abc
( a^3 is a-cubed, b^3 is b-cubed...)

(1) |a|=1, |b|=2, |c|=3

(2) a + b + c = 0

Statement I : Clearly insufficient since we do not know the actual values...we only know absolute values; hence the value of the equation can swing in many directions depending on actual values

Statement II : We can derive that all the 3 values do not have the same sign since none of them are 0; hence if a =3, b=2 and d=-5 value of the equation would be 3
Plug in any value and you will get the same answer

hence B

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