MGMAT CAT #2 PS Question Again

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EMAN: Master | Next Rank: 500 Posts; Posts: 162; Joined: Sun Aug 09, 2009 4:17 pm; Location: Minnesota; Thanked: 1 times

by EMAN » Sun Nov 08, 2009 4:02 pm

If a, b, c, and d are integers and ab2c3d4 > 0, which of the following must be positive?

I. a^2cd
II. bc^4d
III. a^3c^3d^2

Which of the above choices must be positive?

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Source: Beat The GMAT — Problem Solving | Sun Nov 08, 2009 4:02 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: MGMAT CAT #2 PS Question Again

by Stuart@KaplanGMAT » Mon Nov 09, 2009 10:14 am

EMAN wrote:If a, b, c, and d are integers and ab2c3d4 > 0, which of the following must be positive?

I. a^2cd
II. bc^4d
III. a^3c^3d^2

Which of the above choices must be positive?

Please:

1) use brackets to separate terms so we can see where the exponents lie (the question stem isn't clear); and

2) provide the answer choices so we can discuss not only algebra, but also question strategy.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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JohnRapp: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Thu Sep 15, 2011 9:41 am

by JohnRapp » Wed Nov 02, 2011 1:26 pm

If a, b, c, and d are integers and (a)(b^2)(c^3)(d^4) > 0, which of the following must be positive?

I. (a^2)(c)(d)
II. (b)(c^4)(d)
III. (a^3)(c^3)(d^2)

I only
II only
III only
I and III
I, II, and III

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Wed Nov 02, 2011 10:57 pm

From this expression (a)(b^2)(c^3)(d^4) > 0
We can tell - 'a' and 'c' should have the same sign (Both +ve or both -ve)
'b' and 'd' can either be +ve or -ve.

Now use these and try to get a -ve answer from the choices.

I - (a^2)(c)(d) = a^2-always positive. c*d=could be +ve or -ve (both same signs +ve / both opposite signs -ve)

II - (b)(c^4)(d) = c^4-always +ve. b*d again could be +ve or -ve.

III - (a^3)(c^3)(d^2) = (a^3)(c^3)[Always +ve because 'a' and 'c' always have the same sign and (d^2) is always +ve)

C IMO

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