GMAT Prep Inequalities: ?Best way to attack?

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euro: Master | Next Rank: 500 Posts; Posts: 120; Joined: Thu Sep 02, 2010 8:56 am; Location: India; Thanked: 7 times; GMAT Score:730

by euro » Sat Oct 30, 2010 5:56 am

If zt < -3, is z < 4?

(1) z < 9

(2) t < -4

OA is [spoiler](E)[/spoiler]

What is the best way to attack a problem like this?

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 30, 2010 5:56 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Oct 30, 2010 8:07 am

euro wrote:If zt < -3, is z < 4?

(1) z < 9
(2) t < -4

OA is [spoiler](E)[/spoiler]

What is the best way to attack a problem like this?

Given: zt < -3 => z and t are of opposite sign.

Statement 1: z < 9
z may be positive/ negative => t may be negative/positive.
Also not possible to determine whether z < 4 or not. As for t = -5, z = 3 or 5 both satisfies the given inequality: zt < -3

Not sufficient.

Statement 2: t < -4
t is negative => z is positive.
But not possible to determine whether z < 4 or not. As for t = -5, z = 3 or 5 both satisfies the given inequality: zt < -3

Not sufficient.

1 & 2 Together: t < -4 and 0 < z < 9
Taking the same example, t = -5, z = 3 or 5 both satisfies the given inequality: zt < -3
Therefore, z may or may not be less than 4.

Not sufficient.

The correct answer is E.

Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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euro: Master | Next Rank: 500 Posts; Posts: 120; Joined: Thu Sep 02, 2010 8:56 am; Location: India; Thanked: 7 times; GMAT Score:730

by euro » Sat Oct 30, 2010 9:35 am

Great work Rahul. Thanks!

I really like how you quickly deduced (from the stem) that 'z' and 't' are of opposite signs.

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sat Oct 30, 2010 9:53 am

euro wrote:Great work Rahul. Thanks!

I really like how you quickly deduced (from the stem) that 'z' and 't' are of opposite signs.

For two real numbers a and b,

(1) ab > 0 implies a and b are of same sign.
(2) ab < 0 implies a and b are of opposite sign.

Because,

(1) (+ve)*(+ve) = +ve
(2) (+ve)*(- ve) = - ve
(3) (- ve)*(+ve) = - ve
(4) (- ve)*(- ve) = +ve

Hope it is clear now.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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