Rectangle + Inequality

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N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Wed Nov 24, 2010 4:31 am

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Source: Beat The GMAT — Problem Solving | Wed Nov 24, 2010 4:31 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 » Wed Nov 24, 2010 4:49 am

Question Number 1:

|3x - 2 + 4x| > 7 => |7x - 2| > 7, which results in two cases:

(1) (7x - 2) > 7 => x > 9/7 â‰ˆ 1.28
(2) (7x - 2) < -7 => x < -5/7 â‰ˆ -0.71

Option A : -2/3 â‰ˆ -0.67 X
Option B : -1/2 = -0.50 X
Option C : 3/4 = 0.75 X
Option D : 5/4 = 1.25 X
Option E : 4/3 â‰ˆ 1.34 âˆš

The correct answer is E.

After getting |7x - 2| > 7, we can plug the options also.

Last edited by Rahul@gurome on Wed Nov 24, 2010 4:57 am, edited 1 time in total.

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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 » Wed Nov 24, 2010 4:56 am

Question Number 2:

The lengths of the sides of the rectangular pool are a feet and b feet.
Width of the walkaway is 3 feet.

Thus, width of the (pool + walkaway) = (a + 3 + 3) feet = (a + 6) feet
and length of the (pool + walkaway) = (b + 3 + 3) feet = (b + 6) feet

Area of the pool = ab sq. feet
Area of the (pool + walkaway) = (a + 6)*(b + 6) sq. feet

Area of the walkaway = [(a + 6)(b + 6) - ab] sq. feet = (6a + 6b + 36) sq. feet

The correct answer is D.

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N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Wed Nov 24, 2010 5:11 am

Great! Thanks alot Rahul!

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blaster: Master | Next Rank: 500 Posts; Posts: 233; Joined: Mon Jun 09, 2008 1:30 am; Thanked: 5 times

by blaster » Thu Nov 25, 2010 12:09 am

Rahul@gurome wrote:Question Number 1:

|3x - 2 + 4x| > 7 => |7x - 2| > 7, which results in two cases:
(1) (7x - 2) > 7 => x > 9/7 â‰ˆ 1.28
(2) (7x - 2) < -7 => x < -5/7 â‰ˆ -0.71
Option A : -2/3 â‰ˆ -0.67 X
Option B : -1/2 = -0.50 X
Option C : 3/4 = 0.75 X
Option D : 5/4 = 1.25 X
Option E : 4/3 â‰ˆ 1.34 âˆš

The correct answer is E.

After getting |7x - 2| > 7, we can plug the options also.

Am gettin that answers also (9/7:-5/7) . But can you please explain how you came to E?

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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 » Thu Nov 25, 2010 1:40 am

blaster wrote: After getting |7x - 2| > 7, we can plug the options also.

Am gettin that answers also (9/7:-5/7) . But can you please explain how you came to E?[/quote]

If you've got the interval (-5/7, 9/7), then observe that the inequality will be satisfied if x lies outside that interval. Only option E lies outside the interval.

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Thu Nov 25, 2010 1:49 am

blaster wrote:
Rahul@gurome wrote:Question Number 1:

|3x - 2 + 4x| > 7 => |7x - 2| > 7, which results in two cases:
(1) (7x - 2) > 7 => x > 9/7 â‰ˆ 1.28
(2) (7x - 2) < -7 => x < -5/7 â‰ˆ -0.71
Option A : -2/3 â‰ˆ -0.67 X
Option B : -1/2 = -0.50 X
Option C : 3/4 = 0.75 X
Option D : 5/4 = 1.25 X
Option E : 4/3 â‰ˆ 1.34 âˆš

The correct answer is E.

After getting |7x - 2| > 7, we can plug the options also.

Am gettin that answers also (9/7:-5/7) . But can you please explain how you came to E?

Question ask for a possible value of X, and per rule of inequalities ,

When mod(something) > some value
|x| > z
then x<-z OR x>z
Simply to remember: x does not lie between negative and positive values of z

1.28 to -0.71 All other values lie between this except the option E,
So as Rahul say It is the right Answer,

KVCPK has given a very good explanation on this, one, if you want you can take a look at ,
https://www.beatthegmat.com/is-a-quot-x- ... tml#309367

Saurabh Goyal
[email protected]
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EveryBody Wants to Win But Nobody wants to prepare for Win.

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