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Rectangle + Inequality

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by N:Dure » Wed Nov 24, 2010 4:31 am
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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 ≈ 1.28
    (2) (7x - 2) < -7 => x < -5/7 ≈ -0.71
Option A : -2/3 ≈ -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 ≈ 1.34 √

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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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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by N:Dure » Wed Nov 24, 2010 5:11 am
Great! Thanks alot Rahul!
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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 ≈ 1.28
    (2) (7x - 2) < -7 => x < -5/7 ≈ -0.71
Option A : -2/3 ≈ -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 ≈ 1.34 √

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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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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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 ≈ 1.28
    (2) (7x - 2) < -7 => x < -5/7 ≈ -0.71
Option A : -2/3 ≈ -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 ≈ 1.34 √

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
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