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Algebra

This topic has 5 expert replies and 2 member replies

Algebra

Post Sat Apr 11, 2015 9:44 am
1. Last Sunday a certain store sold copies of Newspaper A for 1.00 each and copies of Newspaper B for 1.25. each, and the store sol no other newspapers that day. If r percent of the store's revenue from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of Newspaper A, which of the following express r in terms of p?

A) 100p/125-p
B) 150p/250 - p
C) 300p/375-p
D) 400p/500-p
E) 500p/625-p

How to I calculate this quickly?


2.

(x+1)^2/(X-1)^2

If x is not = 0 or 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

A) (x+1)^2/(x-1)^2
B) (x-1)^2/(x+1)^2
C) x^2+1/1-X^2
D) X^2-1/X^2+1
E) -(x-1)^2/-(X+1)^2

How to I calculate this quickly?


Looking for experts help on this - thank you!
B

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Post Tue Jul 28, 2015 2:33 pm
bethrussell_27@hotmail.co wrote:
(x+1)^2/(X-1)^2

If x is not = 0 or 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

A) (x+1)^2/(x-1)^2
B) (x-1)^2/(x+1)^2
C) x^2+1/1-X^2
D) X^2-1/X^2+1
E) -(x-1)^2/-(X+1)^2
Let x=2, implying that -- everywhere in the given expression -- x must be replaced by 1/x = 1/2.

Replacing x with 1/2, we get:
(1/2 + 1)²/(1/2 - 1)² = (3/2)²/(-1/2)² = (9/4)/(1/4) = 9. This is our target.

Now plug x=2 into the answer choices to see which yields our target of 9.
A quick scan of the numerators reveals that only A is viable:
(x+1)²/(x-1)² = (2+1)²/(2-1)² = 9.

The correct answer is A.

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nikhilgmat31 Legendary Member Default Avatar
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Post Wed Jul 29, 2015 12:48 am
In question 1plugin options seems very difficult as we need to evaluate each answer.

different way to solve.

p newpapers of type A
100- p newpapers of type B

revenue from A = p *1 = p
revenue from B = 1.25(100-p) = 1.25(100-p)

r% = p/(p+ 1.25(100-p) * 100

= 100p /(p +125 -1.25p)
= 100p /(125 -0.25p)

= 400p/(500-p)

Answer is D. without looking at other answers.



Last edited by nikhilgmat31 on Wed Jul 29, 2015 12:52 am; edited 1 time in total

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Post Tue Jul 28, 2015 2:33 pm
bethrussell_27@hotmail.co wrote:
(x+1)^2/(X-1)^2

If x is not = 0 or 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

A) (x+1)^2/(x-1)^2
B) (x-1)^2/(x+1)^2
C) x^2+1/1-X^2
D) X^2-1/X^2+1
E) -(x-1)^2/-(X+1)^2
Let x=2, implying that -- everywhere in the given expression -- x must be replaced by 1/x = 1/2.

Replacing x with 1/2, we get:
(1/2 + 1)²/(1/2 - 1)² = (3/2)²/(-1/2)² = (9/4)/(1/4) = 9. This is our target.

Now plug x=2 into the answer choices to see which yields our target of 9.
A quick scan of the numerators reveals that only A is viable:
(x+1)²/(x-1)² = (2+1)²/(2-1)² = 9.

The correct answer is A.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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nikhilgmat31 Legendary Member Default Avatar
Joined
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Posted:
518 messages
Upvotes:
10
Test Date:
3 Oct
Target GMAT Score:
750
Post Wed Jul 29, 2015 12:48 am
In question 1plugin options seems very difficult as we need to evaluate each answer.

different way to solve.

p newpapers of type A
100- p newpapers of type B

revenue from A = p *1 = p
revenue from B = 1.25(100-p) = 1.25(100-p)

r% = p/(p+ 1.25(100-p) * 100

= 100p /(p +125 -1.25p)
= 100p /(125 -0.25p)

= 400p/(500-p)

Answer is D. without looking at other answers.



Last edited by nikhilgmat31 on Wed Jul 29, 2015 12:52 am; edited 1 time in total

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nikhilgmat31 Legendary Member Default Avatar
Joined
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Posted:
518 messages
Upvotes:
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Test Date:
3 Oct
Target GMAT Score:
750
Post Wed Jul 29, 2015 12:51 am
(x+1)^2 /(x-1)^2
changing x to 1/x

(1/x + 1 )^2 / (1/x - 1 )^2

(1+x)^2 / (1-x)^2 ==> x^2 is cancelled from numerator & denominator

(x+1)^2 / ( x-1)^2

Answer is A

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Post Tue Jul 28, 2015 2:16 pm
(x+1)^2/(X-1)^2

If x is not = 0 or 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

A) (x+1)^2/(x-1)^2
B) (x-1)^2/(x+1)^2
C) x^2+1/1-X^2
D) X^2-1/X^2+1
E) -(x-1)^2/-(X+1)^2

How to I calculate this quickly?


Looking for experts help on this - thank you!
B[/quote]Solution:

Let’s start by substituting 1/x for x. Then we'll find the common denominator for the resulting fractional expressions, and finally we'll simplify the resulting fraction. We have:

ttp://postimg.org/image/wvykkrf3t/" target="_blank">

Even though our answer does not match any of the answer choices, our answer is really similar to answer choice A. In fact, they are the same. We can demonstrate that they are the same by factoring out a “-1” from the denominator of our fraction. So we can say:

1 - x = -(-1 + x) = -(x - 1)

Plugging this back into the fraction we have:

ttp://postimage.org/" target="_blank">

But, because this entire expression is being squared, the negative would turn into a positive, and the end result would be the same as:

ttp://postimage.org/" target="_blank">

The answer is A

Note: If this is difficult to see, let’s do the same thing with an integer. Let’s say we have 2. We could say the following:

(-2)^2 = (2)^2

4 = 4

Notice that because we squared the -2, it ended equaling 4. Although the expression in the problem above seems more complicated, the math behind what we did is exactly the same.

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Jeffrey Miller Head of GMAT Instruction

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Post Sat Apr 11, 2015 1:31 pm
Quote:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenue from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

A) 100p/125-p
B) 150p/250-p
C) 300p/375-p
D) 400p/500-p
E) 500p/625-p
Plug in values that make the math easy.

Let p=50, implying that 50% of the newspapers sold are A, while the other half are B.
In other words, the store sells an EQUAL NUMBER of each type of newspaper.
Since the price of each newspaper B = 1.25 = 5/4, let the store sell 4 OF EACH TYPE of newspaper.

Revenue from 4 copies of newspaper B = 4(1.25) = 5.
Revenue from 4 copies of newspaper A = 4*1 = 4.
Since (revenue from A)/(total revenue) = 4/9, r = (4/9)* 100 = 400/9. This is our target.

Now plug p=50 into the answers to see which yields our target of 400/9.

Answer choice D looks like a good bet, since it includes 400:
400p/(500 - p) = (400*50)/(500-50) = (400*50)/450 = 400/9.

The correct answer is D.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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