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Register now and save up to $200 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code ## Algebra tagged by: Brent@GMATPrepNow This topic has 5 expert replies and 2 member replies bethrussell_27@hotmail.co Junior | Next Rank: 30 Posts Joined 17 Nov 2014 Posted: 29 messages #### Algebra 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 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13608 messages Followed by: 1796 members Upvotes: 13060 GMAT Score: 790 Top Reply 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. Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. nikhilgmat31 Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 Top Reply 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 ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13608 messages Followed by: 1796 members Upvotes: 13060 GMAT Score: 790 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. Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. nikhilgmat31 Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 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 nikhilgmat31 Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 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 ### GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 506 messages Followed by: 6 members Upvotes: 39 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. _________________ Jeffrey Miller Head of GMAT Instruction ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13608 messages Followed by: 1796 members Upvotes: 13060 GMAT Score: 790 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.

_________________
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.
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