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A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] ### Show Tags 19 Jul 2008, 23:15 2 This post received KUDOS 17 This post was BOOKMARKED 00:00 Difficulty: 95% (hard) Question Stats: 58% (03:17) correct 42% (02:51) wrong based on 256 sessions ### HideShow timer Statistics A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $45 and$70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

A. 20, 35, 70
B. 20, 45, 70
C. 20, 35, 40
D. 35, 40, 70
E. 35, 40, 45
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] ### Show Tags 20 Jul 2008, 00:44 6 This post received KUDOS Make the smallest decrease and the highest increase, and you have: - for the smallest: 35% of$20 = $7 decrease - for the highest: 15% of$70 = $10.5 increase ==> maximum increase of the portfolio is$3.5 total

Total value of the portfolio was $20+$35+$40+$45+$70 =$210

So the maximun increase corresponds to 3.5/210 = 1.7%

You cannot be closer to 2%, thus it is $20 that decrease and$70 that increase

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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] ### Show Tags 21 Jul 2008, 04:31 How did you know which price to increase and decrease? Is it by process of elimination (trying each one by one), or is there a quicker method. Oski wrote: Make the smallest decrease and the highest increase, and you have: - for the smallest: 35% of$20 = $7 decrease - for the highest: 15% of$70 = $10.5 increase ==> maximum increase of the portfolio is$3.5 total

Total value of the portfolio was $20+$35+$40+$45+$70 =$210

So the maximun increase corresponds to 3.5/210 = 1.7%

You cannot be closer to 2%, thus it is $20 that decrease and$70 that increase

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21 Jul 2008, 14:09
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How did you know which price to increase and decrease?

Is it by process of elimination (trying each one by one), or is there a quicker method.

I decreased the minimum and increased the maximum, therefore the gap I got is the biggest we can get. And it is still not sufficient to reach the 2% mark : so this is the answer.

A more general method if you do not see it from the begining is as follow :

- compute 2% of the total (here 210*2% = 4.2)

- write down the five numbers and compute for each one what it means to increase it by 15% or decrease it by 35%

20 : +3 ; -7
35 : +5.25 ; -12.25
40 : +6 ; -14
45 : +6.75 ; -15.75
70 : +10.5 ; -24.5

- then, "play" with the 10 numbers you get to be as close as possible to this 4.2
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A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] ### Show Tags 04 Dec 2008, 17:25 4 This post was BOOKMARKED A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $45 and$70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

A. 20, 35, 70
B. 20, 45, 70
C. 20, 35, 40
D. 35, 40, 70
E. 35, 40, 45
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Re: Statistics: % and logic [#permalink]

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04 Dec 2008, 22:07
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snaps wrote:
A certain portfolio consisted of 5 stocks, priced at $20,$35, $40,$45 and $70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant? A) 20, 35, 70 B) 20, 45, 70 C) 20, 35, 40 D) 35, 40, 70 E) 35, 40, 45 E) 35, 40, 45 It has to be E cuz the 2% of of the portfolio is approx 4.00 and the diff between 15% of 70 and 35% of 20 = 3.50. so this is the most closest. _________________ Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html GT Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7173 Location: Pune, India Followers: 2160 Kudos [?]: 13980 [23] , given: 222 Re: Statistics: % and logic [#permalink] ### Show Tags 18 Jul 2011, 20:49 23 This post received KUDOS Expert's post 10 This post was BOOKMARKED snaps wrote: A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $45 and$70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

A) 20, 35, 70

B) 20, 45, 70

C) 20, 35, 40

D) 35, 40, 70

E) 35, 40, 45

Use logic and the calculations involved will be negligible.
Since we have been given that there is an overall increase, the increase should be greater than the decrease. So
15% of A > 35% of B

Now think that 15% of A will be equal to 30% of B if A is twice of B. But 15% of A is greater than 30% of B so A must be greater than twice of B. In fact 15% of A is greater than 35% of B so A must be substantially greater than twice of B. So B has to be 20 because we have values more than twice of 20 (which are 45 and 70). We don't have any values which are more than twice of any other given number (30, 35, 40, 70).

A can be 45 or 70. I would bet on 70 since A has be substantially greater than twice of 20.
Even if I want to confirm, 10% of 20 is 2 so 30% of 20 is 6. 5% of 20 is 1 so 35% of 20 is 7.
15% of A has to be greater than 7. Only 70 satisfies this since 10% of 70 is 7.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 23 Jun 2009 Posts: 361 Location: Turkey Schools: UPenn, UMich, HKS, UCB, Chicago Followers: 5 Kudos [?]: 131 [1] , given: 80 Re: Portfolio Prices [#permalink] ### Show Tags 19 Nov 2011, 11:44 1 This post received KUDOS 1 This post was BOOKMARKED enigma123 wrote: A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $45, and$70, respectively. On a given day, the price of one stock increased by 15%, while the price of another stock decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

(A) $20,$35, and $70 (B)$20, $45, and$70
(C) $20,$35, and $40 (D)$35, $40, and$70

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03 Dec 2013, 01:50
1
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snaps wrote:
A certain portfolio consisted of 5 stocks, priced at $20,$35, $40,$45 and $70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant? A. 20, 35, 70 B. 20, 45, 70 C. 20, 35, 40 D. 35, 40, 70 E. 35, 40, 45 Sum of price of all stocks :$ 210
Avg price : $42 The average price of the stock goes up by 2% of Avg stock price which is$ 0.84-------> This indicates the total increase in the sum is 0.84*5 = $+ 4.20 from the Q we can say that since the avg stock price has gone up therefore 0.15A - 0.35B >0. A has to be greater than B and thus we have or 0.15A- 0.35B ~ 4.2$
Now 35% of 20 = 7 and 15% of 70 = 10.5 Diff : 3.5
0.15*35 = ~ 5.25 and 15 % of 70 =10.5 Diff: ~ 5
0.15*35= 5.25. and 15% of 45 = 6.75, Diff~ 1.5

For any other combination
ex B = 35 and 0.35 B = 12.25 and A =0.15*70 = 10.5 and the difference between A and B is negative and as B increase the the difference of A and B will become more negative.

Hence Ans option E. The values which are constant

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24 Mar 2014, 03:53
snaps wrote:
A certain portfolio consisted of 5 stocks, priced at $20,$35, $40,$45 and $70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant? A. 20, 35, 70 B. 20, 45, 70 C. 20, 35, 40 D. 35, 40, 70 E. 35, 40, 45 Average is 42 2%= .8 (App) Total in Increase in the portfolio is 4 ( As each stock increases by 0.8 => 5 x 0.8) Difference between the varying stock prices should be 4 Lets take the first and the most conservative case: 22 decreases by 35% = 7.7 A corresponding increase in a stock price of approx 11 is required to bring the difference in stock prices to 4 We can quickly conclude that 70 ( 7 x 15= 10.5) is as good as it gets...coz any stock other than 22 will have an even greater numerical decrease with a 35% decline in its value and has no share that can maintain the difference of 4 ...as we have already taken the highest increase of 15% in 70 _________________ Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down.. Manager Joined: 28 Jul 2013 Posts: 93 Location: India Concentration: Marketing, Strategy GPA: 3.62 WE: Engineering (Manufacturing) Followers: 1 Kudos [?]: 37 [0], given: 37 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]

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05 Apr 2014, 08:39
@jlgdr: you mean 15x-35y>0

hence (x/y)>(7/3)
when you put x = 70 and y = 20 this equation is satisfied. here x/y is 7/2 > 7/3
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26 Jul 2014, 19:35
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19 Aug 2015, 10:08
jlgdr wrote:
13x - 37y = 0 therefore X is close to 3 times Y

The above conjecture is incorrect. The right side of the equation is not 0, so making any assumption about the ratio x/y would be poor.

Generalizing the problem we get that a high (H) stock has to increase by 15% and a low (L) stock has to decrease by 35%. (H > L)

Formula looks like: .02*(H + L + Others) = .15*H - .35*L which we can rewrite as .02*Others = .13*H - .37*L.

If the "Other" stocks did not exist you could make an assumption about the ratio of H/L, but since they do, H/L isn't necessarily close to 3.
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] ### Show Tags 07 Sep 2016, 22:24 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 13 Sep 2016 Posts: 105 Followers: 1 Kudos [?]: 35 [0], given: 320 A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $4 [#permalink] ### Show Tags 18 Sep 2016, 01:42 A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $45, and$70, respectively. On a given day, the price of one stock increased by 15%, while the price of another stock decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

(A) $20,$35, and $70 (B)$20, $45, and$70
(C) $20,$35, and $40 (D)$35, $40, and$70
(E) $35,$40, and $45 Last edited by Bunuel on 18 Sep 2016, 01:51, edited 1 time in total. Renamed the topic and edited the question. A certain portfolio consisted of 5 stocks, priced at$20, $35,$40, $4 [#permalink] 18 Sep 2016, 01:42 Go to page 1 2 Next [ 21 posts ] Similar topics Replies Last post Similar Topics: 3 In a certain portfolio, the ratio of the number of domestic stocks to 2 05 Feb 2017, 01:28 At the opening of a trading day at a certain stock exchange, the price 4 25 May 2016, 00:56 4 An investor purchased 20 shares of certain stock at price of$45.75 3 17 Jan 2016, 03:19
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