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# A certain portfolio consisted of 5 stocks, priced at $20,  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Current Student Joined: 11 May 2008 Posts: 562 Followers: 7 Kudos [?]: 53 [0], given: 0 A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  19 Jul 2008, 23:15
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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 [Reveal] Spoiler: OA Current Student Joined: 12 Jun 2008 Posts: 287 Schools: INSEAD Class of July '10 Followers: 6 Kudos [?]: 39 [1] , given: 0 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  20 Jul 2008, 00:44
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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 ==> Answer is (E) Retired Moderator Joined: 18 Jul 2008 Posts: 994 Followers: 10 Kudos [?]: 103 [0], given: 5 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  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 ==> Answer is (E) Manager Joined: 04 Apr 2008 Posts: 228 Location: Pune Followers: 2 Kudos [?]: 22 [0], given: 3 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  21 Jul 2008, 05:05
generally we start with the midlle terms and then you move on one side......But depends upon the experience that one selects the limits.....POE
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] 21 Jul 2008, 14:09 bigfernhead wrote: 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 Manager Joined: 11 Mar 2008 Posts: 117 Location: Canada Followers: 1 Kudos [?]: 13 [0], given: 0 A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  04 Dec 2008, 17:25
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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 SVP Joined: 29 Aug 2007 Posts: 2497 Followers: 57 Kudos [?]: 555 [1] , given: 19 Re: Statistics: % and logic [#permalink] 04 Dec 2008, 22:07 1 This post received KUDOS 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.
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Re: Statistics: % and logic [#permalink]  18 Jul 2011, 03:39
is there any other method to do this except to try 35% of atleast 2-3 values and 15% of 2-3 values before guessing the answer? If there is, pls share. Thanks.

Nice question!
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Re: Statistics: % and logic [#permalink]  18 Jul 2011, 20:49
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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 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29! Veritas Prep Reviews Moderator Joined: 25 Apr 2012 Posts: 734 Location: India GPA: 3.21 WE: Business Development (Other) Followers: 26 Kudos [?]: 416 [0], given: 723 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  03 Dec 2013, 01:50
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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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] 20 Mar 2014, 08:36 Or one can use differentials 13x - 37y = 0 therefore X is close to 3 times Y So the only possibilities that even comes close to this is that X = 70 and Y=20 Therefore, the stocks that remain unchanged are the middle three values: 35, 40,45 Hope this clarifies Cheers J Senior Manager Joined: 17 Sep 2013 Posts: 370 Location: United States Concentration: Marketing, Strategy GMAT 1: 690 Q48 V37 GMAT 2: 730 Q51 V38 GPA: 3.24 WE: Analyst (Consulting) Followers: 8 Kudos [?]: 101 [0], given: 133 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  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: 0 Kudos [?]: 22 [0], given: 37 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  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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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] 01 May 2014, 07:18 sayansarkar wrote: @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 Not so. Its supposed to be 37y by concept of differentials. See if price of total average rose by 2% and the price of one of the components declined by 35% then the difference is -35--2 = 35+2 = 37 Is this clear? Cheers J GMAT Club Legend Joined: 09 Sep 2013 Posts: 4690 Followers: 291 Kudos [?]: 52 [0], given: 0 Re: A certain portfolio consisted of 5 stocks, priced at$20, [#permalink]  26 Jul 2014, 19:35
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Re: A certain portfolio consisted of 5 stocks, priced at $20, [#permalink] 26 Jul 2014, 19:35 Similar topics Replies Last post Similar Topics: 2 An artist's portfolio consisting of 1,000 photos is divided into 20 su 3 13 Feb 2015, 07:46 5 Samantha's investment portfolio consists of three stocks 4 24 Nov 2012, 08:15 Portfolio Prices 6 17 Nov 2011, 15:31 A certain portfolio consisted of 5 stocks, priced at$20, 0 01 May 2014, 07:18