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An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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07 Apr 2016, 10:56
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An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment? (A) 92% (B) 240% (C) 280% (D) 300% (E) 380%
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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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07 Apr 2016, 12:03
If the purchase price was 6$ per share then the investor would have made a profit of 300%.
Since the purchase price is slightly more than 6$ the profit would be slightly less than 300%.
Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.
Answer: C



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An investor purchased 100 shares of stock X at [#permalink]
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09 Apr 2016, 04:26
email2vm wrote: An investor purchased 100 shares of stock X at $6 1/8 (or 49/8 $) per share and sold them all a year later at 24$ per share. If the investor paid a 2% brokerage fee on both the total purchase price and the total selling price, which of the following is the closest to the investors percent gain on the investment.
a> 92% b> 240% c> 280% d> 300% e> 380%
how would you solve this question. For the first time I realized that I need a some sleep before test.
Ravi HI there is enough in the choices to get you close to the correct answer.. A thing of 6 1/8 has become 24... so profit of <18 on 6 1/8.. clearly it is slightly less than 300% ans 280%... Brokerage will make a difference of 24% which is very negligible.. proper way would be Add 2% of 6 1/8 and 24 and subtract from (24  6 1/8)... answer =\((246 \frac{1}{8}  0.02(24+6 \frac{1}{8}))/(6 \frac{1}{8})\)
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Re: An investor purchased 100 shares of stock X at [#permalink]
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09 Apr 2016, 19:55
email2vm wrote: An investor purchased 100 shares of stock X at $6 1/8 (or 49/8 $) per share and sold them all a year later at 24$ per share. If the investor paid a 2% brokerage fee on both the total purchase price and the total selling price, which of the following is the closest to the investors percent gain on the investment.
a> 92% b> 240% c> 280% d> 300% e> 380%
how would you solve this question. For the first time I realized that I need a some sleep before test.
Ravi Some simple calculations to be made for this.. buying price = price os total shares+brokerage charges on buy price =100*49/8 + 2% of (100*49/8) =624.75 similarly selling price = 24*100  2%of 2400(or u can add this to buy price also) =2352 so profit=SPCP =2352662.75=1727.25$ %= 1727.25/662.75 =2.76 ~ 280% Ans C



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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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17 Apr 2016, 23:42
happyface101 wrote: An investor purchased 100 shares of stock X at $6.125 per share and sold them all a year later at $24 dollars per share. If the investor paid 2 percent brokerage fee on both the total purchase price and total selling price, which of the following is closest to the investor's percent gain on this investment?
a. 92% b. 240% c. 280% d. 300% e. 380%
What's the fastest / easiest way to solve this? Calculations can obviously get messy / become a time sink. HI A way I can think of is that the choices will get you close to the correct answer.. A thing of 6 1/8 has become 24... so profit of <18 on 6 1/8.. clearly it is slightly less than 300%ans 280%... Brokerage will make a difference of 24% which is very negligible..
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An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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18 Apr 2016, 00:29
Solution 1100 shares bought for 612.50 Sold 'm for 24002% 2% OF 612.50 is easy to calculate. 12.25 ... 2400 minus 2% is also easy to calculate> 2400/100*2 = 48. So the profit amounts to 2350625 (you can approximate here, it won't make much difference): 1725 1725 divided by 625 can be simplified as 69/25, which equals to 2,8. This can be done within 1.5 minutes. Solution 2But if you're in a hurry, you can just see that the 1/8 is negligible and is only there to hand out complex calculations like the one above. [(240048)(600+12)]/612 =[(2352)(612)]/612 =1740/612 3 times 612 gives you 1836. Which is 96 more than needed. 96/612 is close to 1/6 (a bit less), which is close to 0.2. So you will need 2 times 612 and 80% of 612 to arrive at 1740. Ans, 280%.
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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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29 May 2016, 09:54
Thanks Mathiaskeul, Its very clear now



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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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18 Jul 2016, 13:49
cost of selling shares = (24*(98/100) we multiply by 98, because we loose 2% in brokerage fee reducing our selling price cost of buying shares = (49/8 * 102/100) we multiply by 102, because it costs more to buy the shares, when taking the brokerage fee into account
% profit = (selling price/cost price * 100) 1 % profit = (24*98/100) divided by (49/8 * 102/100) * 100 1 % profit = (24*98/100) * (100*8 / 49*102) * 100  1 % profit = (24*98*100*8)/(100*49*102) * 100 1 % profit = (24*2*8/102) *100 1 % profit = (192/51)*100 1 % profit = (3.76 & 100)  1 = 276%, c is the closest at 280%



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An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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09 Sep 2016, 00:31
Hi all, please let me know if there is something I am not grasping:
Stocks purchased at $6.125. 100% profit on this investment = double the value = $12.50 per stock 200% profit on this investment = triples the value = $18.75 per stock 300% profit on this investment = 4x the original value = $25.00 per stock (roughly)
Therefor profit just below 300% or 280 percent gain (especially after 'fees').
You can do this math in about 30 seconds.
Logic:
If I spend $100 and gain $100, 0% profit on my original investment. If I spend $100 and gain $150, 50% profit on my original investment. If I spend $100 and gain $200, 100% profit on my original investment. If I spend $100 and gain $300, 200% profit on my original investment.
Any critique?



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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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02 Nov 2016, 07:16
i used approximations...yet i took the longer way... purchased price let's say is 49/8 100 * 49/8 * 102/100 (2%) > 49*102/8
selling price: 100*24*98/100 (2% commission fee)  24*98 24*98/(49*102/8) 24*98*8/49*102 98 is a multiple of 49 > simplify 24*2*8/102 24*8/51 192/51 > this is not the end...selling price is 192/51 % greater than the purchase price. 19251/51 (percent increase) = 141/51 > we can clearly see that it's less than 300% and clearly more than 200%. only B and C remain... to have 300%, we need 153/51. since 141 is close to 153  we can assume that it's ~280.
C is the answer.



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An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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06 Feb 2017, 05:04
this one was very annoying. I was between B and C. I knew that it is slightly below %300, but couldn't decide if it is below %290. I think autoboat's and mvictor' approaches are good for this type of question.



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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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08 Feb 2017, 19:52
surupab wrote: An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
(A) 92% (B) 240% (C) 280% (D) 300% (E) 380% Since the investor bought and sold the same number (100) of shares of stock X, the percent change in his gain would be the same if he bought and sold 1 share of the stock. Therefore, let’s calculate the percent change on 1 share instead of 100 shares. Since he had to pay 2% commission on purchasing the stock (which means he actually had to pay 102% of the purchase price), his cost on one share is 6 ⅛ x 102/100 = 49/8 x 51/50. Similarly, since he had to pay 2% commission on selling the stock (which means he only received 98% of the selling price), his revenue on one share is 24 x 98/100 = 24 x 49/50. Therefore, the ratio of the revenue to the cost of 1 share of the stock is: (24 x 49/50)/(49/8 x 51/50) 24 x 49/50 x 8/49 x 50/51 24 x 1 x 8 x 1/51 192/51 192/51 can be approximated as 190/50 = 3.8 = 380%. That is, the revenue is approximately 380% of the cost. In other words, the profit (or gain) is approximately 280%. Answer: C
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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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25 May 2017, 19:34
Let me give away my two cents on this one. This approach didn't take me too much time.
Purchase price \(=\) \(6 \frac{1}{8}\). Since I don't like mixed numbers I quickly transformed it to an improper fraction: \(\frac{49}{8}\).
Purchase price \(*\) quantity of shares \(=\) \(\frac{4900}{8}=\frac{1225}{2}\)
Selling price \(= 24\)
Selling price \(*\) quantity of shares \(= 2400\)
Now let's set up the variation formula: \(\left(\frac{2400(1.02)}{\frac{1225(1.02)}{2}}1\right)*100\)
Simplify it: \(\left(\frac{4800}{1225}1\right)*100\)
Simplify it further until: \(\left(\frac{192}{49}1\right)*100 \rightarrow \left(\frac{143}{49}\right)*100\)
Now, at this stage we now that \(3*49=147\) which is greater than \(143\), so the percent gain is slightly less than \(300\%\). This should be sufficient to select option C; however, if you want more precision, you can try the following multiplication: \(2.5*49=122.5\). Since \(122.5\) is lower than \(143\), we know that the percent gain was greater than \(250\%\). Again, option C is the correct answer.
Hope it helps.



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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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23 Jul 2017, 03:47
The FASTEST and BEST way to solve such problem with ugly number like this one is to APPROXIMATE!
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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]
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04 Aug 2017, 14:53
The formula for percentage change is:
\(\frac{new}{old}1\)
\(new=24*.98 \rightarrow 24*\frac{49}{50}\)
\(old=6\frac{1}{8}*1.02 \rightarrow \frac{49}{8}*\frac{51}{50}\)
\(\frac{new}{old}*\frac{8*50}{8*50}=\frac{192*49}{49*51}=\frac{192}{51}=\frac{384}{102}\)
So the approximate percentage gain the investor made is slightly less than \(384\%  100\% = 284\%\)
Answer C




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