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An investor purchased 100 shares of stock X at 6 1/8 dollars

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An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]

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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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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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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 2-4% which is very negligible..

proper way would be
Add 2% of 6 1/8 and 24 and subtract from (24 - 6 1/8)...
answer =\((24-6 \frac{1}{8} - 0.02(24+6 \frac{1}{8}))/(6 \frac{1}{8})\)
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Re: An investor purchased 100 shares of stock X at [#permalink]

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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=SP-CP
=2352-662.75=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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New post 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 2-4% which is very negligible..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink]

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Solution 1

100 shares bought for 612.50
Sold 'm for 2400-2%

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 2350-625 (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 2

But 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.

[(2400-48)-(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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New post 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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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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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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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.
192-51/51 (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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New post 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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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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New post 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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New post 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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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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Re: An investor purchased 100 shares of stock X at 6 1/8 dollars   [#permalink] 04 Aug 2017, 14:53
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