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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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07 Apr 2016, 10:56
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57% (01:27) correct 43% (01:33) wrong based on 714 sessions

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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%
[Reveal] Spoiler: OA

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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
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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.

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An investor purchased 100 shares of stock X at [#permalink]

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09 Apr 2016, 04:26
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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 =$$(24-6 \frac{1}{8} - 0.02(24+6 \frac{1}{8}))/(6 \frac{1}{8})$$ _________________ 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 Kudos [?]: 5533 [4], given: 112 Director Joined: 05 Mar 2015 Posts: 964 Kudos [?]: 287 [2], given: 41 Re: An investor purchased 100 shares of stock X at [#permalink] ### Show Tags 09 Apr 2016, 19:55 2 This post received KUDOS 1 This post was BOOKMARKED 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..
=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 Kudos [?]: 287 [2], given: 41 Math Forum Moderator Joined: 02 Aug 2009 Posts: 4994 Kudos [?]: 5533 [0], given: 112 Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink] ### Show Tags 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.. _________________ 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 Kudos [?]: 5533 [0], given: 112 Manager Joined: 10 Apr 2016 Posts: 56 Kudos [?]: 9 [4], given: 7 Concentration: Strategy, Entrepreneurship GMAT 1: 520 Q29 V30 GPA: 3.01 An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink] ### Show Tags 18 Apr 2016, 00:29 4 This post received KUDOS 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%. _________________ Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day. Kudos [?]: 9 [4], given: 7 Intern Joined: 29 Nov 2015 Posts: 7 Kudos [?]: [0], given: 80 Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink] ### Show Tags 29 May 2016, 09:54 Thanks Mathiaskeul, Its very clear now Kudos [?]: [0], given: 80 Intern Joined: 13 Jan 2010 Posts: 1 Kudos [?]: [0], given: 175 Schools: HBS '19, Stanford '19 Re: An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink] ### Show Tags 18 Jul 2016, 13:49 1 This post was BOOKMARKED 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% Kudos [?]: [0], given: 175 Intern Joined: 24 Aug 2016 Posts: 29 Kudos [?]: 3 [1], given: 5 An investor purchased 100 shares of stock X at 6 1/8 dollars [#permalink] ### Show Tags 09 Sep 2016, 00:31 1 This post received KUDOS 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
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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.

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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
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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%.

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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
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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 $$384\% - 100\% = 284\%$$

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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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