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

Question

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

(A) 92%
(B) 240%
(C) 280%
(D) 300%
(E) 380%

Kurtosis · Accepted Answer

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

chetan2u · Answer

HI

there is enough in the choices to get you close to the correct answer..

OPTIONS

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 METHOD

I. CP —   6 \frac{1}{8} + \frac{2}{100} \ \ of \ \ 6 \frac{1}{8}=1.02*\frac{49}{8}

II. SP —   24-\frac{2}{100} \ \ of \ \ 24=0.98*24

Profit = 0.98*24-1.02*\frac{49}{8}=\frac{24*98}{100}-\frac{102*49}{100*8}=49*\frac{48*8-102}{800}=49*\frac{282}{800}

Profit %= 100*\frac{49*\frac{282}{800}}{\frac{102*49}{800}}=\frac{100*282}{102} =276~280%

C

rohit8865 · Answer

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
=2352-624.75=1727.25$
%= 1727.25/624.75
=2.76 ~ 280%

Ans C

chetan2u · Answer

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..

mathiaskeul · Answer

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.

/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%.

Autoboat · Answer

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?

mvictor · Answer

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.

JeffTargetTestPrep · Answer

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

Shobhit7 · Answer

chetan2u

Kindly clarify why the denominator in the expression "%= 1727.25/624.75" is not 612.5+12.25+48= 672.75. 
As per my understanding, 
total gain= 2400-612.5= 1787.5
brokerage= 12.25+48= 60.25
net profit= 1727.25
net cost= 612.5+12.25+48= 672.75

% profit= 1727.25/672.75 = 257%.
So, closest approx should be 240%.

chetan2u · Answer

Hi
Why many are going wrong is not taking it step wise.
Let us Work on CP and SP separately 
CP — 6 1/8 + 2% of 6 1/8=1.02*49/8~50/8=6.25
SP — 24-2%of 24=0.98*24 should be between 23 and 24, say 23.5
Profit =23.5-6.25=17.25
Profit %=100*17.25/6.25=100*1725/(625)=(25*4)(25*69)/(25*25)=4*69=276~280%

GMATGuruNY · Answer

Purchase price per share  = \frac{49}{8} 
Selling price per share  = 24 = \frac{192}{8}

Since the fractions above are over the same denominator, we can incorporate the brokerage fee and calculate the percent change using only the NUMERATORS.
Per share purchase price with a 2% brokerage fee = 49 + (2% of 49) ≈ 49 + 1 = 50
Per share selling price less a 2% brokerage fee = 192 - (2% of 192) ≈ 192 - 4 = 188
Percent change from 50 to 188  = \frac{difference}{original} * 100 = \frac{138}{50} * 100 = 276

C

ThatDudeKnows · Answer

6.125? Nah, we'll get the right answer by using 6 and looking for an answer that's close.

If we'd gone from $6 to $24, that would have been a 300% increase without the broker fee (and actually started just a touch higher than $6). D and E are out. A is way too low. I'd feel comfortable with C at this point without doing any additional work. If you don't that's okay.

At purchase, we paid 2% of $6, and at sale, we paid 2% of $24. That's the same as paying 2% of $30, which is $0.60. That means our total gain was $17.40. That's really close to a 300% gain but just shy (definitely more than 240%).

Answer choice C.

Purnank · Answer

found a simple way of doing this. as 2% is going for brokerage on both transactions of selling and buying.
So,
Profit per share equal to  = 0.98 * (24 - \frac{49}{8})  (here 49/8 is actually ratio conversion of 6 1/8)
Now profit %  = \frac{Profit per Share}{Cost per Share} * 100 = ((0.98 * (24 - 49/8))/(49/8)) * 100

Solve this you will get   276% as answer and Option C is close to it.

KarishmaB · Answer

Use estimations here. They are discussed in this video: https://youtu.be/4Wy7BrQrjkM The profit % on 1 stock is same as that on 100 so ignore that. If Buy price were 6 and Sell price is 24, profit would be 18 and profit % would be 300%. Since cost price is slightly more and there are transaction costs of 2%, 280% looks like a good answer. Let's confirm that 240% is not possible. If profit were 250%, the selling price would be around 21 (2.5 times of 6 added to 6). But our selling price is far more than this. Hence 280% is correct. Answer (D)

sarthak1701 · Answer

Purchase price = 49/8, stocks purchased worth = 49/8 * 98/100 (Don't solve it)

Sold for 24, but after brokerage received = 24*98/100

Gain = 24*98/100 - 49/8*98/100 = 98/100 (24 - 49/8) = 98*143/800. This is dollar gain, to calculate percent gain we just divide it by the purchase price and multiply by 100.

*100 = 98*143/800 * 8/49 * 100 = 143*2 = 286%

Ans C.

BelisariusTirto · Answer

Hi I was just wondering why do we need to do sell price / buy price - 1? I was under the impression that we just need to do ( sell price / buy price ) * 100 for profit % in general.

Krunaal · Answer

We calculate profit as,  Profit = Selling Price - Buying Price

Profit % =  (\frac{Profit }{ Buying Price}) * 100

=>  (\frac{Selling Price - Buying Price }{ Buying Price}) * 100

=>  (\frac{Selling Price }{ Buying Price} - \frac{Buying Price }{ Buying Price}) * 100

=>  (\frac{Selling Price}{Buying Price} - 1) * 100

Hope it helps.

siddhantvarma · Answer

Small clarification here:
"...which of the following is closest to the investor's percent gain on this investment?"

"Percent gain on this investment" , by "this investment", I thought we're calculating profit on the investment made and not including the brokerage fee. But here we're simply calculating the profit on the entire cost (which includes brokerage fee) so investment is basically the entire cost right?

Krunaal   KarishmaB

GraemeGmatPanda · Answer

Good question... I think it can be interpreted both ways (I'm not sure this is an official GMAT question)

But I think whether you divide by the investment including the fee or not, since we're looking for an approximate answer the closest one will always be C

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

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