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If the total price of n equally priced shares of a certain stock was $

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If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 21 Jan 2014, 04:15
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?

(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.
(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.

Data Sufficiency
Question: 50
Category: Arithmetic Arithmetic ope rations; Percents
Page: 156
Difficulty: 600

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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 21 Jan 2014, 04:15
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SOLUTION

If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?

(Price per share) = (Total price)/(The number of shares) = $12,000/n. So, basically we need to find the value of n.

(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more. $1 increase per share results in $300 increase of the total price, thus there must be 300 shares. Sufficient..

(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less. $2 decrease per share results in 0.05*12,000=$600 decrease of the total price, thus there must be 600/2=300 shares. Sufficient.

Answer: D.

Similar question to practice: if-x-equally-priced-shares-of-a-certain-stock-were-valued-129106.html
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post Updated on: 21 Jan 2014, 21:21
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Let no. of share=n
and price per share=x


GIven total price of n share -----> nx = 12000

Condition 1:
(x+1)n=12000+300
nx+n=12000+300
n=300

Condition 2:
(x-2)n=12000*0.95
nx-2n=11400
2n=600
n=300

Since BOTH condition can individually answer the question so answer is (D)

Originally posted by beatthegmat05 on 21 Jan 2014, 08:21.
Last edited by beatthegmat05 on 21 Jan 2014, 21:21, edited 1 time in total.
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 21 Jan 2014, 20:46
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Consider the price per share as 'x'.
Given that, x*n = 12000

(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.
SUFFICIENT: this says \((x+1)*n=12000+300\). As we know \(xn=12000\), we can solve this equation to find out x & n. (no need to solve further)

(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.
SUFFICIENT: this says \((x-2)*n=12000 (1-\frac{5}{100})\). As we know \(xn=12000\), we can solve this equation to find out x & n. (no need to solve further)

Hence choice(D) is the answer.
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 22 Jan 2014, 02:00
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Since the total price of shares is given by no. of shares(n)*Price/share(p), we can make the following statement:
np=12,000;

The idea would be to equate given information with the information obtained from statements.

Statement(1):
n(p+1) = np(Total value) + 300;
np + n = np + 300;
=> n = 300;
From this, Price per share(p) can be determined; Sufficient;

Statement(2):
n(p-2) = np - (0.05)(12,000);
np - 2n = np - 600;
2n = 600;
=> n = 300;
From this, Price per share(p) can be determined; Sufficient;

Ans is (D).

Note: It is not even required to find n; If we understand that p can be determined from the statements alone, it is sufficient;
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 24 Jan 2014, 00:54
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Since there are n shares which cost 12,000, therefore 1 share originally costs \(\frac{12,000}{n}\)

so we need n ( total shares) to get the value per share

(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.

\((\frac{12,000}{n}+1)*n\)= 12,300 we can get n , sufficient

(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.

\((\frac{12,000}{n}-2)*n\)= 11685, we can get n , sufficient

Answer D

( n= 300 therefore price per share is 40 )
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 23 Mar 2014, 23:37
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I think you are referring to OG Q review - 2nd Edition.


let share price = f

total share price = f*n

i) Consider st1: we can derive following equation:
(f+1)*n - fn = 300
n = 300
thus f = 12000/300 = 40
Sufficient

ii) Consider st2: we can derive following equation
(f-2)*n = 0.95 * f * n ... (5 % less mean new share equals 95% of old)
thus f = 2/0.05 = 40.
Sufficient.

Answer: D
Hope this helps!
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 23 Apr 2018, 11:55
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?

(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.
(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.

Data Sufficiency
Question: 50
Category: Arithmetic Arithmetic ope rations; Percents
Page: 156
Difficulty: 600


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let \(n\) be total number of shares
let \(x\) be price per share

x*n = 12000

first statement :)

\((x+1)n = 12300\)

\(x = \frac{12000}{n}\) price per share original

(\(\frac{12000}{n}\) +1)n = \(12300\)

\(12000+n = 12300\)

\(n = 300\)

second statement :)

\((x-2)n =12000 -0.5xn\)

\(\frac{12000}{n} =x\) price per share (plu in in the first one)


\((\frac{12000}{n} -2)n = 11,400\)

\(12000- 2n = 11400\)

\(600 = 2n\)

\(n = 300\)


DDDDDDD :)
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Re: If the total price of n equally priced shares of a certain stock was $  [#permalink]

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New post 08 Jan 2019, 20:04
Hello, please let me know if my logic works for this problem. At first, I had no idea how to set up the probably algebraicly but realized each statement allows you to solve for one variable to determine the answer and hence D. This is what I originally thought:

12,000(Total Value)/X(Price per share)=12,300/X+1
Essentially, this is the change to the original equation which allows you to solve for the share price ($40)
Similarly, 12,000/x=11400/x-2 for statement 2 which again gets you $40 share price (11400>>> 95% of 12,000)
In the future, despite not knowing how to PROPERLY set up algebraic expressions and equations on certain DS questions, as long as I can see that I can solve for a particular variable, I can feel confident the statement will be sufficient?
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Re: If the total price of n equally priced shares of a certain stock was $   [#permalink] 08 Jan 2019, 20:04
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