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If the total price of n equally priced shares of a certain s

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If the total price of n equally priced shares of a certain s [#permalink]

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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 s [#permalink]

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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 s [#permalink]

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New post 21 Jan 2014, 07:21
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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)

Last edited by beatthegmat05 on 21 Jan 2014, 20:21, edited 1 time in total.
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Re: If the total price of n equally priced shares of a certain s [#permalink]

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New post 21 Jan 2014, 19:46
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Here's how I solved it:

n = Number of shares
x = Price Per share

12000/n=x or 12000/x=n

a) 12000+300/n=x+1 --> 12300/n=x+1 --> 12300/x+1=n
Set equation equal to the one above since number of shares is constant
12300/x+1=12000/x
12300x=12000x+12000
Don't need to go any further since you know you can solve for x.

b) 12000*.95/n=x-2 --> 11400/n=x-2 --> 11400/x-2=n
Set equation equal to the one above since number of shares is constant
11400/x-2=12000/x
11400x=12000x-24000
Don't need to go any further since you know you can solve for x.

Just in case you solved for x, x=40

Each equation is sufficient. Answer is D.
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Re: If the total price of n equally priced shares of a certain s [#permalink]

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New post 22 Jan 2014, 01:00
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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 s [#permalink]

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New post 23 Jan 2014, 23:54
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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: Help : Data Sufficiency - OG13 Question 50 [#permalink]

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New post 23 Mar 2014, 22:37
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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 s [#permalink]

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Re: If the total price of n equally priced shares of a certain s   [#permalink] 14 Jan 2018, 12:26
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