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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 $ &nbs [#permalink] 23 Apr 2018, 11:55
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