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

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Math Expert
Joined: 02 Sep 2009
Posts: 46334
If the total price of n equally priced shares of a certain s [#permalink]

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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 s [#permalink]

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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 _________________ Intern Joined: 13 Feb 2013 Posts: 19 Location: United States Concentration: Finance, General Management Schools: HBS '16 GMAT Date: 07-28-2014 GPA: 3.75 WE: Consulting (Computer Software) Re: If the total price of n equally priced shares of a certain s [#permalink] ### Show Tags Updated on: 21 Jan 2014, 21:21 3 1 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. Senior Manager Joined: 27 Jun 2012 Posts: 391 Concentration: Strategy, Finance Schools: Haas EWMBA '17 If the total price of n equally priced shares of a certain s [#permalink] ### Show Tags 21 Jan 2014, 20:46 2 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)

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

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22 Jan 2014, 02:00
1
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;
Senior Manager
Joined: 27 May 2012
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Re: If the total price of n equally priced shares of a certain s [#permalink]

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24 Jan 2014, 00:54
1
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 ) _________________ - Stne Manager Joined: 03 Dec 2013 Posts: 62 Re: Help : Data Sufficiency - OG13 Question 50 [#permalink] ### Show Tags 23 Mar 2014, 23:37 1 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! Director Joined: 09 Mar 2016 Posts: 615 If the total price of n equally priced shares of a certain s [#permalink] ### Show Tags 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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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
If the total price of n equally priced shares of a certain s   [#permalink] 23 Apr 2018, 11:55
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