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

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.

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;

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 )

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!

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

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?

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.

This statement directly tells us that there are 300 shares. We can conclude the price per share is $40. 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.

If the price had been $2 less, the total price would have been 5% less. This mean 100% = $40. SUFFICIENT.

Answer is D.

Solution:

Question Stem Analysis:

We need to determine the price per share of the stock, given that the total price of n shares of this stock was $12,000. Therefore, the price per share of the stock was 12,000/n dollars. In other words, if we can determine the value of n, then we can determine the price per share of the stock.

Statement One Alone:

We can create the equation:

(12,000/n + 1) * n = 12,000 + 300

12,000 + n = 12,300

n = 300

Since n = 300, the price per share of the stock was 12,000/300 = $40. Statement one alone is sufficient.

Statement Two Alone:

(12,000/n - 2) * n = 12,000 * 0.95

12,000 - 2n = 11,400

600 = 2n

300 = n

Once again, we see the price per share of the stock was $40. Statement two alone is sufficient.

Answer: D

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.