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

Question

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.

ID: 700113

Bunuel · Accepted Answer

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

beatthegmat05 · Answer

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)

PrashantPonde · Answer

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.

nutshell · 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;

stne · Answer

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 )

riskietech · Answer

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!

dave13 · Answer

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

gmatconqueror2018 · Answer

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?

Basshead · Answer

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.

ScottTargetTestPrep · Answer

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

piyushnagre99 · Answer

Hi  Bunuel  ,

Please help me understand how did you arrive at the following statements?

Thanks,
Piyush

Bunuel · Answer

Think of it like this:

If each share costs $1 more, then the total cost goes up by $1 for every share. Since the total went up by $300, there must be 300 shares.

If each share costs $2 less, the total goes down by $2 for every share. Since the total went down by $600, that means 600/2 = 300 shares.

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

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