What was price per share of the stock?

[GmatGreen]

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.

[Patrick_GMATFix]

Great question. The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

[GMATGuruNY]

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.

n = the number of shares.
Let p = the price per share.

Statement 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.
n = (total price increase)/(increase per share) = 300/1 = 300.
Thus, p = 12000/n = 12000/300 = $40.
SUFFICIENT.

Statement 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 total price decreases by 5%, then the value of p also decreases by 5%.
Statement 1 indicates that p=$40.
Decreasing p=40 by 5% would yield a decrease of $2 per share.
Thus, statement 2 implies the same information as statement 1: p=40.
SUFFICIENT.

The correct answer is D.

[[email protected]]

Hi GmatGreen,

This DS question is built around "system math."

The prompt tells us that N equally priced shares total $12,000. This can be written as:

N = Number of Shares
P = Price per share
NP = $12,000

This is 1 equation with 2 variables.

Fact 1: If the price per share was $1 MORE, then the total price would have been $300 more.

This Fact can be translated into:

N(P+1) = $12,300

Now we have a second equation, so we have "2 variables and 2 unique equations, so we CAN solve it."
Fact 1 is SUFFICIENT

Fact 2: If the price per share was $2 LESS, then the total price would be 5% less.

This Fact can be translated into:

N(P-2) = .95($12,000)

Again, we end up with a second equation, so this too is "2 variables and 2 unique equations, so we CAN solve it."
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Bill@VeritasPrep]

As Rich said, once you know that you CAN solve for a definite value of the variable, you are done. You don't actually have to solve for a price of $40; you just have to recognize that the pieces are in place to do so. An easy way to save time on DS.

[Scott@TargetTestPrep]

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.

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