What is the total value of Company H's stock?

Both statements are not sufficient because we cannot assume that only P and Q are the investors of the company H. Am i correct?

Hi All,

In DS questions, you have to be very clear on the information you've been given (what do you KNOW for sure vs. what are the possibilities).

In this prompt, we have a serious lack of information. We're asked for the total value of Company H's stock, but we're given no information to start off with.

Fact 1: Investor P owns 1/4 of the shares.

This tells us nothing about the value of those shares, nor does it tell us how many people own the remaining 3/4 of the shares, so there's no way to determine the total value of the stock.
Fact 1 is INSUFFICIENT.

Fact 2: The value of Investor Q's shares of Company H's stock is $16,000.

This doesn't tell us what fraction of the total shares are owned by Investor Q, so there's no way to determine the total value of the stock.
Fact 2 is INSUFFICIENT.

Combined, we know...
Investor P owns 1/4 of the shares.
Investor Q owns an unknown fraction of the shares, which are valued at $16,000

Since we don't know if Investor Q owns 3/4 of the shares or less than 3/4 of the shares (there MIGHT be other investors), there's no way to use the value of the shares that he does own to figure out the total value of the stock.
Combined, INSUFFICIENT.

Final Answer:

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

Never assume on the GMAT... be literal. There can be many investors in a company.

Hello Rich.
If the second statement would have been that total amount of investor P's share is 160000. Then we would have been able to get the answer correct?
1/4 X Total shares = 160000
Total shares(value) = 640000

Hi Prerana94,

In the context of this question... YES - if we knew the fraction of the total shares owned by a person AND the value of those shares, then we could determine the total value of all of the shares (using the equation that you have created).

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

From statement I alone, Investor P owns ¼ of the shares of company H’s total stock.

This only gives us a relationship between two unknowns viz., one equation in two unknowns. Therefore, we will not be able to find unique solutions for the unknown.

Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, the total value of Investor Q’s shares of Company H’s stock is $16000.

Knowing an investor’s shares of a company’s stock is not sufficient to find the total value of the company’s stock.
Statement II alone is woefully insufficient. Answer option B can be eliminated.

Combining statements I and II, we have the following:

From statement I alone, investor P owns 1/4th of company H’s total stock.
From statement II alone, investor Q owns $16000 worth of company H’s stock.

However, we do not know whether the 16000 represents the remaining 3/4th; it could represent any fraction of the total value of company H’s stock.
The combination of statements is insufficient to find the total value of company H’s stock. Answer option C can be eliminated.

The correct answer option is E.

Hope that helps!
Aravind B T

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