Hi kamalakarthi,

This DS question is essentially just a wordy algebra question. Properly translating the language in the main prompt into "math" will make the rest of the work really easy to do.

We're told that an investor owns some shares of stock, 30% of those total shares are of Stock X and 1/7 or the REMAINING shares are of Stock Y. Before doing anything else, I'm going to translate all of this into algebra:

T = Total shares owned
.3T = number of shares of Stock X

Now, to figure out the number of shares of Stock Y, we need to take the REMAINING shares (in this case, .7T shares) and multiply by 1/7...
.7T(1/7) = (7/10)(T)(1/7) = T/10 = .1T

.1T = number of shares of Stock Y

The question asks for the number of shares of Stock X, so it's asking for the value of .3T (in other words, if you can figure out the value of T, then you can answer the question).

Fact 1: The investor owns 100 shares of Stock Y

This means that .1T = 100.
We CAN solve for T and there is just one answer (and we can save time since we don't have to do the work to see that there's just one answer).
Fact 1 is SUFFICIENT

Fact 2: The investor owns 200 MORE shares of Stock X than Stock Y.

We can translate this into an equation:

.3T = .1T + 200
.2T = 200

Again, we CAN solve for T and there is just one answer.
Fact 2 is SUFFICIENT

Final Answer: D

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

Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

(1) The investor owns 100 shares of Company Y stock.
(2) The investor owns 200 more shares of Company X stock than of Company Y stock.

Target question: What is the value of n?

Given - part a: Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock ..
If 30% of the shares are Company X, then 70% of the shares are NOT in Company X

Given - part b: ... and 1/7 of the remaining shares are shares of Company Y stock
1/7 of 70% = 10%, so 10% of the shares are in Company Y

Statement 1: The investor owns 100 shares of Company Y stock.
If 30% of the shares are Company X and 10% of the shares are in Company Y, then there are 3 TIMES as many shares in Company X as in Company Y.
(3)(100) = 300, so there are 300 shares in Company X.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The investor owns 200 more shares of Company X stock than of Company Y stock.
So, (# of Company X shares) - (# of Company Y shares) = 200
Let T = total number of shares
So, (30% of T) - (10% of T) = 200
Rewrite as 0.3T - 0.1T = 200
Simplify: 0.2T = 200
Solve: T = 1000
So, there are 1000 shares altogether.
30% of the shares are in Company X, and 30% of 1000 = 300
So there are 300 shares in Company X.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent