Of the shares of stock owned by a certain investor, 30

Question

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.

EMPOWERgmatRichC · Accepted Answer

Hi All,

The speed and ease with which you handle this DS question will likely be based on how you organize your information. You can 'set up' this question using percents, fractions or decimals (depending on whatever 'format' you think is easiest to deal with).

We're told that an investor owns a variety of shares of stock:
1) 30 percent are shares of Company X stock 
2) 1/7 of the REMAINING shares are shares of Company Y stock.

This means that we can organize the shares into 3 categories:
1) Shares of Company X (30% of the investor's shares)
2) Shares of Company Y (1/7 of 70% = 10% of the investor's shares)
3) Shares of Other Companies (the remaining 60% of the investor's shares)

We're asked for the number of shares of Company X stock that the investor owns.

Fact 1: The investor owns 100 shares of Company Y stock.

Since these 100 shares represent 10% of the investor's shares, then the TOTAL shares = 100(10) = 1,000. Since 30% of the TOTAL shares = Company X shares, we know that (30%)(1000) = 300 is the number of shares.
Fact 1 is SUFFICIENT

Fact 2: The investor owns 200 more shares of Company X stock than of Company Y stock.

This Fact helps us to create the following equation:

(30%)(Total shares) = (10%)(Total shares) + 200
(20%)(Total shares) = 200
Total shares = 1,000

Again, we can calculate the total shares of Company X stock = (30%)(1,000) = 300
Fact 2 is SUFFICIENT

Final Answer:  D

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

BabySmurf · Answer

Let N be the number of total shares the investor owns.
0.3 N = number of Company X stock he owns
1/7 of 0.7 N (the remaining shares) = 0.1 N = number of Company Y stock he owns

Goal is to calculate N. X is 30% of N (which is what we are asked to calculate).

Statement 1: 
100 Y shares and we know Y shares are 10% of the total N.
0.1 N = 100. N is therefore 1,000. SUFFICIENT.

Statement 2: 
He owns 30% N shares and 10% Y shares. And that differential is 200.
0.3 N - 0.1 N = 200. N is therefore 1,000. SUFFICIENT.

mcelroytutoring · Answer

Attached is a visual that should help.

CrushTHYGMAT · Answer

Hello,  Bunuel . This is a GMAT Prep question. Could you please tag it?

Thank you!

Bunuel · Answer

_____________________
Added the OA. Thank you.

gmatpro15 · Answer

Let N be the number of total shares the investor owns.
0.3 N = number of Company X stock he owns
1/7 of 0.7 N (the remaining shares) = 0.1 N = number of Company Y stock he owns

Goal is to calculate N. X is 30% of N (which is what we are asked to calculate).

Statement 1:
100 Y shares and we know Y shares are 10% of the total N.
0.1 N = 100. N is therefore 1,000. SUFFICIENT.

Statement 2:
He owns 30% N shares and 10% Y shares. And that differential is 200.
0.3 N - 0.1 N = 200. N is therefore 1,000. SUFFICIENT

MarkGMATMentor · Answer

One pattern you’ll see sometimes on the GMAT is that a  difference  (as in one quantity subtracted from another) can be more helpful than it first appears.  This pattern shows up in several contexts, one of which is in Data Sufficiency.

Before testing the statements, make sure you’re clear on the prompt. If 30% of the shares are shares of X, then 70% of the shares remain. Then, 1/7 of that 70% are shares of Y, so Y represents 10% of the overall shares. 60% of the shares remain, which are neither X nor Y.

Statement 1: 
If the investor owns 100 shares of Y, and you know that Y represents 10% of the shares, you’ll be able to determine both the total number of shares and the 30% that are shares of X. (No need to actually calculate, but if 100 represents 10% of the shares, then there are 1,000 total shares and 300 shares of X.)  Sufficient.
 
 Statement 2: 
This tells you that X – Y = 200. This may at first seem insufficient, because we don’t have a number of shares for X or Y that we can match up to 30% or 10%.

However, we do know that X represents 30% of the total and Y represents 10% of the total. Thus, the  difference  between the two is equivalent to 30% - 10% = 20% of the total. In other words, the 200 represents 20% of the total. Knowing that, you can find the total shares and then the number of shares of X.  Sufficient.
  
 The answer is D.
 
The trap answer here is A.  If you recognize that the difference between the two shares can be treated as a quantity like any other, you can solve this question and others like it without falling into the trap.

Of the shares of stock owned by a certain investor, 30

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Of the shares of stock owned by a certain investor, 30

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