artisood17 wrote:

When a player in a certain game removed a marble from a bag a certain number of times, 3 more blue marbles than red marbles resulted. The bag consisted of only blue and red marbles. How many times did a blue marble result?

(1) A red marble resulted 3/7 of the time.

(2) The player received 2 points each time a blue marble resulted and lost 2 points each time a red marble resulted, for a total of 6 points.

Dear

artisood17I'm happy to respond.

I don't have the highest opinion of this question. The phrasing of the stem is awkward: it makes me suspect that this question was written by a non-native speaker whose understanding of math far exceeds his understanding of English. All the Quant questions on the GMAT are impeccable in their language: the words and numbers are handled with the same level of precision.

It's not clear to me that the picking marbles set-up is the clearest set-up for what the question writer was trying to test.

Here's the solution.

Let R = # of red marbles picked, and B = # of blue marbles picked

He picks a total of N marbles. We want to know N. We know N = R + B, and B = R + 3. We have three variables.

Statement #1:

A red marble resulted 3/7 of the time. This means that

R = (3/7)N

The direct implication is that if 3/7 were red, the other 4/7 had to be blue.

B = (4/7)N

We know

B - R = 3

(4/7)N - (3/7)N = 3

(1/7)N = 3

N = 21

He picked a total of 21 marbles, 12 blues and 9 red.

With this statement, we were able to compute everything. This statement, alone and by itself, is

sufficient.

Statement #2:

The player received 2 points each time a blue marble resulted and lost 2 points each time a red marble resulted, for a total of 6 points.

This statement is way way too long to be one of the statements of a GMAT DS question. Much of this information easily could have be included in the prompt description. The question writer here is woefully uninformed about the standards of the GMAT.

Nevertheless, this is a mathematically interesting statement because it's a

tautological statement.

If he gains two points for every blue and loses two for every red, then every red + blue pair would be worth zero. We know from the prompt that we could pair up all the marbles into red + blue pairs, and we would be left with just 3 unpaired blues, which would be worth 6 points. From the prompt information, we already know this numerical result: this new statement adds no new mathematical information--that's precisely the definition of a tautological statement.

This statement is completely

insufficient. In essence, it contains no information different from that in the prompt.

OA =

(A)A mathematically interesting yet ultimately flawed question. One really has to understand many things to write a solid GMAT Quant practice question, although these are considerably easier to produce than are solid GMAT Verbal practice questions.

Here's a high quality DS practice question:

Ratios Inside Two CirclesDoes all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep