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Probability Q

by prachi18oct » Sat Aug 01, 2015 4:34 pm
In order to make the national tennis team, Matt has to play a three-game series against Larry and Steve, and in doing so win two games in a row. He's given a choice, however: he can choose the order in which he plays against his opponents but cannot play the same opponent in consecutive games (so he could play Larry-Steve-Larry OR Steve-Larry-Steve). Assuming that Matt chooses the three-game sequence that maximizes his probability of making the national team, is his probability of making the team greater than 51%?

(1) Matt's probability of beating Steve are better than Matt's probability of beating Larry

(2) The probability that Matt beats Larry is 30%.

a Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
d EACH statement ALONE is sufficient to answer the question asked
e Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
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Source: — Data Sufficiency |
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by MartyMurray » Sat Aug 01, 2015 5:49 pm
prachi18oct wrote:In order to make the national tennis team, Matt has to play a three-game series against Larry and Steve, and in doing so win two games in a row. He's given a choice, however: he can choose the order in which he plays against his opponents but cannot play the same opponent in consecutive games (so he could play Larry-Steve-Larry OR Steve-Larry-Steve). Assuming that Matt chooses the three-game sequence that maximizes his probability of making the national team, is his probability of making the team greater than 51%?

(1) Matt's probability of beating Steve are better than Matt's probability of beating Larry

(2) The probability that Matt beats Larry is 30%.
Statement 1 doesn't give us much to go on. Even though one has to be greater than the other, the probability of Matt's beating Larry and that of his beating Steve could both be close to 0, in which case the probability of his making the team would be well under 51 percent. The probability of Matt's beating Larry and that of his beating Steve could also both be close to 100 percent, in which case the probability of his making the team would be well over 51%.

So by simply looking at extreme cases that fit the minimal constraints of Statement 1, we can tell that Statement 1 is insufficient.

Statement 2 is a little different, because now we have a number to constrain us a little. Let's try using extremes again.

The question asks whether Matt has a greater than 51% chance of making the team. So let's give him the highest chance we can, by making the probability of his beating Steve 100%.

There are two ways this could be set up. We could have Matt play Steve twice and Larry once or we could have him play Steve once and Larry twice.

If he plays Steve twice and Larry once, there is only one way he can win two games in a row. He has to beat Larry in that middle game. So we calculate the probability of win - win - win.

1 x .3 x 1 = .3

If he were to play Larry twice and Steve once, there are three ways he could win two in a row.

win - win - win .3 x 1 x .3 = .09

win - win - lose .3 x 1 x .7 = .21

lose - win - win .7 x 1 x .3 = .21

.21 + .21 + .09 = .51

So if he were to have a 100% chance of beating Steve and if the games were set up this way, Matt would have a 51% chance of making the team.

(I find it a little surprising that Matt has a greater chance of making the team when he twice plays the guy he has a harder time beating, but I guess it makes sense. He gets two cracks at him, and he only has to beat him once.)

51% is the maximum possible probability of his making the team, and the question asks whether his chance is greater than 51%. Since 51% is the maximum, we know that there is no way he can have a chance greater than 51%, and so Statement 2 is sufficient and the correct answer is B.
Last edited by MartyMurray on Sat Aug 01, 2015 6:40 pm, edited 2 times in total.
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by prachi18oct » Sat Aug 01, 2015 6:22 pm
Thnks Marty!
You rock!
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by nikhilgmat31 » Wed Aug 05, 2015 12:57 am
what is the source of this question. Is this a real GMAT question.

never see such question.
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by MartyMurray » Wed Aug 05, 2015 5:58 am
nikhilgmat31 wrote:what is the source of this question. Is this a real GMAT question.
Veritas. It may be a touch more complex than any official question.
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