MGMAT CAT 6

[ankur.agrawal]

8 cities, including Memphis, are finalists to be chosen to host a political convention. Exactly one city will be chosen to host the convention. What is the probability that Memphis is not chosen?

(1) The probability that any one of the 8 cities does not win the competition is 7/8.

(2) The probability that Memphis wins the competition is 1/8.

OA after some discussion.

[Stuart@KaplanGMAT]

8 cities, including Memphis, are finalists to be chosen to host a political convention. Exactly one city will be chosen to host the convention. What is the probability that Memphis is not chosen?

(1) The probability that any one of the 8 cities does not win the competition is 7/8.

(2) The probability that Memphis wins the competition is 1/8.

OA after some discussion.

Hi!

Some tricky working in (1) which we need to carefully translate, but once we do it's clear that each statement is sufficient alone.

Q: What's the probability that Memphis isn't chosen to host?

First, we need to recognize that if we can answer "what's the probability that Memphis IS chosen to host?" we can also answer the original question, since:

Chance not chosen = 1 - Chance chosen.

Realizing that makes us quickly see that (2) is sufficient alone: eliminate (A), (C) and (E).

Now let's look at (1):

(1) The probability that any one of the 8 cities does not win the competition is 7/8. (Emphasis mine.)

The only way that the probability of any one city not winning could be 7/8 is if each city has exactly the same chance of winning. Since there are 8 cities, each must have a 1/8 chance to win. Now that we know that Memphis has a 1/8 chance to win, we can answer the original question.

Of course, as soon as you realize that (1) means that each city has a 7/8 chance of losing, you can directly conclude that Memphis, one of the cities, has a 7/8 chance of losing - we didn't really need to calculate the chance of Memphis winning to identify (1) as sufficient.

(1) and (2) are each sufficient alone: choose (D).

[ankur.agrawal]

8 cities, including Memphis, are finalists to be chosen to host a political convention. Exactly one city will be chosen to host the convention. What is the probability that Memphis is not chosen?

(1) The probability that any one of the 8 cities does not win the competition is 7/8.

(2) The probability that Memphis wins the competition is 1/8.

OA after some discussion.

Hi!

Some tricky working in (1) which we need to carefully translate, but once we do it's clear that each statement is sufficient alone.

Q: What's the probability that Memphis isn't chosen to host?

First, we need to recognize that if we can answer "what's the probability that Memphis IS chosen to host?" we can also answer the original question, since:

Chance not chosen = 1 - Chance chosen.

Realizing that makes us quickly see that (2) is sufficient alone: eliminate (A), (C) and (E).

Now let's look at (1):

(1) The probability that any one of the 8 cities does not win the competition is 7/8. (Emphasis mine.)

The only way that the probability of any one city not winning could be 7/8 is if each city has exactly the same chance of winning. Since there are 8 cities, each must have a 1/8 chance to win. Now that we know that Memphis has a 1/8 chance to win, we can answer the original question.

Of course, as soon as you realize that (1) means that each city has a 7/8 chance of losing, you can directly conclude that Memphis, one of the cities, has a 7/8 chance of losing - we didn't really need to calculate the chance of Memphis winning to identify (1) as sufficient.

(1) and (2) are each sufficient alone: choose (D).

Hmm . My confusion is:

We are being asked the probability of a city getting chosen as a host. But both the options tell us about the probability of winning not getting chosen as a host.

How do we connect both?

[Ian Stewart]

Hmm . My confusion is:

We are being asked the probability of a city getting chosen as a host. But both the options tell us about the probability of winning not getting chosen as a host.

While I'm sure the interpretation Stuart makes above is what was intended here, the wording of the question is pretty bad. The stem talks about cities being chosen to host a convention, while the statements mention 'winning the competition'. You could very reasonably ask 'what on earth competition are they talking about?' since no 'competition' is mentioned in the stem. The two statements should really read:


1) The probability that any one of the eight cities is not chosen to host the convention is 7/8
2) The probability that Memphis is chosen to host the convention is 1/8


and they should avoid the potentially confusing mention of a competition altogether.