Answer: A
Explanation:
To answer this question, you can do the math, or you can rely on the experience you have gained thus far. Let’s work out statement 1 by thinking it through:
Statement 1: We know there are a specific number of girls (q). Since each number of girls would yield a different probability of choosing 2 girls, there must be only one specific number that would yield 1/11. So it must be enough information.
Now, statement 2 requires a little more thought. Let’s work it out by doing the math: Statement 2: This one may seem to follow the same logic, as they are giving us a specific probability. However, this time we are asked to pick one boy and one girl. Look at Table 1 to see why this isn’t enough information.
As you can see, each probability is repeated for inverse combinations of boys and girls. There are two ways to get 16/33, once with 4 boys and 8 girls, and also with 4 girls and 8 boys. This is not enough information. We do not know what q is.
*Note: we will multiply each probability by 2, because we can choose a boy and a girl, or a girl and a boy, and both will yield the desired result.
The answer and explanation to GMAT Practice Question #8 was written by Integrated Learning, a company that provides professional and private one on one tutoring services.
Table 1
| Boys | Girls | P(1 boy and 1 girl)* |
| 1 | 11 | 1/12 x 11/11 = 1/12 x 2 = 1/6 |
| 2 | 10 | 2/12 x 10/11 = 5/33 x 2 = 10/33 |
| 3 | 9 | 3/12 x 9/11 = 9/44 x 2 = 9/22 |
| 4 | 8 | 4/12 x 8/11 = 8/33 x 2 = 16/33 |
| 5 | 7 | 5/12 x 7/11 = 35/132 x 2 = 35/66 |
| 6 | 6 | 6/12 x 6/11 = 1/4 x 2 = 1/2 |
| 7 | 5 | 7/12 x 5/11 = 35/132 x 2 = 35/66 |
| 8 | 4 | 8/12 x 4/11 = 8/33 x 2 = 16/33 |
| 9 | 3 | 9/12 x 3/11 = 9/44 x 2 = 9/22 |
| 10 | 2 | 10/12 x 2/11 = 5/33 x 2 = 10/33 |
| 11 | 1 | 11/12 x 1/11 = 1/12 x 2 = 1/6 |
