IR Two-Part Question Bank #1

[Mk.d]

MGMAT IR Two-Part Question Bank #1:

A gardener is planning a garden layout. There are two rectangular beds, A and B, that will each contain a total of 5 types of shrubs or flowers. For each bed, the gardener can choose from among 6 types of annual flowers, 4 types of perennial flowers, and 7 types of shrubs. Bed A must contain exactly 1 type of shrub and exactly 2 types of annual flower. Bed B must contain exactly 2 types of shrub and at least 1 type of annual flower. No flower or shrub will used more than once in each bed.
Identify the number of possible combinations of shrubs and flowers for bed A and the number of possible combinations of shrubs and flowers for bed B. Make only two selections, one in each column.

Question:
For Bed B, you need exactly 2 shrubs and at least 1 annual flower. I'm just wondering why my method yields a different answer.

For Shrub: 7*6/2 = 21 --> This part is fine
For Annual: 6
For the rest - there remains 4 perennial flowers and 5 annuals flowers for a total of 9 types --> 9*8/2 = 36

21*6*36 = 4,536 --> This is clearly not the right answer. However, I am uncertain as to why you have to break the second part (for annual flowers) into different scenarios instead of lumping them together with the perennial flowers? After all, I have satisfied the minimum requirement of at least 1 annual.

Much appreciated.

[tim]

You seem to be randomly multiplying numbers together without much thought to what the numbers represent. I would recommend with this one we focus on the "at least" part and remember our 1-x trick: figure out what you DON'T want and subtract it from the total:

It sounds like you agree that there are 21 ways to choose shrubs. As for the rest, there are 10 remaining types of plants from which to choose the 3 remaining ones. 10C3 = 120. What about the ones that DON'T contain an annual flower? For that we have to choose 3 from among 4 options. 4C3 = 4. These are the ones we DON'T want from among the 120 choices. 120 - 4 = 116 options for the remaining 3 plants. Multiplying this by the 21 ways to choose shrubs gives us 116 * 21 = 2436.

[IlyaR508]

Dear MGMAT,
This question seems confusing because the answer assumes that the number of flowers resets after they are used up in Bed A. Realistically, if you have 7 shrubs, of which at least 1 was planted in Box A, then at most there should 6 shrubs left for plant B.

Also it is confusing what is meant by "No flower or shrub will used more than once in each bed."

Please comment.

Thanks

[tim]

Here is my comment: It sounds as though you don't like this question. Unfortunately there are a lot of GMAT questions you won't like. Your job is to deal with that and learn to interpret questions the way the GMAT intends for you to.