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An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

The answer to this question is 3*2 or am I missing out on something?
1. For 6 cylinders ( Manual or automatic), (with trailer hitch or not), for a total of 2*2=4
2. For 4 cylinders - Manual or automatic for a total of 2
3. Total number of possibilities is 4+2=6.
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fozzzy
An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

We are given that an automobile manufacturer offers a station wagon with the following:

1) 6-cylinder engine or 4-cylinder engine

2) manual transmission or automatic transmission

3) trailer hitch - only with a 6-cylinder engine.

We need to determine the number of possible combinations.

So, we have 2 possible scenarios:

Scenario #1:

6-cylinder engine (1 option)

manual or automatic transmission (2 options)

trailer hitch or no trailer hitch (2 options)

Thus, for scenario #1, there are 1 x 2 x 2 = 4 possible options.

Scenario #2:

4-cylinder engine (1 option)

manual or automatic transmission (2 options)

Thus, for scenario #2, there are 1 x 2 = 2 possible options.

The total number of combinations is 4 + 2 = 6.

Alternative solution:

By looking at the answer choices, we see that the largest number is 8. That means it won’t be more than 8 combinations. Therefore, we also could list out each combination.

Let’s use the following shorthand: 6c for 6-cylinder engine, 4c for 4-cylinder engine, m for manual transmission, a for automatic transmission, t for trailer hitch, and n for no trailer hitch. We have:

1) 6c-m-n
2) 6c-m-t
3) 6c-a-n
4) 6c-a-t
5) 4c-m-n
6) 4c-a-n

Recall that a trailer hitch can’t be on a station wagon with a 4-cylinder engine, so we can’t have 4c-m-t and 4c-a-t. Thus, there are only 6 combinations.

Answer: D
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fozzzy
An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

The answer to this question is 3*2 or am I missing out on something?

Possible Combinations:

6,M,H
6,M,N
6,A,H
6,A,N
4,M
4,A

Total = 6
ANSWER: D
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fozzzy
An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

We are given that an automobile manufacturer offers a station wagon with the following:

1) 6-cylinder engine or 4-cylinder engine

2) manual transmission or automatic transmission

3) trailer hitch - only with a 6-cylinder engine.

We need to determine the number of possible combinations.

So, we have 2 possible scenarios:

Scenario #1:

6-cylinder engine (1 option)

manual or automatic transmission (2 options)

trailer hitch or no trailer hitch (2 options)

Thus, for scenario #1, there are 1 x 2 x 2 = 4 possible options.

Scenario #2:

4-cylinder engine (1 option)

manual or automatic transmission (2 options)

Thus, for scenario #2, there are 1 x 2 = 2 possible options.

The total number of combinations is 4 + 2 = 6.

Alternative solution:

By looking at the answer choices, we see that the largest number is 8. That means it won’t be more than 8 combinations. Therefore, we also could list out each combination.

Let’s use the following shorthand: 6c for 6-cylinder engine, 4c for 4-cylinder engine, m for manual transmission, a for automatic transmission, t for trailer hitch, and n for no trailer hitch. We have:

1) 6c-m-n
2) 6c-m-t
3) 6c-a-n
4) 6c-a-t
5) 4c-m-n
6) 4c-a-n

Recall that a trailer hitch can’t be on a station wagon with a 4-cylinder engine, so we can’t have 4c-m-t and 4c-a-t. Thus, there are only 6 combinations.

Answer: D


Thanks for your explanation ScottTargetTestPrep!

But i always thought that in cases where order does not matter, we must divide the results in the end, for example in scenario 1 by 1*2*3 and in scenario 2 by 1*2, because we are dealing with a combination?

So why can we neglect that order does not matter in this question? I dont think we are dealing with a permutation here, since the question asks " How many combinations of the five options listed does the manufacturer offer for its station wagon?"

Thanks in advance! :)
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Hi,

I dont really get what this mean "five options listed "?
The question is confusing indeed.
Why not how many combinations that the manufacturer could offer? :?
This question is not hard, but by saying 5 options listed, I could assume there is no 6-cylinder without trailer hitch. That's why I choose 4 :))

fozzzy
An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

The answer to this question is 3*2 or am I missing out on something?
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kirudang

I dont really get what this mean "five options listed "?
The question is confusing indeed.
Why not how many combinations that the manufacturer could offer? :?
This question is not hard, but by saying 5 options listed, I could assume there is no 6-cylinder without trailer hitch. That's why I choose 4 :))


The language in the question can be improved. However, the language is technically written in correct manner.

There are indeed five options offered: 6 cylinder, 4 cylinder, manual, auto, trailer.

6 cylinder model with either manual or auto transmission - This provides two combinations.

4 cylinder model with either manual or auto transmission - This provides two combinations.

6 cylinder model with trailer for both the models with manual or auto transmission - This provides two more combinations.

So, in total, we have six (6) combinations.

ANSWER: (D)
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