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
OA:D
Source:GMATPrep
An automobile manufacturer offers a station wagon with
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Case 1: 6-cylinder engineNandishSS wrote: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
Number of transmission options = 2. (manual or automatic)
Number of trailer-hitch options = 2. (included or not included)
To combined these options, we multiply:
2*2 = 4.
Case 2: 4-cylinder engine
Here, a trailer-hitch is not available.
Number of transmission options = 2.
Total ways = Case 1 + Case 2 = 4 + 2 = 6.
The correct answer is D.
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As soon as you glance at the answer choices and see that there's no option greater than 8, brute force is also an option. List 'em out.NandishSS wrote: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
OA:D
Source:GMATPrep
6 cylinder - manual - hitch
6 cylinder - manual - no hitch
6 cylinder - automatic - hitch
6 cylinder - automatic - no hitch
4 cylinder - manual (no option for hitch)
4 cylinder - automatic (no option for hitch)
There are 6 options. The answer is D
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Alternatively, you can see how many options there'd have been without restrictions first.NandishSS wrote: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
OA:D
Source:GMATPrep
We have three choices with two options
1) 4 or 6 cylinder
2) manual or automatic
3) hitch or no-hitch
If there were no restrictions then there'd be 2 * 2 * 2 = 8 options.
But the 4 cylinder can't have a hitch. So those 8 options included 2 possibilities that aren't allowed: 4-cylinder manual hitch and a 4-cylinder automatic hitch. So we have 2 undesired options.
Total - undesired = 8 - 2 = 6. Answer is D
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Hi NandishSS,
Sometimes Combination Formula questions come with answers that are relatively small. In this prompt, we know that there are at least 3 options, but no more than 8 options. In these situations, it's usually pretty easy to "map out" all of the possible combinations, without having to do any special math.
We're told that a station wagon has a variety of 'traits':
1) Either a 6-cylinder engine or a 4-cylinder engine
2) Either a manual transmission or an automatic transmission
3) A trailer hitch (but ONLY on a 6-cylinder engine)
We're asked for the number of different combinations of traits on a station wagon. We can list them out:
6 cyl and manual
6 cyl and manual and hitch
6 cyl and automatic
6 cyl and automatic and hitch
4 cyl and manual
4 cyl and automatic
Total combinations = 6
Final Answer: D
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Sometimes Combination Formula questions come with answers that are relatively small. In this prompt, we know that there are at least 3 options, but no more than 8 options. In these situations, it's usually pretty easy to "map out" all of the possible combinations, without having to do any special math.
We're told that a station wagon has a variety of 'traits':
1) Either a 6-cylinder engine or a 4-cylinder engine
2) Either a manual transmission or an automatic transmission
3) A trailer hitch (but ONLY on a 6-cylinder engine)
We're asked for the number of different combinations of traits on a station wagon. We can list them out:
6 cyl and manual
6 cyl and manual and hitch
6 cyl and automatic
6 cyl and automatic and hitch
4 cyl and manual
4 cyl and automatic
Total combinations = 6
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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I'd take the special case first:
SW + 6c + MT + TH
SW + 6c + AT + TH
Then look at the other cases:
Cylinder choices: 2
Transmission choices: 2
Total other choices: 2 * 2 = 4
So you've got two special cases and four regular cases, for a total of 6.
SW + 6c + MT + TH
SW + 6c + AT + TH
Then look at the other cases:
Cylinder choices: 2
Transmission choices: 2
Total other choices: 2 * 2 = 4
So you've got two special cases and four regular cases, for a total of 6.
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As David sagely points out above, the numbers on this one are so small that you're almost better off listing them manually to see each case. (When a combinatorics question has under ten cases, listing them often gives you a good feel for how combinatorics work, and under test conditions can help you from making any sloppy conceptual mistakes.)
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We are given that an automobile manufacturer offers a station wagon with the following:NandishSS wrote: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
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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