One's initial inclination when one is doing this question might be to remove 2 and 4 from the set, {1, 2, 3, 4}, and say that the remaining two elements, 1 and 3, constitute the one two element subset that can be created.
However, that such an easy answer would be the right one does not make sense, and in fact, what the question is actually asking is how many subsets can be created that do not contain within them BOTH 2 and 4. So any subset that contains either 2 or 4 works.
Using 4 elements chosen 2 at a time we can create (4 x 3)/(2 x 1) = 6 subsets.
Of those two element subsets, the only one that includes both 2 and 4 is the subset {2, 4}.
So the number of two element subsets that don't include the pair 2 and 4 is 6 - 1 = 5.
The correct answer is D.
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Hi sukhman,,
You can use the Combination Formula to answer this question, although we have to do a little bit of extra work at the end. Since the number of possible outcomes is so small, you could also list them all out.
4C2 = 4!/(2!2!) = 6 pairs
The pairs would be 12, 13, 14, 23, 24 and 34
Since we're asked to NOT use 24, there are 5 options remaining.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
You can use the Combination Formula to answer this question, although we have to do a little bit of extra work at the end. Since the number of possible outcomes is so small, you could also list them all out.
4C2 = 4!/(2!2!) = 6 pairs
The pairs would be 12, 13, 14, 23, 24 and 34
Since we're asked to NOT use 24, there are 5 options remaining.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Brent@GMATPrepNow
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Given the small numbers in the answer choices, we can simply list the allowable outcomes:how many two element subsets of (1,2,3,4) are there that do not contain the pair of elements 2 and 4
a) one b) two c)four d) five e) six
(1,2), (1,3), (1,4), (2,3), (3,4)
So, the answer is D - five
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
