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Difficulty:
25%
(medium)
Question Stats:
75% (01:42) correct
25%
(01:59)
wrong
based on 642
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The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)
(A) 1
(B) 4
(C) 7
(D) 11
(E) 10
(A) 1
(B) 4
(C) 7
(D) 11
(E) 10
27 Aug 2014, 04:34
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royQV
The number of bins with 2 different ingredients = \(C^2_4=6\);
The number of bins with 3 different ingredients = \(C^3_4=4\);
The number of bins with 4 different ingredients = 1 (\(C^4_4=1\)).
The total number of bins with at least two ingredients = 6 + 4 + 1 = 11.
Answer: D.
Hope it's clear.
General Discussion
17 May 2015, 14:02
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Hi All,
The answers to this question are relatively small, so if you don't see the "math" approach to solving this question, then you can 'brute force' the solution by "mapping out" all of the possibilities...
We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 2 ingredients...
2 ingredient blends:
AB
AC
AD
BC
BD
CD
3 ingredient blends:
ABC
ABD
ACD
BCD
4 ingredient blends:
ABCD
Total blends = 6+4+1 = 11
Final Answer:
GMAT assassins aren't born, they're made,
Rich
The answers to this question are relatively small, so if you don't see the "math" approach to solving this question, then you can 'brute force' the solution by "mapping out" all of the possibilities...
We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 2 ingredients...
2 ingredient blends:
AB
AC
AD
BC
BD
CD
3 ingredient blends:
ABC
ABD
ACD
BCD
4 ingredient blends:
ABCD
Total blends = 6+4+1 = 11
Final Answer:
GMAT assassins aren't born, they're made,
Rich
