Monday, September 13, 2010

Marla buys two types of pencils only, which costs 21 cents or 23 cents. How many 23 cent pencils did she buy?

(A) She bought 6 pencils in total
(B) The total cost of her purchase was 130 cents


statement (1) is the easier statement: if all you know is that she bought 6 pencils, you of course have no idea how many of those 6 were of each type. this statement is therefore insufficient.

statement (2):
you have 21x + 23y = 130. because that's one equation in two variables, your first instinct is probably to say 'insufficient!!'
the problem here, though, is that this equation must have solutions that are nonnegative integers (and is therefore called a 'diophantine equation', if you like mathematical terms). because of that restriction, it's quite possible that there's only one feasible solution; the only way to find out within a reasonable amount of time is to exhaust the possibilities:
the total cost was 130 cents. so, you can just find all possible values of the total cost of the 23-cent pencils, and then subtract these from 130 and find whether the resulting differences are possible.

so, here we go:

POSSIBLE MULTIPLES OF 23 CENTS ... REMAINING CENTS
0 ...................................................... 130
23 .................................................... 107

46 .................................................... 84
69 .................................................... 61
92 .................................................... 38
115 .................................................. 15


black don't work (because the 'remaining' quantities aren't multiples of 21 cents). green light works.
sufficient.

THERE IS NO FASTER WAY TO HANDLE STATEMENTS / EQUATIONS LIKE THIS ONE WHEN THE SOLUTIONS MUST BE WHOLE NUMBERS.
YOU MUST TEST CASES.
to all the theory types out there: sorry. :(

answer = b

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