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Junior | Next Rank: 30 Posts
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by RobertP » Sun Feb 21, 2016 3:44 pm
Hello everyone,

Mathey is traveling by a country where the coins are issued in only two values, 2c and 5c, which are made of iron and copper, respectfully. If he has 10 iron coins and 10 copper coins, how many different sumons between 1c and 70c can he combine with his coins.

(A) 66
(B) 67
(C) 68
(D) 69
(E) 70

Thank you.
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by MartyMurray » Mon Feb 22, 2016 2:31 am
The ten iron coins alone can be used to create any even sum from 2 to 20.

The ten copper coins alone can be used to create any sum that is a multiple of 5 from 5 to 50.

Counting by 2's or 5's there is no way for him to create sums of 1 or 3.

However, once he gets to 5 he can create odd sums by adding 2's to multiples of 5.

He can continue in that manner until he gets close to 70, at which point he will have used up all of the fives.

So counting down from 70 there is no way to create the sums 69 or 67.

So of the numbers from 1 to 70 there are four numbers he cannot create. 70 - 4 = 66

The correct answer is A.
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by Matt@VeritasPrep » Thu Mar 03, 2016 12:58 am
I'm not sure how the text of the stem changed so much -- purple monkey dishwasher, I guess -- but this is one of our questions, and we have a nice blog post devoted to it here. Check it out!
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