vkb16 wrote:Billy has an unlimited supply of the following coins: pennies (1¢), nickels (5¢), dimes (10¢), quarters (25¢), and half-dollars (50¢). On Monday, Billy bought one candy for less than a dollar and paid for it with exactly four coins (i.e., he received no change). On Tuesday, he bought two of the same candy and again paid with exactly four coins. On Wednesday, he bought three of the candies, on Thursday four of the candies, and on Friday five of the candies; each day he was able to pay with exactly four coins. Which of the following could be the price of one candy in cents?
8
13
40
53
66
OA is C
Does anyone knw a short method to do this? MGMAT has two really complex methods...
thanks
Before we do a lot of algebra, let's start with some common sense to narrow down the playing field.
On Friday he bought 5 candies with 4 coins. Since the biggest coin he has is 50 cents, 5 candies must be cheaper than 4*50 = 200 cents. Therefore, the maximum price per candy is 40 cents: eliminate D and E.
So, we have:
8
13
40
Now we have a couple of solid options: we could set up some algebraic equations; alternatively, we could work with the answer choices. Since we have a LOT of variables and a LOT of equations, I'm going for door #2.
Let's start with 8 cents:
1 candy (8 cents) for 4 coins: 5, 1, 1, 1
2 candies (16 cents) for 4 coins: 5, 5, 5, 1
3 candies (24 cents) for 4 coins: no way to get the "4" at the end... bzzt! Eliminate A.
13 cents:
1 candy (13 cents) for 4 coins: 10, 1, 1, 1
2 candies (26 cents) for 4 coins: 10, 10, 5, 1
3 candies (39 cents) for 4 coins: no way to get the "9" at the end... bzzt! Eliminate B.
C is the only choice left, so it must be correct.
Just for fun:
40 cents:
1 candy (40 cents) for 4 coins: 10, 10, 10, 10
2 candies (80 cents) for 4 coins: 50, 10, 10, 10
3 candies (120 cents) for 4 coins: 50, 50, 10, 10
4 candies (160 cents) for 4 coins: 50, 50, 50, 10
5 candies (200 cents) for 4 coins: 50, 50, 50, 50
Ding ding!
Now, if we had thought ahead a bit, we would have reasoned that it's going to be far easier to make our payments if the per candy price ends in a "5" or "0", since the only way to get a different units digit is to use pennies. If we had made that deduction, then we would have either just guessed C if we were in a rush or started by testing 40 cents before 8 or 13.
