Billy has an unlimited supply of the following coins:

Question

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

I solved this by back solving and it took me 6 minutes. Need expert guidance on how to crack this faster?

8
13
40
53
66

I solved this by back solving and it took me 6 minutes. Need expert guidance on how to crack this faster?

walker · Answer

I don't know how to solve it directly but have some ideas how to make back-solving faster.

1. Five candies cannot cost more than 2$ (4*50¢). So, maximum price for candy is 200/5=40 (8,13,40 survive.)
2. All prices has not to be presented as 5n+4, because we need at least 5 coins.
3. So, in the case of 40, price of 1..5 candies cannot be 5n+4

8: 8=5+3, 16=15+1,  24=20+4  - red flag
13: 13=10+3, 26=20+1,  39=35+4  - red flag

40 is an answer.

FN · Answer

I get 40..too.. just had to plug numbers in..and really didnt know where to start so..started with C..and got lucky

kevincan · Answer

Focus on the remainders when x, 2x, 3x, 4x and 5x are divided by 5. If these are high (3 or 4) then a lot of pennies are needed! Be wary of any unit price that is not a multiple of 5!

8 X 3 --- remainder 4
13 x 3 --- remainder 4
53 x 3---remainder 4
66 x 4--- remainder 4

rahulgoyal1986 · Answer

40 is the answer. and I spent 8 mins. So, come out with an approach :shock:

GMATBLACKBELT · Answer

MTWTF
12345

C. Just did it in my head. Took bout 3min.

FN · Answer

this here is the key..you have to realize that the answer choice has to be a multiple of 5..

chronic · Answer

If we are allowed to assume that on Friday he bought the maximum number of candies that he could buy with 4 coins, then he must have used 4 50 cents coins to buy 5 candies at 40 cents each.

zeenie · Answer

got it ! but by trial and error. The price should be a multiple of 5, thats all I remebered to use

rpmodi · Answer

I still don't get how did u come up with 5n+4?

zeenie · Answer

Let me try to explain it.
Lets say the price of one of the candys is 9 cents
which is of the form 5n+4
for this we need to shel out a 5 cent coin + 4 coins of 1 cent each
But the quesion says we can use only 4 coins !
so we cant use a price of the form 5n+4

The price of each candy is given.
you multiply by 2, 3,4 for tue, wed , thur and so on
AS walker has shown, some proces will be of the form 5n+4, 
discard !!

Walker you must be a genius ! I could never come up with this

ritula · Answer

If a question like this comes in my exam day ,i will b dead for sure! :cry:

buffdaddy · Answer

u should be smiling since if u get these type of hard questions, u are doing VERY well..

Billy has an unlimited supply of the following coins:

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