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19 Aug 2006, 11:17
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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?
A: 8¢
B: 13¢
C: 40¢
D: 53¢
E: 66¢
OA Later.. I took a hell lot of time to sove this one. A short solution would be appreciated.
Are MGMAT questions usually harder?
A: 8¢
B: 13¢
C: 40¢
D: 53¢
E: 66¢
OA Later.. I took a hell lot of time to sove this one. A short solution would be appreciated.
Are MGMAT questions usually harder?
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19 Aug 2006, 11:51
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Last question first... yes MGMAT is a little harder than usual.. but is good for thinking.
The coins are 1c, 5c, 10c, 25c, 50c
Maximum value of 4 coins = 200 cents.
Therefore, to buy 5 candies and pay 200cents would imply a price of less than or equal to 40cents.
This eliminates D and E
Lets do PoE for A-C
Cost of 8c =>
8 : 5 + 1 + 1 + 1
16: 5 + 5 + 5 + 1
24:10 + 5 + 5 + ?? Not possible... Eliminate
Cost of 13c =>
13 : 10 + 1 + 1 + 1
26 : 10 + 10 + 5 + 1
39 : 25 + 10 + 1 + 1 + 1 + 1 Not possible ... Eliminate
Answer : C 40c.
40c = 10 x 4
80c = 50 + 10x3
120c = 50x2 + 10x2
160c = 50x3 + 10x1
200c = 50x4
Took about 2mins...
The coins are 1c, 5c, 10c, 25c, 50c
Maximum value of 4 coins = 200 cents.
Therefore, to buy 5 candies and pay 200cents would imply a price of less than or equal to 40cents.
This eliminates D and E
Lets do PoE for A-C
Cost of 8c =>
8 : 5 + 1 + 1 + 1
16: 5 + 5 + 5 + 1
24:10 + 5 + 5 + ?? Not possible... Eliminate
Cost of 13c =>
13 : 10 + 1 + 1 + 1
26 : 10 + 10 + 5 + 1
39 : 25 + 10 + 1 + 1 + 1 + 1 Not possible ... Eliminate
Answer : C 40c.
40c = 10 x 4
80c = 50 + 10x3
120c = 50x2 + 10x2
160c = 50x3 + 10x1
200c = 50x4
Took about 2mins...
19 Aug 2006, 11:52
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Would be interested to find out if I did it right? 
