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13 Apr 2020, 01:03
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (02:34) correct
59%
(01:57)
wrong
based on 81
sessions
History
Date
Time
Result
Not Attempted Yet
With plenty of pennies, nickels and dimes in my pockets, I can buy a cup of coffee for $1.50 in any possible way. In how many different ways a cup of coffee can be bought with the exact amount of money ($1.50)?
A. 100
B. 150
C. 192
D. 256
E. 300
A. 100
B. 150
C. 192
D. 256
E. 300
13 Apr 2020, 01:39
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Bookmarks
nick1816
Penny = ¢1
Nickel = ¢5
Dime = ¢10
$1.5 = ¢150
p + 5n + 10d = 150
@d = 0, (p, n) may have following ordered pairs
(150, 0)
(145, 1)
---
---
(0, 30)
i.e. 31 ordered pairs
@d = 1, (p, n) may have following ordered pairs
(140, 0)
(135, 1)
---
---
(0, 28)
i.e. 29 ordered pairs
@d = 2, (p, n) may have following ordered pairs
(130, 0)
(125, 1)
---
---
(0, 26)
i.e. 27 ordered pairs
i.e. total Solutions = 31+29+27+....+1 = Sum of 16 Odd consecutive numbers (sum of odd from1 to 32)
CONCEPT: 1+3+5+.... (2n-1) = Sum of first n Concecutive odd integers \(= n^2\)
i.e. total Solutions = 31+29++27+....+1 = Sum of 16 Odd consecutive numbers \(= 16^2 = 256\)
Answer: Option D
