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19 Mar 2019, 09:41
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:25) correct
30%
(02:50)
wrong
based on 205
sessions
History
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Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or n pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of n?
(A) 18
(B) 21
(C) 24
(D) 25
(E) 28
(A) 18
(B) 21
(C) 24
(D) 25
(E) 28
06 Jun 2021, 13:40
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Its basically an lcm problem,
lcm of 12,14,15 =420
since cost of 1 purple candy =20
therefore total number of candy =\(\frac{420}{20}\) =21
lcm of 12,14,15 =420
since cost of 1 purple candy =20
therefore total number of candy =\(\frac{420}{20}\) =21
07 Jun 2021, 00:02
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Solution:
Let the cost of each red candy be \(r\)
Let the cost of each green candy be \(g\)
let the cost of each blue candy be \(b\)
So, according to the problem, Casper has \(12r+14g+15b\) cents
The smallest value Casper has is LCM of 12, 14 and 15 which is = \(420\) cents
The problem also states that she can buy n purple candies costing n each.
So to get the least value of n we can write: \(20n=420\)
or, \(n=21\).
Hence the right answer is Option B.
Let the cost of each red candy be \(r\)
Let the cost of each green candy be \(g\)
let the cost of each blue candy be \(b\)
So, according to the problem, Casper has \(12r+14g+15b\) cents
The smallest value Casper has is LCM of 12, 14 and 15 which is = \(420\) cents
The problem also states that she can buy n purple candies costing n each.
So to get the least value of n we can write: \(20n=420\)
or, \(n=21\).
Hence the right answer is Option B.
