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A
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Difficulty:
65%
(hard)
Question Stats:
61% (02:37) correct
39%
(02:44)
wrong
based on 181
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Mrs. Williams has a certain number of coins in her bag in denominations of 25 cents, 50 cents and $1. If she has a total of $5 in her bag, what is the number of 25 cents in her bag? Given that she has at least one coin of each denomination. ($1 = 100cents)
(1) Number of $1 coins = number of 50 cent coins > number of 25 cent coins.
(2) The number of 25 cents coins is 2/3 of the number of 50 cent coins.
Kudos for each and every explanation
(1) Number of $1 coins = number of 50 cent coins > number of 25 cent coins.
(2) The number of 25 cents coins is 2/3 of the number of 50 cent coins.
Kudos for each and every explanation
19 Jan 2019, 23:13
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mangamma
Let the number of 25-cents, 50-cents and 1$ be a,B, and c respectively.
So 25a+50b+100c=500....a+2b+4c=20
Statements..
I..c=b>a
So substitute b as c...a+2c+4c=20...a+6c=20..
Now c>a...so if a=1, c can be 3... possible
If a=2, no value of c satisfies c>a
So a=2, b=c=3
Sufficient
II.. some error in statement II
Now after editing the second statement as The number of 25 cents coins is 2/3 of the number of 50 cent coins.
a+2b+4c=20 and \(a=\frac{2b}{3}\)
thus \(\frac{2b}{3}+2b+4c=20......8b+12c=60......2b+3c=15\)
Possible values b=c=3, and a=2..
OR b=6, c=1, and a = 4..
so different possibilities
Insufficient
A
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 755
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
19 Jan 2019, 23:21
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mangamma
So i went for A, Now when i read the 2nd statement, its not clear what it meant by 23 of the number of 50 cent coins.
Statement 1, can be solved very easily
x = number of 25 cents, y number of 50 cents and z number of 1 dollar
0.25 x + 0.50 y + 1 z = 5.00
25x + 50 y + 100z = 500
Number of $1 coins = number of 50 cent coins > number of 25 cent coins.
y=z > x, can only be true when you take values as y=z= 3 and x =2
50 + 150 + 300 = 500.
Sufficient.
OP do share your thoughts.
