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Mrs. Williams has a certain number of coins in her bag in denomination

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mangamma
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Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   Updated on: 20 Jan 2019, 22:11
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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.

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A

Originally posted by mangamma on 19 Jan 2019, 22:41.
Last edited by chetan2u on 20 Jan 2019, 22:11, edited 3 times in total.
edited the question and corrected the OA
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   19 Jan 2019, 23:13
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mangamma wrote:
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 $1 coins is 23 of the number of 50 cent coins.

Kudos for each and every explanation



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
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   19 Jan 2019, 23:21
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mangamma wrote:
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 $1 coins is 23 of the number of 50 cent coins.


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.
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   20 Jan 2019, 21:48
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chetan2u wrote:
mangamma wrote:
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 $1 coins is 23 of the number of 50 cent coins.

Kudos for each and every explanation



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


II edited
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   20 Jan 2019, 21:58
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mangamma wrote:
chetan2u wrote:
mangamma wrote:
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 $1 coins is 23 of the number of 50 cent coins.

Kudos for each and every explanation



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


II edited



Hi,

still the question is required to be edited, it is not the number of 1$ coins 2/3 of number of 50 cents coin because statement I gives you both as equal and you cannot have different information from the two statements.
It should be the number of 25 cents coins is 2/3 of number of 50 cents coin.

I am editing it accordingly
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   20 Jan 2019, 23:13
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Thank you "chetan2u"


II edited[/quote]


Hi,

still the question is required to be edited, it is not the number of 1$ coins 2/3 of number of 50 cents coin because statement I gives you both as equal and you cannot have different information from the two statements.
It should be the number of 25 cents coins is 2/3 of number of 50 cents coin.

I am editing it accordingly[/quote]
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   17 Feb 2021, 06:33
i think statement 2 is sufficient enough to provide us with single ans.
25a+50b+100c = 500
given, c=2b/3
so, 2b=3c

25a+50b+100c= 500
25 (a+2b+4c)= 500
a+2b+4c=20
a+3c +4c = 20
a= 20 - 7c
If c=1 b=1.5 (not possible) it must be an integer as its a number of denomination.
Only possible value for c=2 , b= 3 and c= 6.
so , c=6. Sufficient.

Ans Option D.
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] New post   12 Sep 2023, 09:01
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Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink]
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