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Senior Manager  V
Joined: 25 Dec 2018
Posts: 484
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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Question Stats: 62% (02:33) correct 38% (02:20) wrong based on 59 sessions

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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

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
Math Expert V
Joined: 02 Aug 2009
Posts: 7941
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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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]

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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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Senior Manager  V
Joined: 25 Dec 2018
Posts: 484
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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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
Math Expert V
Joined: 02 Aug 2009
Posts: 7941
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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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$coins 2/3 of number of 50 cents coin because statement I gives you both as equal and you cannot have different information from the two statements. It should be the number of 25 cents coins is 2/3 of number of 50 cents coin. I am editing it accordingly _________________ Senior Manager  V Joined: 25 Dec 2018 Posts: 484 Location: India Concentration: General Management, Finance GMAT Date: 02-18-2019 GPA: 3.4 WE: Engineering (Consulting) Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] Show Tags 1 Thank you "chetan2u" II edited[/quote] Hi, still the question is required to be edited, it is not the number of 1$ 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] Re: Mrs. Williams has a certain number of coins in her bag in denomination   [#permalink] 20 Jan 2019, 23:13
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