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

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Intern
Joined: 25 Dec 2018
Posts: 45
Location: India
Concentration: General Management, Finance
GMAT 1: 590 Q48 V23
Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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Updated on: 20 Jan 2019, 21:11
1
1
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Difficulty:

85% (hard)

Question Stats:

65% (02:32) correct 35% (02:10) wrong based on 49 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, 21:41.
Last edited by chetan2u on 20 Jan 2019, 21:11, edited 3 times in total.
edited the question and corrected the OA
Math Expert
Joined: 02 Aug 2009
Posts: 7335
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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19 Jan 2019, 22:13
2
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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19 Jan 2019, 22:21
2
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.

_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 25 Dec 2018
Posts: 45
Location: India
Concentration: General Management, Finance
GMAT 1: 590 Q48 V23
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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20 Jan 2019, 20:48
1
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
Joined: 02 Aug 2009
Posts: 7335
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

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20 Jan 2019, 20:58
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$coins 2/3 of number of 50 cents coin because statement I gives you both as equal and you cannot have different information from the two statements. It should be the number of 25 cents coins is 2/3 of number of 50 cents coin. I am editing it accordingly _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Intern Joined: 25 Dec 2018 Posts: 45 Location: India Concentration: General Management, Finance GMAT 1: 590 Q48 V23 Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] ### Show Tags 20 Jan 2019, 22:13 1 Thank you "chetan2u" II edited[/quote] Hi, still the question is required to be edited, it is not the number of 1$ 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, 22:13
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