GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 18:35

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
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]

### Show Tags

Updated on: 20 Jan 2019, 22:11
1
1
3
00:00

Difficulty:

85% (hard)

Question Stats:

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

### HideShow timer Statistics

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

### Show Tags

19 Jan 2019, 23:13
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
_________________
Director
Joined: 09 Mar 2018
Posts: 997
Location: India
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

### Show Tags

19 Jan 2019, 23:21
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.
Senior Manager
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

20 Jan 2019, 21:48
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: 7941
Re: Mrs. Williams has a certain number of coins in her bag in denomination  [#permalink]

### Show Tags

20 Jan 2019, 21:58
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$coins 2/3 of number of 50 cents coin because statement I gives you both as equal and you cannot have different information from the two statements. It should be the number of 25 cents coins is 2/3 of number of 50 cents coin. I am editing it accordingly _________________ Senior Manager Joined: 25 Dec 2018 Posts: 484 Location: India Concentration: General Management, Finance GMAT Date: 02-18-2019 GPA: 3.4 WE: Engineering (Consulting) Re: Mrs. Williams has a certain number of coins in her bag in denomination [#permalink] ### Show Tags 20 Jan 2019, 23:13 1 Thank you "chetan2u" II edited[/quote] Hi, still the question is required to be edited, it is not the number of 1$ 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, 23:13
Display posts from previous: Sort by