GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 19 Jun 2021, 22:59
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
A collection of 16 coins, each with a face value of either 10 cents or
21 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
B
AbdurRakib
Director
Director
Joined: 11 May 2014
Status:I don't stop when I'm Tired,I stop when I'm done
Posts: 504
Location: Bangladesh
Concentration: Finance, Leadership
Schools: Wharton '20, Yale '20, Tepper '20
GPA: 2.81
WE:Business Development (Real Estate)
GMAT ToolKit User Top Member of the Month
A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  14 Jun 2016, 13:09
8
Kudos
55
Bookmarks
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (01:42) correct 18% (01:55) wrong based on 2510 sessions

Hide Show timer Statistics

A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Expert Reply
User avatar
V
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 5482
Location: Canada
Top Member of the Month
A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  Updated on: 06 Aug 2020, 15:53
9
Kudos
5
Bookmarks
Expert Reply
Top Contributor
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


Another approach is to use algebra:

Let Q = # of quarters ($0.25)
So, 16 - Q = # of dimes ($0.10)

We're told that: (value of quarters) + (value of dimes) = $2.35
So, we get: 0.25Q + 0.10(16 - Q) = 2.35
Expand: 0.25Q + 1.6 - 0.1Q = 2.35
Simplify: 0.15Q + 1.6 = 2.35
0.15Q = 0.75
Q = 5

Answer:
Show Spoiler
B


Here are some videos that cover the concepts required to answer this question:



_________________
Image

A focused approach to GMAT mastery
Signature Read More

Originally posted by BrentGMATPrepNow on 14 Jun 2016, 15:06.
Last edited by BrentGMATPrepNow on 06 Aug 2020, 15:53, edited 1 time in total.
General Discussion
User avatar
V
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 5482
Location: Canada
Top Member of the Month
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  14 Jun 2016, 15:01
4
Kudos
3
Bookmarks
Expert Reply
Top Contributor
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


One solution is to start TESTING answer choices.

A) 3
If there are 3 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 13 coins must be dimes (worth $0.10 each)
3 quarters = $0.75 and 13 dimes = $1.30
So the TOTAL value = 0.75 + $1.30 = $2.05
NO GOOD - we want a total of $2.35

B) 5
If there are 5 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 11 coins must be dimes (worth $0.10 each)
5 quarters = $1.25 and 11 dimes = $1.10
So the TOTAL value = 1.25 + $1.10 = $2.35
BINGO!

Answer:
Show Spoiler
B

_________________
Image

A focused approach to GMAT mastery
Signature Read More
avatar
sauravpaul
Intern
Intern
Joined: 01 May 2015
Posts: 34
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  14 Jun 2016, 23:52
12
Kudos
4
Bookmarks
25x + 10(16-x) = 235
15x = 75
x = 5
User avatar
paidlukkha
Senior Manager
Senior Manager
Joined: 11 Nov 2014
Posts: 296
Location: India
Concentration: Finance, International Business
Schools: ISB '18, Great Lakes '18, SPJ PGPM"17, LBS '18, NTU '18, NUS '18
WE:Project Management (Telecommunications)
GMAT ToolKit User
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  06 Aug 2016, 00:47
1
Bookmarks
x+y = 16
y=16-x

10x+25y=235
2x+5y=47
2x+80-5x=47
-3x=-33
x=11
y=5

B
User avatar
V
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 14293
Location: United States (CA)
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  02 Dec 2016, 05:48
3
Kudos
1
Bookmarks
Expert Reply
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


We can let the number of 10-cent coins = d and the number of 25-cent coins = q. We are given that there are 16 total coins; thus, d + q = 16.

We are also given that the total face value is $2.35, thus:

0.1d + 0.25q = 2.35

10d + 25q = 235

Isolating d in our first equation, we have d = 16 - q. We can substitute 16 - q for d in our second equation and we have:

10(16 - q) + 25q = 235

160 - 10q + 25q = 235

15q = 75

q = 5

There are 5 coins with a face value of 25 cents.

Answer: B
_________________

★ ★ ★ ★ ★   350 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (Pre-Launch)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Signature Read More
avatar
G
LeonidK
Manager
Manager
Joined: 28 Jul 2016
Posts: 128
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  09 Mar 2017, 15:04
x - number of 10-cent coins
y - number of 25-cent coins

x+y=16
x*0.10 + y*0.25 = 2.35
x*0.10 + y*0.10 + y*0.15 = 2.35
0.10*(x+y) + y*0.15 = 2.35
0.15*y = 2.35-1.60
y = 5

Answer B
User avatar
G
nkmungila
Manager
Manager
Joined: 07 Jun 2017
Posts: 147
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE:Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  13 Sep 2017, 21:50
1
Kudos
let x be 10 cents coin and y be 25 cents coin
then
10x+25y = 235.................(i)
x+y = 16 .................(ii)

(ii) * 10
10x+10Y = 160 ............(iii)

then (i) - (iii)
15 y = 75
y=5
Hence Answer B
User avatar
V
adkikani
IIM School Moderator
Joined: 04 Sep 2016
Posts: 1398
Location: India
WE:Engineering (Other)
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  17 Mar 2018, 03:46
pushpitkc niks18 Hatakekakashi
amanvermagmat

Quote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35.


Let x: no coins with 10 cents as face value
Let y: no coins with 25 cents as face value

I am clear about forming x + y = 16

How can I be sure to form which of two below algebraic equations?

0.1 x + 0.25 y = 2.35 OR

0.25 x + 0.1 y = 2.35

Since I am getting y = 5 (or x= 11) in first case and (x=5 or y=11) in second case.
What mistake I am making since I must get an unique solution from answer choice in PS.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Signature Read More
avatar
D
niks18
Retired Moderator
Joined: 25 Feb 2013
Posts: 1092
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  17 Mar 2018, 03:53
adkikani wrote:
pushpitkc niks18 Hatakekakashi
amanvermagmat

Quote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35.


Let x: no coins with 10 cents as face value
Let y: no coins with 25 cents as face value

I am clear about forming x + y = 16

How can I be sure to form which of two below algebraic equations?

0.1 x + 0.25 y = 2.35 OR

0.25 x + 0.1 y = 2.35

Since I am getting y = 5 (or x= 11) in first case and (x=5 or y=11) in second case.
What mistake I am making since I must get an unique solution from answer choice in PS.


Hi adkikani

in your assumption x represents 10 cents or 0.1 dollars, so total contribution from x coins will be 0.1x

similarly y represents 25 cents or 0.25 dollars, so total contribution from y coins=0.25y

Hence total amount =0.1x+0.25y=2.35

and total number of coins =16 i.e x+y=16
User avatar
P
Hatakekakashi
Current Student
Joined: 07 Jan 2016
Posts: 1310
Location: United States (MO)
GMAT 1: 710 Q49 V36
Premium Member Reviews Badge CAT Tests
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  17 Mar 2018, 03:58
adkikani wrote:
pushpitkc niks18 Hatakekakashi
amanvermagmat

Quote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35.


Let x: no coins with 10 cents as face value
Let y: no coins with 25 cents as face value

I am clear about forming x + y = 16

How can I be sure to form which of two below algebraic equations?

0.1 x + 0.25 y = 2.35 OR

0.25 x + 0.1 y = 2.35

Since I am getting y = 5 (or x= 11) in first case and (x=5 or y=11) in second case.
What mistake I am making since I must get an unique solution from answer choice in PS.


Adding to what niks18 said

If you have confusion regarding two choices

Always verify

If x=5 y=11

Substitute in the equation

And if the answer equals 2.35 that's the answer

Posted from my mobile device
_________________
Verbal Guidance
Signature Read More
User avatar
V
AkshdeepS
SVP
SVP
Joined: 13 Apr 2013
Status:It's near - I can see.
Posts: 1637
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Reviews Badge
A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  18 Mar 2018, 06:47
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


We know x + y = 16 ----- I

x = 16 - y -----(II)

Now, 0.10x + 0.25y = 2.35

0.10(16 - y) + 0.25y = 2.35

1.6 - 0.10y +0.25y = 2.35

1.6 - 0.15y = 2.35

y = 5

(B)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Signature Read More
avatar
B
FANewJersey
Intern
Intern
Joined: 01 May 2017
Posts: 31
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  07 Apr 2018, 06:02
GMATPrepNow wrote:
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


One solution is to start TESTING answer choices.

A) 3
If there are 3 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 13 coins must be dimes (worth $0.10 each)
3 quarters = $0.75 and 13 dimes = $1.30
So the TOTAL value = 0.75 + $1.30 = $2.05
NO GOOD - we want a total of $2.35

B) 5
If there are 5 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 11 coins must be dimes (worth $0.10 each)
5 quarters = $1.25 and 11 dimes = $1.10
So the TOTAL value = 1.25 + $1.10 = $2.35
BINGO!

Answer:
Show Spoiler
B


GMATPrepNow, How and When do you we know that we can solve a word problem (or any other problem for that matter) by using Testing "The Answer Choices Method"
User avatar
V
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 5482
Location: Canada
Top Member of the Month
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  08 Apr 2018, 05:58
1
Kudos
Expert Reply
Top Contributor
FANewJersey wrote:
GMATPrepNow wrote:
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


One solution is to start TESTING answer choices.

A) 3
If there are 3 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 13 coins must be dimes (worth $0.10 each)
3 quarters = $0.75 and 13 dimes = $1.30
So the TOTAL value = 0.75 + $1.30 = $2.05
NO GOOD - we want a total of $2.35

B) 5
If there are 5 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 11 coins must be dimes (worth $0.10 each)
5 quarters = $1.25 and 11 dimes = $1.10
So the TOTAL value = 1.25 + $1.10 = $2.35
BINGO!

Answer:
Show Spoiler
B


GMATPrepNow, How and When do you we know that we can solve a word problem (or any other problem for that matter) by using Testing "The Answer Choices Method"


For most word problems, you should at least consider the possibility of testing the answer choices. HOWEVER this doesn't necessarily mean that testing the answer choices will be the best/fastest approach.

I'd say that, in most cases, testing the answer choices is not the best approach. That said, it's a great strategy if you can't think of any other ways to solve the question.

In other situations, testing the answer choices is impossible. For example:

In how many ways can we arrange the letters in the word FAST?
A) 4
B) 8
C) 12
D) 16
E) 24

As you can see, there is no way to actually test the answer choices for this question.

I hope that helps.

Cheers,
Brent
_________________
Image

A focused approach to GMAT mastery
Signature Read More
avatar
B
FANewJersey
Intern
Intern
Joined: 01 May 2017
Posts: 31
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  09 Apr 2018, 04:38
Thank you GMATPrepNow
User avatar
B
sarahfiqbal
Intern
Intern
Joined: 06 Jan 2015
Status:Studying for GMAT
Posts: 22
Location: United Kingdom
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  23 May 2019, 18:47
Let's assume x are the coins valued at 0.10 and y are the coins valued at 0.25. We want to find value of y.

First, remove decimal bits and form algebraic equations:

10x + 25y = 235 --> equation 1
x+y = 16 --> equation 2
x= 16-y --> equation 3

Second, insert equation 3 into equation 1:

10 (16-y) + 25y = 235
160 - 10y + 25y = 235
160 + 15y = 235
15y= 75
y= 5

Answer: B
User avatar
B
LeonZhiba
Intern
Intern
Joined: 14 Jun 2019
Posts: 4
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  15 Jun 2019, 05:18
25=5*5
235=5*47
GCF=5 => answer B
Can check:
5*25=125
(16-5)*10=110
125+110=235
User avatar
V
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 4393
Location: India
Schools: HBS '22, CBS '22, Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  15 Sep 2019, 09:14
1
Kudos
1
Bookmarks
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


Given: A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35.

Asked: How many of the coins have a face value of 25 cents?

Let the number of 10 cents coin and 25 cents coins be x & y respectively
10x + 25y = 235
x + y = 16

Q. y = ?

x = 16 - y
10 (16-y) + 25y = 235
160 + 15y = 235
15y = 235 - 160 = 75
y = 5

IMO B
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Signature Read More
User avatar
D
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 5516
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
GMAT ToolKit User
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  28 Sep 2020, 09:56
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11

\(\frac{a}{10} + \frac{(16-a)}{4 }= \frac{235}{100}\)

Or, \(\frac{10a+25(16-a)}{100}= \frac{235}{100}\)

Or, \(10a+400 - 25a = 235\)

Or, \(-15a = -165\)

So, a = 11 and thus there are 5 no of 25 cents coins, Answer must be (B)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Signature Read More
User avatar
P
MHIKER
VP
VP
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 1332
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink] New post  24 Dec 2020, 05:09
1
Kudos
Top Contributor
AbdurRakib wrote:
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11


\(x= 10\) cents coin

\(y= 25\) cents coin

\(x+y=16; x=16-y\)

\(0.10x+0.25y=2.35\)

\(10x+25y=235\)

\(10(16-y)+25y=235\)

\(160-10y+25y=235\)

\(15y=75\)

\(y=5 \)

The answer is \(B\)
_________________
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html
Signature Read More
GMAT Club Bot
gmatclubot
Re: A collection of 16 coins, each with a face value of either 10 cents or [#permalink]
24 Dec 2020, 05:09
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
 1   2   
Moderators:
chetan2u
Math Expert
10017 posts
Bunuel
Math Expert
77301 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2543 posts
generis
Senior SC Moderator
4812 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions