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

 It is currently 09 Dec 2019, 18:42 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The average value of all the pennies, nickels, dimes,

Author Message
TAGS:

### Hide Tags

Senior Manager  P
Status: Manager
Joined: 02 Nov 2018
Posts: 280
The average value of all the pennies, nickels, dimes,  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 50% (01:03) correct 50% (02:55) wrong based on 14 sessions

### HideShow timer Statistics

The average value of all the pennies, nickels, dimes, and quarters in Paula’s purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4
Senior Manager  P
Status: Manager
Joined: 02 Nov 2018
Posts: 280
The average value of all the pennies, nickels, dimes,  [#permalink]

### Show Tags

1
hi stne

If the new coin was worth 20 cents, adding it would not change the mean.
The additional 5 cents raise the mean by 1, thus the new number of coins must be 5.
Therefore there were 4 coins worth a total of 4X20=80 cents. only way to get 80 cents using 4 coins is 25+25+25+5.
Thus, having three quarters, one nickel, and no dimes
Director  V
Joined: 27 May 2012
Posts: 945
Re: The average value of all the pennies, nickels, dimes,  [#permalink]

### Show Tags

1
hi stne

If the new coin was worth 20 cents, adding it would not change the mean.
The additional 5 cents raise the mean by 1, thus the new number of coins must be 5.
Therefore there were 4 coins worth a total of 4X20=80 cents. only way to get 80 cents using 4 coins is 25+25+25+5.
Thus, having three quarters, one nickel, and no dimes

Thank you, but really not able to understand the solution.
Can you help me with the algebraic solution , I tried this way:

$$\frac{1P +5N+10D+25Q}{P+N+D+Q}=20$$ (I)

$$\frac{1P +5N+10D+25(Q+1)}{P+N+D+Q}=21$$ (II)

solving I we get 5Q=19P+15N+10D
solving II we get 4Q+25=20P+16N+11D

II-I ( Subtracting I from II) -Q+25=P+N+D or P+N+D+Q =25

After this, how do we deduce the solution?
_________________
- Stne
Senior Manager  P
Status: Manager
Joined: 02 Nov 2018
Posts: 280
The average value of all the pennies, nickels, dimes,  [#permalink]

### Show Tags

2
hi @
ur way is too complex and time consuming .
if u want algebraic way do this way
Let the total value, in cents, of the coins Paula has originally be v
and the number of coins she has be n
so, v/n = 20
v= 20n
and ,
v+25/n+1=21
Substituting yields: 20n+25=21(n+1),
so n=4 thats mean total number of coin = 4
so v= 20x4
v= 80 cents
Then, we see that the only way Paula can satisfy this rule is if she had 3 quarters and 1 nickel in her purse.(3X25+5)
so no dimes

Originally posted by Noshad on 16 Mar 2019, 12:13.
Last edited by Noshad on 16 Mar 2019, 12:28, edited 1 time in total.
Director  V
Joined: 27 May 2012
Posts: 945
Re: The average value of all the pennies, nickels, dimes,  [#permalink]

### Show Tags

hi @
ur way is too complex and time consuming .
if u want algebraic way do this way
Let the total value, in cents, of the coins Paula has originally be v
and the number of coins she has be n
so, v/n = 20
v= 20n
and ,
v+25/n+1=21
Substituting yields: 20n+25=21(n+1),
so n=4 thats mean total number of coin = 4
so v= 20x4
v= 80 cents
Then, we see that the only way Paula can satisfy this rule is if she had 3 quarters and 1 nickel in her purse.(3X20+10)
so no dimes

Thank you +1, great solution. But there is small typo at the end , you may wish to edit (3X20+10) to (3*25 +5). Thanks.
_________________
- Stne Re: The average value of all the pennies, nickels, dimes,   [#permalink] 16 Mar 2019, 12:22
Display posts from previous: Sort by

# The average value of all the pennies, nickels, dimes,  