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705-805 (Hard)|   Arithmetic|      
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EBITDA
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Mary has $3,60 in nickels, dimes and quarters in her purse... 28 May 2016, 15:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

49% (01:55) correct 51% (01:59) wrong based on 153 sessions

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Mary has $3,60 in nickels, dimes and quarters in her purse. How many dimes does she have (in her purse)?

1) The ratio of quarters to dimes to nickels is 4:5:6.
2) Twice the number of dimes equals the number of nickels plus five times the number of quarters.

I can guess how much is a quarter, but are we suposed to know how much is a nickel and a dime?

That would be very unfair.

Cheers.
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D
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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Mary has $3,60 in nickels, dimes and quarters in her purse... 28 May 2016, 19:01
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EBITDA
Mary has $3,60 in nickels, dimes and quarters in her purse. How many dimes does she have (in her purse)?

1) The ratio of quarters to dimes to nickels is 4:5:6.
2) Twice the number of dimes equals the number of nickels plus five times the number of quarters.

I can guess how much is a quarter, but are we suposed to know how much is a nickel and a dime?

That would be very unfair.

Cheers.
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No point in getting upset.

A Dollar has 100 cents. Quarter= 25 cents. Dime = 10 cents. Nickel = 5 cents.

Statement 1
Q:D:N = 4:5:6
4x:5x:6x

4x(0.25)+5x(0.10)+6x(0.05) = 360
x+0.5 x+0.3x = 360
1.8x = 360
x = 200

Dimes : 5x = 1000 (We dont need to calculate)
Sufficient

Statement 2

Twice the number of dimes equals the number of nickels plus five times the number of quarters.

2d = n+5q

q(0.25)+d(0.10)+n(0.05) = 360
0.05(n+5q)+0.10d = 360
0.10 d + 0.10 d = 360
d can be calculated.
Sufficient

D is the answer.
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Mary has $3,60 in nickels, dimes and quarters in her purse... 28 May 2016, 23:03
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EBITDA
Mary has $3,60 in nickels, dimes and quarters in her purse. How many dimes does she have (in her purse)?

1) The ratio of quarters to dimes to nickels is 4:5:6.
2) Twice the number of dimes equals the number of nickels plus five times the number of quarters.

I can guess how much is a quarter, but are we suposed to know how much is a nickel and a dime?

That would be very unfair.

Cheers.
Show more

Hi,

It may be unfair to expect students to know this and most likely in ACTUALS, the values will be given..

But here you do not require to know the value for statement I but yes for statement II, it is required...

let the nickels, dime and quarter be of value n,d and q AND be x,y and z in number
so xn+yd+zq = 360......
we require to know x,y and z to answer

lets see the statements--



1) The ratio of quarters to dimes to nickels is 4:5:6.
since all three are in some ratio, say commom term = t..
x = 4t...........y=5t...........z=6t...
so by substituting above we can find value of t from xn+yd+zq = 360......
and then x,y and z can be found
Suff

2) Twice the number of dimes equals the number of nickels plus five times the number of quarters.
2y=x+5z....
here we require to know nickel =.05$, dime = 0.1$ and quarter = 0.25$..
and \(xn+yd+zq = 360........ 0.05x+0.1y+025z = 360.............5x+10y+25z=36000............x+2y+5z = 7200...........\\
2y+2y=7200\)
Y can be found..
suff
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Mary has $3,60 in nickels, dimes and quarters in her purse... 29 May 2016, 02:39
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Thank you for your responses.

I would appreciate though that you would also solve the problems until the very end.

So:

0,05N + 0,10D + 0,25Q = 3,60

1) Q:D:N = 4:5:6

4x · 0,25 + 5x · 0,10 + 6x · 0,05 = 3,60
x + 0,5x + 0,3x = 3,60
1,8x = 3,60
x=2 ---> # of dimes = 5 · 2 = 10 ---> 8 Quarters : 10 Dimes : 12 Nickels ---> 2,00 + 1,00 + 0,60 = 3,60

Sufficient.

2) 2D = N + 5Q
0,05N + 0,10D + 0,25Q = 3,60
5N + 10D + 25Q = 360
10D + 5N + 25Q = 360

Since 2D = N + 5Q, 10D = 5N + 25Q

10D + 10D = 360; 20D = 360; # of dimes = D = 18.

Sufficient.

However, this solution contradicts the solution to the first statement, and the solution to each of the statements shall not contradict each other.

Could someone help?

Thank you so much.
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Mary has $3,60 in nickels, dimes and quarters in her purse... 29 May 2016, 02:51
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EBITDA
Thank you for your responses.

I would appreciate though that you would also solve the problems until the very end.

So:

0,05N + 0,10D + 0,25Q = 3,60

1) Q:D:N = 4:5:6

4x · 0,25 + 5x · 0,10 + 6x · 0,05 = 3,60
x + 0,5x + 0,3x = 3,60
1,8x = 3,60
x=2 ---> # of dimes = 5 · 2 = 10 ---> 8 Quarters : 10 Dimes : 12 Nickels ---> 2,00 + 1,00 + 0,60 = 3,60

Sufficient.

2) 2D = N + 5Q
0,05N + 0,10D + 0,25Q = 3,60
5N + 10D + 25Q = 360
10D + 5N + 25Q = 360

Since 2D = N + 5Q, 10D = 5N + 25Q

10D + 10D = 360; 20D = 360; # of dimes = D = 18.

Sufficient.

However, this solution contradicts the solution to the first statement, and the solution to each of the statements shall not contradict each other.

Could someone help?

Thank you so much.
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Questions require a unique value. But not exactly same value.

Please cross-check the applicability of the statement: "solution to each of the statements shall not contradict each other" . This might be applicable to solution of inequalities.

By the way, I differ from you observation that we need to solve these question (where unique result can be obtained) to the very end and then check values. That would not be a recommended strategy, considering that time availability is an issue in Quant section.
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Mary has $3,60 in nickels, dimes and quarters in her purse... 23 Aug 2023, 07:54
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