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28 May 2016, 15:08
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Difficulty:

55% (hard)

Question Stats:

53% (01:09) correct 47% (01:23) wrong based on 68 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. [Reveal] Spoiler: OA Senior Manager Joined: 18 Jan 2010 Posts: 256 Re: Mary has$3,60 in nickels, dimes and quarters in her purse... [#permalink]

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28 May 2016, 19:01
EBITDA wrote:
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. 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. Math Expert Joined: 02 Aug 2009 Posts: 5721 Re: Mary has$3,60 in nickels, dimes and quarters in her purse... [#permalink]

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28 May 2016, 23:03
EBITDA wrote:
Mary has $3,60 in nickels, dimes and quarters in her purse. How many dimes does she have (in her purse)? 1) The ratio of quarters to dimes to nickels is 4:5:6. 2) Twice the number of dimes equals the number of nickels plus five times the number of quarters. I can guess how much is a quarter, but are we suposed to know how much is a nickel and a dime? That would be very unfair. Cheers. Hi, It may be unfair to expect students to know this and most likely in ACTUALS, the values will be given.. But here you do not require to know the value for statement I but yes for statement II, it is required... let the nickels, dime and quarter be of value n,d and q AND be x,y and z in number so xn+yd+zq = 360...... we require to know x,y and z to answer lets see the statements-- 1) The ratio of quarters to dimes to nickels is 4:5:6. since all three are in some ratio, say commom term = t.. x = 4t...........y=5t...........z=6t... so by substituting above we can find value of t from xn+yd+zq = 360...... and then x,y and z can be found Suff 2) Twice the number of dimes equals the number of nickels plus five times the number of quarters. 2y=x+5z.... here we require to know nickel =.05$, 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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29 May 2016, 02:51
1
KUDOS
EBITDA wrote:

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.

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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Re: Mary has $3,60 in nickels, dimes and quarters in her purse... [#permalink] ### Show Tags 19 Sep 2017, 06:43 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Mary has$3,60 in nickels, dimes and quarters in her purse...   [#permalink] 19 Sep 2017, 06:43
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