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Out of a jar that is filled with quarters, nickels and dimes, k coins

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Intern
Joined: 09 Dec 2017
Posts: 2
Out of a jar that is filled with quarters, nickels and dimes, k coins  [#permalink]

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Updated on: 09 Dec 2017, 04:28
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Difficulty:

95% (hard)

Question Stats:

17% (02:21) correct 83% (02:02) wrong based on 51 sessions

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Out of a jar that is filled with quarters, nickels and dimes, k coins are randomly chosen. The total value of these coins is 45 cents. What is he value of k?

(1) half of the k coins are nickels
(2) half of the k coins are dimes

Originally posted by ich on 09 Dec 2017, 03:01.
Last edited by Bunuel on 09 Dec 2017, 04:28, edited 2 times in total.
Renamed the topic, edited the question
Math Expert
Joined: 02 Aug 2009
Posts: 7434
Out of a jar that is filled with quarters, nickels and dimes,  [#permalink]

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09 Dec 2017, 03:44
ich wrote:
Out of a jar that is filled with quarters, nickels and dimes, k coins are randomly chosen. The total value of these coins is 45 cents. What is he value of k?
1) half of the k coins are nickels
2) half of the k coins are dimes

Posted from my mobile device

Let the number be q, n and d.
So $$25q+5n+10d=45$$

Let's see the statements
I. Half the coins are nickels.
So $$n=q+d$$..
$$25q+5q+5d+10d=45.................30q+15d=45$$..
Two cases possible..
1) $$q=d=1$$..so $$n=2....25+10+2*5=45$$
2) $$q=0, d=3.$$.so $$n=3....10*3+5*3=45$$
Insuff

II. Half the coins are dimes.
$$d=q+n$$....
$$25q+10q+10n+5n=45........ 35q+15n=45..$$
q has to be 0 as then we will not get n as integer value.
So $$15n=45...n=3$$
So d=3
K=3+3=6
Suff

B

If it is from OG, it would already be discussed.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Joined: 09 Dec 2017
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Re: Out of a jar that is filled with quarters, nickels and dimes, k coins  [#permalink]

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14 Dec 2017, 02:50
Is it legal to assume that the value of q might be equal to 0 as the wording of the prompt “out of a jar that is filled with quarters, dimes and nickels” indicates that there must be at least 1 coin of each type?

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Re: Out of a jar that is filled with quarters, nickels and dimes, k coins  [#permalink]

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14 Dec 2017, 08:04
chetan2u wrote:
ich wrote:
Out of a jar that is filled with quarters, nickels and dimes, k coins are randomly chosen. The total value of these coins is 45 cents. What is he value of k?
1) half of the k coins are nickels
2) half of the k coins are dimes

Posted from my mobile device

Let the number be q, n and d.
So $$25q+5n+10d=45$$

Let's see the statements
I. Half the coins are nickels.
So $$n=q+d$$..
$$25q+5q+5d+10d=45.................30q+15d=45$$..
Two cases possible..
1) $$q=d=1$$..so $$n=2....25+10+2*5=45$$
2) $$q=0, d=3.$$.so $$n=3....10*3+5*3=45$$
Insuff

II. Half the coins are dimes.
$$d=q+n$$....
$$25q+10q+10n+5n=45........ 35q+15n=45..$$
q has to be 0 as then we will not get n as integer value.
So $$15n=45...n=3$$
So d=3
K=3+3=6
Suff

B

If it is from OG, it would already be discussed.

Hi chetan2u

May I please know how did you get $$25q+5n+10d=45$$. In the question, the value of Quartz, Nickel & Dime is not mentioned.
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Joined: 02 Aug 2009
Posts: 7434
Re: Out of a jar that is filled with quarters, nickels and dimes, k coins  [#permalink]

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14 Dec 2017, 08:09
1
rahul16singh28 wrote:
chetan2u wrote:
ich wrote:
Out of a jar that is filled with quarters, nickels and dimes, k coins are randomly chosen. The total value of these coins is 45 cents. What is he value of k?
1) half of the k coins are nickels
2) half of the k coins are dimes

Posted from my mobile device

Let the number be q, n and d.
So $$25q+5n+10d=45$$

Let's see the statements
I. Half the coins are nickels.
So $$n=q+d$$..
$$25q+5q+5d+10d=45.................30q+15d=45$$..
Two cases possible..
1) $$q=d=1$$..so $$n=2....25+10+2*5=45$$
2) $$q=0, d=3.$$.so $$n=3....10*3+5*3=45$$
Insuff

II. Half the coins are dimes.
$$d=q+n$$....
$$25q+10q+10n+5n=45........ 35q+15n=45..$$
q has to be 0 as then we will not get n as integer value.
So $$15n=45...n=3$$
So d=3
K=3+3=6
Suff

B

If it is from OG, it would already be discussed.

Hi chetan2u

May I please know how did you get $$25q+5n+10d=45$$. In the question, the value of Quartz, Nickel & Dime is not mentioned.

Hi..

we would require to know these conversions. It may be not given in the question at times..
Quartz, Nickel & Dime are 25 cents, 5 cents and 10 cents respectively..
dollar is 100 cents..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Out of a jar that is filled with quarters, nickels and dimes, k coins  [#permalink]

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14 Dec 2017, 08:37
“out of a jar that is filled with quarters, dimes and nickels” means that jar is used to store quarters, dimes and nickels. But it is not necessary that all of them are present in a particular condition.

ich wrote:
Is it legal to assume that the value of q might be equal to 0 as the wording of the prompt “out of a jar that is filled with quarters, dimes and nickels” indicates that there must be at least 1 coin of each type?

Posted from my mobile device

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Location: India
Re: Out of a jar that is filled with quarters, nickels and dimes, k coins  [#permalink]

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15 Dec 2017, 03:40
ich wrote:
Is it legal to assume that the value of q might be equal to 0 as the wording of the prompt “out of a jar that is filled with quarters, dimes and nickels” indicates that there must be at least 1 coin of each type?

Posted from my mobile device

I think in GMAT, it will be clearly specified. From the statement, "out of a jar that is filled with quarters, dimes and nickels.." I also had the first thought that there should be at least one of each type. But as per the question solution for statement 2 (as solved by Chetan2u), there is only one case possible where no of quarters =0. So we will have to go by that and take no of quarters as 0 only.

But still, I believe GMAT will take care of such issues so as to have complete clarity in the question (eg, by mentioning something like 'there is at least one coin of each type' or 'its not necessary to have one coin of each type' etc).
Re: Out of a jar that is filled with quarters, nickels and dimes, k coins   [#permalink] 15 Dec 2017, 03:40
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