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What is the ratio of nickels to dimes in a bag of change that contains

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New post 08 Jan 2018, 23:34
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What is the ratio of nickels to dimes in a bag of change that contains only nickels and dimes? (nickel = $0.05; dime = $0.1)

(1) The total amount of money in the bag is $8.70.
(2) If the number of nickels was increased by 10%, the number of nickels in the bag would be 50% of the total number of dimes in the bag.

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New post Updated on: 12 Jun 2019, 14:06
Bunuel wrote:
What is the ratio of nickels to dimes in a bag of change that contains only nickels and dimes? (nickel = $0.05; dime = $0.1)

(1) The total amount of money in the bag is $8.70.
(2) If the number of nickels was increased by 10%, the number of nickels in the bag would be 50% of the total number of dimes in the bag.


We'll use easy numbers to eliminate contradictory answers.
This is an Alternative approach.

(1) Say there was only 1 dime. Then there would be $8.6 worth of nickels. Say there were 2 dimes. Then there would be $8.5 of nickels.
As these are different, (1) is insufficient.

(2) Say we had 10 nickels. Then this was increased to 11 and we would have 22 dimes in the bag.
This is enough to calculate the ratio!
If we try different numbers of nickles, we can SEE that we will always have 2*(n+ n*10%) = 2.2n dimes in the bag
Sufficient!

(B) is our answer.
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Originally posted by DavidTutorexamPAL on 09 Jan 2018, 04:28.
Last edited by DavidTutorexamPAL on 12 Jun 2019, 14:06, edited 2 times in total.
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Re: What is the ratio of nickels to dimes in a bag of change that contains  [#permalink]

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New post 12 Jun 2019, 06:19
question asks for ratio of n/d
A) n* 0.05 + d* 0.1 = 8.70
we can't get n/d
B) n2= increased no of nickel
n2= 1.1n
n2= 50%of (d)
n2= d/2 but n2 = 1.1 n
so we can get n/d So B is sufficient
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Re: What is the ratio of nickels to dimes in a bag of change that contains  [#permalink]

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New post 12 Jun 2019, 07:53
DavidTutorexamPAL wrote:
(2) Say we had 10 nickels. Then this was increased to 11 and we would have 22 dimes in the bag.
This is enough to calculate the ratio!
If we try different numbers of nickles, we can SEE that we will always have 2*(n+1) dimes in the bag
Sufficient!


If that were true -- if any time you had n nickels, you had 2(n+1) dimes -- then the Statement would not be sufficient. The question asks for the ratio of nickels to dimes, and the ratio n/2(n+1) is different for different values of n.

It is not true that we have 2(n+1) dimes, except when n is exactly equal to 10. Here we know if we multiply n by 1.1 (increase it by 10%), we get 1/2 the number of dimes. So

1.1n = d/2
n/d = 1/2.2 = 5/11

so Statement 2 gives us the ratio we need. Since Statement 1 clearly does not, the answer is B.
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New post 12 Jun 2019, 14:05
IanStewart wrote:
DavidTutorexamPAL wrote:
(2) Say we had 10 nickels. Then this was increased to 11 and we would have 22 dimes in the bag.
This is enough to calculate the ratio!
If we try different numbers of nickles, we can SEE that we will always have 2*(n+1) dimes in the bag
Sufficient!


If that were true -- if any time you had n nickels, you had 2(n+1) dimes -- then the Statement would not be sufficient. The question asks for the ratio of nickels to dimes, and the ratio n/2(n+1) is different for different values of n.

It is not true that we have 2(n+1) dimes, except when n is exactly equal to 10. Here we know if we multiply n by 1.1 (increase it by 10%), we get 1/2 the number of dimes. So

1.1n = d/2
n/d = 1/2.2 = 5/11

so Statement 2 gives us the ratio we need. Since Statement 1 clearly does not, the answer is B.


Thanks for pointing out the typo! It shouldn't be "+1" but "+10%" of course, i.e. +0.1n. Which reduces to what you wrote. Fixed.
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Re: What is the ratio of nickels to dimes in a bag of change that contains   [#permalink] 12 Jun 2019, 14:05
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