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To settle mutual debts, two gamblers agree that phones are worth $300

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irida
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To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink] New post   19 Jan 2019, 04:37
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To settle mutual debts, two gamblers agree that phones are worth $300 each and that watches are worth $210 each. When one gambler owes money to the other, he settles the debt in phones and/or watches, with “balance” received in the form of phones or watches as well (For example, a $480 debt could be paid with three phones, with two watches received in balance). What is the smallest amount of debt that can be settled in this way?

A) 10
B) 30
C) 50
D) 70
E) 90

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I am quite confused on the amount of money---from the statement, the minimum should be 210 (the watch's price)? But all of the 5 answers are below 210.

How to solve the problem? Seek advise.
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KarishmaB
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Re: To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink] New post   19 Jan 2019, 04:53
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irida wrote:
To settle mutual debts, two gamblers agree that phones are worth $300 each and that watches are worth $210 each. When one gambler owes money to the other, he settles the debt in phones and/or watches, with “balance” received in the form of phones or watches as well (For example, a $480 debt could be paid with three phones, with two watches received in balance). What is the smallest amount of debt that can be settled in this way? A) 10 B) 30 C) 50 D) 70 E) 90

I am quite confused on the amount of money---from the statement, the minimum should be 210 (the watch's price)? But all of the 5 answers are below 210.

How to solve the problem? Seek advise.


Notice the example they have given. 480 debt can be paid with 3 phone (total = $900) with receiving 2 watches is balance (receiving $420).
900 - 420 = 480

So to pay a debt of $90, one would need to give a phone ($300) and receive a watch ($210). In effect, one would have paid 300 - 210 = $90

We need a multiple of 300 to be as close as possible to a multiple of 210.

300 -> 600, 900, 1200, 1500, 1800, 2100, 2400, 2700 ...
210 -> 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100 ...

So you can settle a debt of $30 by paying 5 phones ($1500) and receiving 7 watches in return ($1470).
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Re: To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink] New post   19 Jan 2019, 05:04
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irida wrote:
To settle mutual debts, two gamblers agree that phones are worth $300 each and that watches are worth $210 each. When one gambler owes money to the other, he settles the debt in phones and/or watches, with “balance” received in the form of phones or watches as well (For example, a $480 debt could be paid with three phones, with two watches received in balance). What is the smallest amount of debt that can be settled in this way?

A) 10 B) 30 C) 50 D) 70 E) 90

I am quite confused on the amount of money---from the statement, the minimum should be 210 (the watch's price)? But all of the 5 answers are below 210.

How to solve the problem? Seek advise.


If you can realize how they got 480, you should be good with the question(These type of questions give us a hint on to solve them.)

480 was obtained when paid with three phones(x)(300* 3), with two watches received in balance(y)(2* 210)

How do you get that amount paid off ?? => 480 = 300 * 3 - 210*2
=> 480 = 900 - 420

Debt paid off has to be minimum, now just substitute values for x and y

Debt = 300* x - 210 * y
when x = y=1 , you get debt as 90(not the minimum value though)
Just make a table and notice the minimum difference, that will be your answer

When you substitute x as 5 and y as 7

You get minimum debt as 30.
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Re: To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink] New post   19 Jan 2019, 05:42
KanishkM wrote:
irida wrote:
To settle mutual debts, two gamblers agree that phones are worth $300 each and that watches are worth $210 each. When one gambler owes money to the other, he settles the debt in phones and/or watches, with “balance” received in the form of phones or watches as well (For example, a $480 debt could be paid with three phones, with two watches received in balance). What is the smallest amount of debt that can be settled in this way?

A) 10 B) 30 C) 50 D) 70 E) 90

I am quite confused on the amount of money---from the statement, the minimum should be 210 (the watch's price)? But all of the 5 answers are below 210.

How to solve the problem? Seek advise.


If you can realize how they got 480, you should be good with the question(These type of questions give us a hint on to solve them.)

480 was obtained when paid with three phones(x)(300* 3), with two watches received in balance(y)(2* 210)

How do you get that amount paid off ?? => 480 = 300 * 3 - 210*2
=> 480 = 900 - 420

Debt paid off has to be minimum, now just substitute values for x and y

Debt = 300* x - 210 * y
when x = y=1 , you get debt as 90(not the minimum value though)
Just make a table and notice the minimum difference, that will be your answer

When you substitute x as 5 and y as 7

You get minimum debt as 30.


Thank you for the advice on how to solve the problem! The steps you provided are clear and helpful.
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Re: To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink] New post   19 Jan 2019, 05:43
VeritasKarishma wrote:
irida wrote:
To settle mutual debts, two gamblers agree that phones are worth $300 each and that watches are worth $210 each. When one gambler owes money to the other, he settles the debt in phones and/or watches, with “balance” received in the form of phones or watches as well (For example, a $480 debt could be paid with three phones, with two watches received in balance). What is the smallest amount of debt that can be settled in this way? A) 10 B) 30 C) 50 D) 70 E) 90

I am quite confused on the amount of money---from the statement, the minimum should be 210 (the watch's price)? But all of the 5 answers are below 210.

How to solve the problem? Seek advise.


Notice the example they have given. 480 debt can be paid with 3 phone (total = $900) with receiving 2 watches is balance (receiving $420).
900 - 420 = 480

So to pay a debt of $90, one would need to give a phone ($300) and receive a watch ($210). In effect, one would have paid 300 - 210 = $90

We need a multiple of 300 to be as close as possible to a multiple of 210.

300 -> 600, 900, 1200, 1500, 1800, 2100, 2400, 2700 ...
210 -> 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100 ...

So you can settle a debt of $30 by paying 5 phones ($1500) and receiving 7 watches in return ($1470).


Thank you for the detailed explanation! Very helpful!
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Re: To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink] New post   04 May 2024, 09:19
Isn't it possible that at some point, the difference will be 10?
KarishmaB wrote:
irida wrote:
To settle mutual debts, two gamblers agree that phones are worth $300 each and that watches are worth $210 each. When one gambler owes money to the other, he settles the debt in phones and/or watches, with “balance” received in the form of phones or watches as well (For example, a $480 debt could be paid with three phones, with two watches received in balance). What is the smallest amount of debt that can be settled in this way? A) 10 B) 30 C) 50 D) 70 E) 90

I am quite confused on the amount of money---from the statement, the minimum should be 210 (the watch's price)? But all of the 5 answers are below 210.

How to solve the problem? Seek advise.

Notice the example they have given. 480 debt can be paid with 3 phone (total = $900) with receiving 2 watches is balance (receiving $420).
900 - 420 = 480

So to pay a debt of $90, one would need to give a phone ($300) and receive a watch ($210). In effect, one would have paid 300 - 210 = $90

We need a multiple of 300 to be as close as possible to a multiple of 210.

300 -> 600, 900, 1200, 1500, 1800, 2100, 2400, 2700 ...
210 -> 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100 ...

So you can settle a debt of $30 by paying 5 phones ($1500) and receiving 7 watches in return ($1470).

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Re: To settle mutual debts, two gamblers agree that phones are worth $300 [#permalink]
04 May 2024, 09:19
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