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irida
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To settle mutual debts, two gamblers agree that phones are worth $300 19 Jan 2019, 04:37
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66% (02:26) correct 34% (02:12) wrong based on 324 sessions

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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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To settle mutual debts, two gamblers agree that phones are worth $300 19 Jan 2019, 04:53
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irida
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.
Show more

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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To settle mutual debts, two gamblers agree that phones are worth $300 19 Jan 2019, 05:04
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irida
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.
Show more

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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To settle mutual debts, two gamblers agree that phones are worth $300 19 Jan 2019, 05:42
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KanishkM
irida
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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Thank you for the advice on how to solve the problem! The steps you provided are clear and helpful.
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To settle mutual debts, two gamblers agree that phones are worth $300 19 Jan 2019, 05:43
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VeritasKarishma
irida
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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Thank you for the detailed explanation! Very helpful!
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To settle mutual debts, two gamblers agree that phones are worth $300 04 May 2024, 09:19
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Isn't it possible that at some point, the difference will be 10?
KarishmaB

irida
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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­
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To settle mutual debts, two gamblers agree that phones are worth $300 06 Jul 2024, 22:13
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KarishmaB It could be the combination of 2 phones and 3 watches too.

2*300 = 600
3*210 = 630

630 - 600 = 30
KarishmaB

irida
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).
Show more
­
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To settle mutual debts, two gamblers agree that phones are worth $300 08 Jul 2024, 06:00
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The reason I find this question difficult is that I saw that you could reach a difference of $30 quite easily with an exchange of 3 watches for 2 phones -->($630 - $600). However, how do you prove that at NO POINT will it ever get to a difference of 10? If we're talking about tens of thousands of watches and phones. Because the question doesn't specify that there are limited quantities of phones and watches. So how would you be able to prove that at no point will there ever be a moment when the multiples of 210 and 300 will get as close as 10? Many thanks!
 
irida
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

Show Spoiler
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.
Show more
­
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To settle mutual debts, two gamblers agree that phones are worth $300 08 Jul 2024, 10:19
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irida
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

Show Spoiler
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.
Show more
­Here's my attempt:

300x+210y= difference.

Now if we start with smallest option give ie 10 
we get 30x+21y=1
The LHS is a multiple of 3 but RHS isn't. Hence not possible.
Now trying the bigger value ie 30 we get 10x+7y=1..which is possible.
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To settle mutual debts, two gamblers agree that phones are worth $300 08 Jul 2024, 12:10
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Kindly let me know your  opinion on this . chetan2u GMATinsight
sayan640
KarishmaB It could be the combination of 2 phones and 3 watches too.

2*300 = 600
3*210 = 630

630 - 600 = 30
KarishmaB

irida
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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To settle mutual debts, two gamblers agree that phones are worth $300 30 Jul 2024, 10:50
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Combo of 2 phones and 3 watches
630-600 = 30
Option B.
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To settle mutual debts, two gamblers agree that phones are worth $300 28 Aug 2024, 02:13
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Here's an easier approach:
­
­The difference between 300x - 210y should be as low as possible. So I went up from the lowest option to highest.

Option 1:
300x - 210y = 10
30x - 21y = 1 (since both 30 and 21 are multiples of 3, their difference should also be a multiple of 3 so this equation won't work)

Option 2:
300x - 210y = 30
30x - 21y = 3 (since both 30 and 21 are multiples of 3, their difference should be a multiple of 3. So this equation is possible)

You can also check:
10x - 7y = 1 (so x = 5, y = 7 works)­
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To settle mutual debts, two gamblers agree that phones are worth $300 10 Nov 2024, 11:08
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Required to minimise

mod (300x- 210y)

or, 30 mod (10x - 3y)


For minimum debt value
For x=2, y=3 ---> mod (10x - 3y) = 1

therefore,

MIN value of 30 mod (10x - 3y) = 30 x 1 = 30

B is the CORRECT answer
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To settle mutual debts, two gamblers agree that phones are worth $300 10 Mar 2026, 09:06
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