Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Max has $125 consisting of bills each worth either $5 or $20. How many bills worth $5 does Max have?

Let \(x\) be the # of 5$ bills and \(y\) the # of 20$ bills --> \(5x+20y=125\) --> \(x=?\)

(1) Max has fewer than 5 bills worth $5 each. \(x<5\) --> \(5x+20y=125\) --> \(y=\frac{125-5x}{20}=\frac{25-x}{4}\) as \(x<5\) and \(y\) must be an integer then only possible value for \(x\) is 1. Sufficient.

(2) Max has more than 5 bills worth $20 each. \(y>5\) --> \(5x+20y=125\) --> \(x=\frac{125-20y}{5}=25-4y\) as \(y>5\) and \(x\) must not negative then only possible value for \(y\) is 6, hence \(x=1\). Sufficient.

Re: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

08 Oct 2012, 02:16

2

This post received KUDOS

From stem 5x + 20y = 125 Question is x=? Note :- x & y can take only integer values because we can not tear either $5 or $20 notes 1) x<5--> The only possible integer value is x=1 -->Sufficient 2) y>5--> The only possible integer value is y=6 & x = 1 -->Sufficient Answer D
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

08 Oct 2012, 02:20

imo d...each alone is sufficient let the number of bills of 5$ b x and bills for 20$ be y now we have only two situations where 5x+20y=125 either x=1 and y=6 --> (true wen we use statement 1) or x=5 and y=5 --> (true wen we use statement 2)

using any of the above two statements we can find out the answer.

Re: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

08 Oct 2012, 02:23

1

This post was BOOKMARKED

Let x be $5 bill & y be $20 bill, 5x+20y =125, Find x? ST1: Sufficient: x<5, Therefore x can be 0,1,2,3,4. Here only x=1 satisfy the given equation and for all other value y will not be an integer value. ST2: Sufficient: y>5, y=6,7,8... Now for y =7 the total value exceeds 125. Therefore Y must be 6. And so x will be 1.

Hence Answer D.
_________________

Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Re: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

08 Oct 2012, 04:07

6

This post received KUDOS

1

This post was BOOKMARKED

SOURH7WK wrote:

Let x be $5 bill & y be $20 bill, 5x+20y =125, Find x? ST1: Sufficient: x<5, Therefore x can be 0,1,2,3,4. Here only x=1 satisfy the given equation and for all other value y will not be an integer value. ST2: Sufficient: y>5, y=6,7,8... Now for y =7 the total value exceeds 125. Therefore Y must be 6. And so x will be 1.

Hence Answer D.

A suggestion: always divide an equation by the GCD of the coefficients, it becomes easier to handle. In this case, 5x + 20y = 125, divide through by 5 and get: x + 4y = 25. Smaller numbers, positive integers...isn't it easier to see the solutions?

(1): Another approach would be to look at 25 as being a M4+1 (remainder 1 when divided by 4). 4y is divisible by 4, therefore x must leave a remainder of 1 when divided by 4. Since x is less than 5, the only possibility is x = 1. Just to practice divisibility properties...:O) (2): y > 5, then 4y > 20. Because 4*7 = 28 > 25, the only possible value for y is 6, and x must be 1.

Nonetheless, your answer is absolutely correct: D.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Max has $125 consisting of bills each worth either $5 or $20. How many bills worth $5 does Max have?

Let \(x\) be the # of 5$ bills and \(y\) the # of 20$ bills --> \(5x+20y=125\) --> \(x=?\)

(1) Max has fewer than 5 bills worth $5 each. \(x<5\) --> \(5x+20y=125\) --> \(y=\frac{125-5x}{20}=\frac{25-x}{4}\) as \(x<5\) and \(y\) must be an integer then only possible value for \(x\) is 1. Sufficient.

(2) Max has more than 5 bills worth $20 each. \(y>5\) --> \(5x+20y=125\) --> \(x=\frac{125-20y}{5}=25-4y\) as \(y>5\) and \(x\) must not negative then only possible value for \(y\) is 6, hence \(x=1\). Sufficient.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

Re: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

10 Jan 2014, 07:45

1

This post received KUDOS

1

This post was BOOKMARKED

Bunuel wrote:

Max has $125 consisting of bills each worth either $5 or $20. How many bills worth $5 does Max have?

(1) Max has fewer than 5 bills worth $5 each. (2) Max has more than 5 bills worth $20 each.

Practice Questions Question: 59 Page: 280 Difficulty: 600

Basically, the stem gives us: 5*x + 20*y = 125, and asks us what x is.

1) tells us that x < 5, so we try to maximize for 20 to control what possible values x can take. For y = 5 we have x = 5 and for y = 6 we have x = 1, no other combinations in that range are possible between X and Y. And since 1) makes it impossible for x = 5, x must be = 1.. So 1 is sufficient.

2) tells us that y > 5, so again we test if there are different possible values for y. For y = 6 we have x = 1.. And y can't actually be a higher value than 6 because then we break the restriction of 125 USD.. So clearly, y = 6 and x = 1, so 2 is sufficient.

Re: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

09 Aug 2015, 12:00

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: Max has $125 consisting of bills each worth either $5 or $20 [#permalink]

Show Tags

17 Nov 2016, 00:33

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.
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...