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# Max has $125 consisting of bills each worth either$5 or

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Max has $125 consisting of bills each worth either$5 or [#permalink]  05 Nov 2009, 11:26
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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.

Official Guide 12 Question

 Question: 57 Page: 277 Difficulty: 600

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Video Explanations:

OPEN DISCUSSION OF THIS QUESTION IS HERE: max-has-125-consisting-of-bills-each-worth-either-5-or-140249.html
[Reveal] Spoiler: OA
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Re: Q57, OG 12 Max bills [#permalink]  05 Nov 2009, 11:54
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pm4553 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

Discuss..

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

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

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

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Re: Q57, OG 12 Max bills [#permalink]  05 Nov 2009, 23:13
agree with Bunuel, i wud go by assuming numbers than forming equations, saves time..
in 1, take values less than 5 and only value satisying the result is 1. must be sufficient to get the answer.
in 2, take values more than 20, and only value satisfying the result is 6, giving us resultant value of 5$bills to be 1. hence sufficient. Ans must be D. Director Joined: 27 Jun 2008 Posts: 547 WE 1: Investment Banking - 6yrs Followers: 1 Kudos [?]: 48 [0], given: 92 Re: Q57, OG 12 Max bills [#permalink] 06 Nov 2009, 00:25 Bunuel wrote: pm4553 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 $20 Discuss.. Let x be the # of 5$ bills and y # of 20$bills --> $$5x+20y=125$$ --> $$x=?$$ (1) $$x<5$$ --> $$5x+20y=125$$ --> $$y=\frac{125-5x}{20}=\frac{25-x}{4}$$ as x<5 and y is an integer value only possible value for x is 1. Sufficient. (1) $$y>5$$ --> $$5x+20y=125$$ --> $$x=\frac{125-20y}{5}=25-4y$$ as y>5 and x is not negative only possible value for y is 6, hence x=1. Sufficient. Answer: D. Good explanation, thanks! OA is D Math Expert Joined: 02 Sep 2009 Posts: 27215 Followers: 4227 Kudos [?]: 41002 [0], given: 5654 Re: Max has$125 consisting of bills [#permalink]  15 Nov 2010, 00:14
Expert's post
monirjewel wrote:
Max has $125 consisting of bills each worth either$5 or $20. How many bills worth$5 Max have?
(1) Max has fewer than 5 bills worth $5 each (2) Max has more than 5 bills worth$20 each

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

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

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

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Re: Max has $125 consisting of bills [#permalink] 15 Nov 2010, 07:10 2 This post received KUDOS Expert's post monirjewel wrote: Max has$125 consisting of bills each worth either $5 or$20. How many bills worth $5 Max have? (1) Max has fewer than 5 bills worth$5 each
(2) Max has more than 5 bills worth $20 each Bunuel has already discussed the algebraic way pretty elegantly. Let me just give you the non-algebra method here. When we say we need$125, in $5 and$20 bills, first thing that comes to mind is that I need at least one $5 bill to get the 5 of 125. If I have only one$5 bill, I will need six $20 bills to make$120.

Also, if I have more than one $5 bill, I will need to reduce$20 bills. For every one $20 bill I reduce, I need four$5 bills to make up for it.
So number of $5 bills will be 1 or 5 or 9 or 13 and so on.. Stmnt 1: If$5 bills are fewer than 5, Max must have only one $5 bill. Sufficient. Stmnt 2: If he has more than five$20 bills, he must have six $20 bills because that is the maximum number of$20 bills he can have. In that case he must have only one $5 bill. Sufficient. Answer (D) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29! Veritas Prep Reviews Manager Joined: 13 Jul 2010 Posts: 169 Followers: 1 Kudos [?]: 27 [0], given: 7 Re: Max has$125 consisting of bills [#permalink]  15 Nov 2010, 18:42
The answer is D, and I didn't need to use the algebra method although it was helpful to see that as on a harder question it could be very useful.
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Re: Max has $125 consisting of bills [#permalink] 17 Nov 2010, 06:55 answer is D, without any algebra Intern Joined: 12 Sep 2011 Posts: 13 Followers: 0 Kudos [?]: 0 [0], given: 3 Re: Q57, OG 12 Max bills [#permalink] 19 Sep 2012, 17:55 Bunuel wrote: pm4553 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 $20 Discuss.. Let x be the # of 5$ bills and y # of 20$bills --> $$5x+20y=125$$ --> $$x=?$$ (1) $$x<5$$ --> $$5x+20y=125$$ --> $$y=\frac{125-5x}{20}=\frac{25-x}{4}$$ as $$x<5$$ and $$y$$ must be an integer then only possible value for $$x$$ is 1. Sufficient. (1) $$y>5$$ --> $$5x+20y=125$$ --> $$x=\frac{125-20y}{5}=25-4y$$ as $$y>5$$ and $$x$$ must not negative then only possible value for $$y$$ is 6, hence $$x=1$$. Sufficient. Answer: D. Dude, you're the **** best - thanks! Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 17 Kudos [?]: 257 [0], given: 11 Re: Max has$125 consisting of bills each worth either $5 or [#permalink] 19 Sep 2012, 21:13 pm4553 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. Official Guide 12 Question  Question: 57 Page: 277 Difficulty: 600 Find All Official Guide Questions Video Explanations: 125 = 5x + 20y x = ? the units digit of 125 is 5. From the equation 20y will always yield a value with 0 as it's units digit. While 5x will then have to yield a value that ends with 5. (1) if x is less than 5 then, we can choose from 0,1,2,3,4 but 5x should end with 5 so, we are left with 1 and 3 as possibilities. Let x=1, the 20y should be 120, y=6 let x=3, then 5x=15 so 20y should be 125-15=110. But 110 is not a multiple of 20 so, not possible. Thus, x=1. SUFFICIENT (2) if y is greater than 5 Let us try y=6, this is possible! Let us try y=7, 20y = 140, this is not possible or our eq. thus, y=6. SUFFICIENT Answer: D _________________ Impossible is nothing to God. GMAT Club Legend Joined: 09 Sep 2013 Posts: 4767 Followers: 296 Kudos [?]: 52 [0], given: 0 Re: Max has$125 consisting of bills each worth either $5 or [#permalink] 19 Nov 2013, 09:55 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. _________________ Math Expert Joined: 02 Sep 2009 Posts: 27215 Followers: 4227 Kudos [?]: 41002 [0], given: 5654 Re: Max has$125 consisting of bills each worth either $5 or [#permalink] 19 Nov 2013, 14:30 Expert's post OPEN DISCUSSION OF THIS QUESTION IS HERE: max-has-125-consisting-of-bills-each-worth-either-5-or-140249.html _________________ Re: Max has$125 consisting of bills each worth either $5 or [#permalink] 19 Nov 2013, 14:30 Similar topics Replies Last post Similar Topics: 9 Max has$125 consisting of bills each worth either $5 or$20 8 08 Oct 2012, 01:53
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