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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # Sam’s car was fined when he gave Joe and Peter a ride, so they decided  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 51218 Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 12 Mar 2015, 05:46 1 3 00:00 Difficulty: 45% (medium) Question Stats: 72% (02:39) correct 28% (02:58) wrong based on 149 sessions ### HideShow timer Statistics Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid$3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay$4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13 B.$15
C. $20 D.$28
E. $48 Kudos for a correct solution. _________________ Intern Joined: 26 Mar 2010 Posts: 10 Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 12 Mar 2015, 10:59 1 Joe=1/4f+3 Peter= 1/3f-3 Sam=1/2f-4 We can find F=48 Thus Sam paid 24-4=20 Answer C Manager Status: Kitchener Joined: 03 Oct 2013 Posts: 89 Location: Canada Concentration: Finance, Finance GPA: 2.9 WE: Education (Education) Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 12 Mar 2015, 13:31 the answer is C let say the total fine=T so Joe paid 3+T/4 Peter paid T/3-3 sam paied T/2-4 T=(3+T/4)+(T/3-3)+(T/2-4) T=48 sam paied=20 _________________ Click +1 Kudos if my post helped Senior Manager Joined: 28 Feb 2014 Posts: 294 Location: United States Concentration: Strategy, General Management Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 12 Mar 2015, 15:17 1 Bunuel wrote: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid$3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay$4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13 B.$15
C. $20 D.$28
E. $48 Kudos for a correct solution. (1/4)x + 3 + (1/3)x - 3 + (1/2)x -4 = x x=48 1/2(48) - 4 = 20 Answer: C SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1825 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 12 Mar 2015, 20:04 1 Answer = C.$20

Sam .......... Joe ................. Peter .................. Total

$$\frac{x}{2} - 4$$ ......... $$\frac{x}{4} + 3$$ ........... $$\frac{x}{3} - 3$$ ............ x (Say total fine = x)

Setting up the equation with above variables

$$\frac{x}{2} + \frac{x}{4} + \frac{x}{3} - x = 4$$

x = 48

Sam's contribution = 24-4 = 20
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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided  [#permalink]

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15 Mar 2015, 20:38
1
Bunuel wrote:
Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid$3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay? A.$13
B. $15 C.$20
D. $28 E.$48

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Call the fine F. Joe paid (1/4)F + 3 and Peter paid (1/3)F – 3, leaving (1/2)F – 4 left. If we add those three up, they should add up to F.
F = [(1/4)F + 3] + [(1/3)F – 3] + [(1/2)F – 4]
F = (1/4)F + (1/3)F + (1/2)F – 4

Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 48
12F = 13 F – 48
–F = – 48
F = 48

Well, if the fine cost $48, then Sam paid the part not covered by Joe or Peter. Half the fine is$24, and Sam paid $4 less than this:$20.

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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided  [#permalink]

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24 Jul 2015, 10:38
Bunuel wrote:
Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid$3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay? A.$13
B. $15 C.$20
D. $28 E.$48

Kudos for a correct solution.

I did the same way as most of the people have done. I have also solved in the following way, a little bit reverse thing, please let me know if I am doing wrong here.

As given sam' payment is [1][/2]*Fine -4
i.e Total Fine = 2 * (Sam's payment + 4)

Now, as everything looks integer, Fine should be able to divide by 4 and 3 . Because Joe's contribution has 1/4 of the fine and Peter's contribution has 1/3 of the fine

So, that leads me to following :

Options , Sam's pay , Total Fine (F) , F/4 , F/3

A) , 13 , 34 , No i.e 34/4 , No i.e 34/3

B) , 14 , 38 , No , No

C) , 20 , 48 , Yes Yes
,
No need to further go on as we have got F/4 and F/3 correct, just for confirmation we go further

D) , 28 , 64 , Yes , No

E) , 48 , 104 , Yes , No

So we can see the Option C has the correct values
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Re: Sam's car was fined for parking when he gave Joe and Peter a ride  [#permalink]

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06 Jun 2017, 22:32
mkrishnabdrr wrote:
Sam's car was fined for parking when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid$3 less than 1/3 of the fine, leaving Sam $4 less than 1/2 the fine to complete the payment. How much did Sam pay? A. 48 B. 24 C. 20 D. 15 E. 50 Let the fine be $$x$$ Joe paid = $$\frac{1}{4}x$$ + 3 Peter paid = $$\frac{1}{3}x$$ - 3 Sam has to pay = $$\frac{1}{2}x$$ - 4 From the question; $$x = \frac{1}{4}x + 3 + \frac{1}{3}x - 3 + \frac{1}{2}x - 4$$ $$x = \frac{1}{4}x + \frac{1}{3}x + \frac{1}{2}x - 4$$ $$x = \frac{3x + 4x + 6x}{12} - 4$$ = $$\frac{13x}{12} - 4$$ $$\frac{13x}{12} - x = 4$$ $$\frac{13x - 12x}{12}$$ = $$\frac{x}{12} = 4$$ $$x = 12 * 4 = 48$$ . Answer A... _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 13 Aug 2015 Posts: 208 GMAT 1: 710 Q49 V38 GPA: 3.82 WE: Corporate Finance (Retail Banking) Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 07 Jun 2017, 06:16 sashiim20 wrote: mkrishnabdrr wrote: Sam's car was fined for parking when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid$3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving Sam$4 less than 1/2 the fine to complete the payment. How much did Sam pay?
A. 48
B. 24
C. 20
D. 15
E. 50

Let the fine be $$x$$
Joe paid = $$\frac{1}{4}x$$ + 3

Peter paid = $$\frac{1}{3}x$$ - 3

Sam has to pay = $$\frac{1}{2}x$$ - 4

From the question;
$$x = \frac{1}{4}x + 3 + \frac{1}{3}x - 3 + \frac{1}{2}x - 4$$

$$x = \frac{1}{4}x + \frac{1}{3}x + \frac{1}{2}x - 4$$

$$x = \frac{3x + 4x + 6x}{12} - 4$$ = $$\frac{13x}{12} - 4$$

$$\frac{13x}{12} - x = 4$$

$$\frac{13x - 12x}{12}$$ = $$\frac{x}{12} = 4$$

$$x = 12 * 4 = 48$$ . Answer A...

Question stem asks for how much did sam pay:
So,
Sam has to pay = $$\frac{1}{2}x$$ - 4
=1/2 x 48 -4
=24-4
=20
Hence, Ans is C. You found out the fine.

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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided  [#permalink]

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10 Jun 2017, 06:33
Bunuel wrote:
Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid$3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay? A.$13
B. $15 C.$20
D. $28 E.$48

We can let t = the total amount of the fine.

Joe’s payment = 3 + (1/4)t

Peter’s payment = (1/3)t - 3

Sam’s payment = (1/2)t - 4

We can create the following equation to determine t:

3 + (1/4)t + (1/3)t - 3 + (1/2)t - 4 = t

(1/4)t + (1/3)t + (1/2)t - 4 = t

Multiplying by 12, we have:

3t + 4t + 6t - 48 = 12t

48 = t

Thus, Sam paid (1/2)(48) - 4 = 24 - 4 = $20. Answer: C _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions VP Joined: 07 Dec 2014 Posts: 1128 Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 10 Jun 2017, 14:52 [quote="Bunuel"]Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid$3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay$4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13 B.$15
C. $20 D.$28
E. $48/quote] let f=amount of fine 13/12*f-4=f f=$48
Sam's share=f/2-4=$20 C Manager Joined: 19 Aug 2016 Posts: 150 Location: India GMAT 1: 640 Q47 V31 GPA: 3.82 Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 23 Sep 2017, 02:45 Bunuel wrote: Bunuel wrote: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid$3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay$4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13 B.$15
C. $20 D.$28
E. $48 Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION: Call the fine F. Joe paid (1/4)F + 3 and Peter paid (1/3)F – 3, leaving (1/2)F – 4 left. If we add those three up, they should add up to F. F = [(1/4)F + 3] + [(1/3)F – 3] + [(1/2)F – 4] F = (1/4)F + (1/3)F + (1/2)F – 4 Multiply all terms by 12 to clear the fractions. 12F = 3F + 4F + 6F – 48 12F = 13 F – 48 –F = – 48 F = 48 Well, if the fine cost$48, then Sam paid the part not covered by Joe or Peter. Half the fine is $24, and Sam paid$4 less than this: \$20.

Hi,

I don't understand. Doesn't the question say what 'fraction' of the fine did sam say? Here, we're stating his share of the fine.
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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided &nbs [#permalink] 23 Sep 2017, 02:45
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