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# Luis spent a certain amount of money in a supermarket. He spent a thir

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Math Expert
Joined: 02 Sep 2009
Posts: 58116
Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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26 Jul 2019, 08:00
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25% (medium)

Question Stats:

86% (02:09) correct 14% (02:31) wrong based on 176 sessions

Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket? A. 60 B. 66 C. 72 D. 78 E. 84 _________________ GMAT Club Legend Joined: 18 Aug 2017 Posts: 4799 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:11 2 Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables,$12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?
A. 60
B. 66
C. 72
D. 78
E. 84

let total money be 72
so Fruits ; 24 ; Vegetable ; 12 ; Pasta ; 12 ; total 48
left with 24 half is 12 chocolate and soda ; 12
total 72
IMO C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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Updated on: 26 Jul 2019, 17:55
1
Let the total spent = x

--> Spent on fruits = x/3
--> Spent on vegetables = x/6
--> Spent on pasta = 12

Remainder amount = x - (x/3 + x/6 + 12) = x - x/2 - 12 = x/2 - 12

--> Spent on chocolate = 1/2*(x/2 - 12) = x/4 - 6
--> Spent on soda = x/6

Now, Total = x/3 + x/6 + 12 + (x/4 - 6) + x/6
--> x = 2x/3 + x/4 + 6
--> x = (8x + 3x + 72)/12
--> 12x = 11x + 72
--> x = 72 $IMO Option C Pls Hit Kudos if you like the solution Originally posted by Dillesh4096 on 26 Jul 2019, 08:22. Last edited by Dillesh4096 on 26 Jul 2019, 17:55, edited 1 time in total. Senior Manager Joined: 10 Aug 2018 Posts: 320 Location: India Concentration: Strategy, Operations WE: Operations (Energy and Utilities) Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags Updated on: 27 Jul 2019, 20:20 Now I get it. It's 72. after all deductions, we are left with 12. and a 6th of 72 is 12. Picking up an answer choice worked well. _________________ Don't forget to give KUDOS. On the way to conquer the GMAT and I will not leave it until I win. WHATEVER IT TAKES. Target 720+ " I CAN AND I WILL" Your suggestions will be appreciated here---> https://gmatclub.com/forum/your-one-advice-could-help-me-poor-gmat-scores-299072.html 1) Gmat prep: [620 Q48 V27], 2) Gmat prep: [610 Q47 V28], 3) Gmat prep: [620 Q47 V28], 4) Gmat prep: [660 Q47 V34], 5) Gmat prep: [560 Q37 V29], 6) Gmat prep: [540 Q39 V26], 7) Veritas Cat: [620 Q46 V30], 8) Veritas Cat: [630 Q45 V32], 9) Manhattan:[630 Q41, V35] Originally posted by Prasannathawait on 26 Jul 2019, 08:25. Last edited by Prasannathawait on 27 Jul 2019, 20:20, edited 1 time in total. RC Moderator Joined: 24 Aug 2016 Posts: 795 GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:27 2 Say the total money be x. The Eqn: $$\frac{x}{3}$$ + $$\frac{x}{6}$$ + $$12$$ + $$\frac{1}{2}$$ ( $$x$$ - $$\frac{x}{3}$$ - $$\frac{x}{6}$$ - $$12$$ ) + $$\frac{x}{6}$$ = $$x$$ Now solving for $$x$$ , we get the total money as $$72$$ ..... Ans C. _________________ Please let me know if I am going in wrong direction. Thanks in appreciation. Intern Joined: 13 Mar 2019 Posts: 28 Location: India Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:29 1 We can solve either by taking x or by options.I went for options as equation looked fuzzy and complex. started with C. Total Spent Money=72 Fruits: 1/3 of 72=24 vegetables: 1/6 of 72=12 pasta=12 remaining=72-24-12-12=24 chocolates=24/2=12 soda =12 (as much on soda as he spent on vegetables). This option exactly matches all the cases and therefore option C is the answer. Manager Joined: 30 May 2018 Posts: 154 Location: Canada GMAT 1: 710 Q49 V36 GPA: 3.8 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:30 1 C Pretty straight forward. Assume x is the total amount spent in supermarket. So, x/3 - fruits x/6 - vegetables$12 - pasta
remainder is x - all of the above = x/2 - 12
half of remainder on chocolate, so x/4 - 6 - chocolate
remaining half on soda - same as vegetables

So, x/4 - 6 = x/6, solve for x, we get x = $72 SVP Joined: 03 Jun 2019 Posts: 1543 Location: India Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:32 1 Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables,$12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84

Given : Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. Asked: How much money did Luis spend in the supermarket? Let the money he spend in the supermarket be x Money spent on fruits = x/3 Money spent on vegetables = x/6 Money spent on fruits and vegetables = x/3+x/6 =x/2 Money spent on pasta =$12
Remaining money = x - (x/2 + 12) = x/2 -12
Money spent on chocolate = x/4 - 6
Money spent on soda = x/6

Total money spent = x/2 + 12 + x/4 -6 + x/6 = x
11x/12 +6 = x
x/12 = 6
x = 12*6 = 72

IMO C
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Posts: 129
Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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Updated on: 26 Jul 2019, 22:38
1
Let, “X” be the total amount of money that Luis spent in a supermarket.

A third of the money on fruits: $$\frac{X}{3}$$
A sixth on vegetables: $$\frac{X}{6}$$
$12 on pasta: $$12$$ Half the remainder of the money on chocolate: Let’s calculate the remainder first:$$X – [\frac{X}{3} + \frac{X}{6} + 12] = \frac{3X – 72}{6}$$ Hence, Half the remainder = $$\frac{3X – 72}{12}$$ -> (a) Rest on soda. As much on soda as he spent on vegetables: $$\frac{X}{6}$$ -> (b) If (a) and (b) both are half the remainders, then (a) = (b) i.e. $$\frac{3X – 72}{12}$$ = $$\frac{X}{6}$$ => X = 72 Answer C Originally posted by Sayon on 26 Jul 2019, 08:32. Last edited by Sayon on 26 Jul 2019, 22:38, edited 1 time in total. Manager Joined: 10 Mar 2019 Posts: 75 Location: Russian Federation Schools: Haas '21 GPA: 3.95 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:35 1 Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables,$12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket

Given
$$1/3$$ - fruits
$$1/6$$- vegetables
12$- pasta if chocolate is half the remainder then soda is another half if soda =$$1/6$$ then chocolate =$$1/6$$ too using this data, create an equation $$1/3+1/6+x$$(this is pasta) $$+1/6+1/6=1$$ $$x=1/6$$ thus $$12=1/6$$ Then the amount of money Luis spend in the supermarket $$= 12*6=72$$ The answer is C Manager Joined: 28 Jan 2019 Posts: 125 Location: Peru Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags Updated on: 26 Jul 2019, 18:49 1 certain amount: x List of expenses Fruits:x/3 Vegetables: x/6 pasta:12 chocolate:x/2 - x/6 - x/12 - 6 soda:x/6 so, we have that: x/3 + x/6 + 12 + x/2 - x/6 - x/12 - 6 + x/6 = x 6 = x/12 x=72 So (C) is our answer Originally posted by Mizar18 on 26 Jul 2019, 08:40. Last edited by Mizar18 on 26 Jul 2019, 18:49, edited 1 time in total. Senior Manager Joined: 27 Aug 2014 Posts: 325 Location: Netherlands Concentration: Finance, Strategy Schools: LBS '22, ISB '21 GPA: 3.9 WE: Analyst (Energy and Utilities) Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:42 1 IMO answer is C: wring the equation as: D/3+D/6+12+(D-(D/3+D/6+12))/2+D/6 = D answer for this equation will be 72 Manager Joined: 26 Jan 2016 Posts: 179 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:43 1 Quote: Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables,$12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84

Equation we have

1/3x+1/6x+12+1/2(x-(1/3x+1/6x+12))+1/6x=x

Resolving this we get x=72

Hence C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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Updated on: 26 Jul 2019, 09:18
1
Quote:
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket? A. 60 B. 66 C. 72 D. 78 E. 84 total=fruits+vegetables+pasta+chocolate+soda total=x fruits+vegetables+pasta=x/3+x/6+12=3x/6+12=(3x+72)/6 chocolate=[x-((3x+72)/6)]/2=[6x-3x-72/6…(3x-72)/6]/2=(3x-72)/12 soda=x/6 x=(3x+72)/6+(3x-72)/12+x/6 x=(6x+144+3x-72)/12+x/6 x=(9x+72)/12+x/6 x=(9x+72+2x)/12 12x=11x+72 x=72 Answer (C). Originally posted by exc4libur on 26 Jul 2019, 08:43. Last edited by exc4libur on 26 Jul 2019, 09:18, edited 1 time in total. Manager Joined: 24 Jun 2017 Posts: 71 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:43 1 Using PoE A. 60 20-> fruits 10 -> Veggies 12 -> Pasta 9 -> C 10 -> Soda -- does not add up to 60 B. 66 33 -> 11 -> 12 -> 5 -> 11 -- adds upto more than 66 C. 72 24 -> 12 -> 12 -> 12 -> 12 -- adds upto 72 -- CORRECT D. 78 E. 84 So, C Intern Joined: 29 May 2018 Posts: 22 Location: India GMAT 1: 680 Q49 V33 Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags Updated on: 26 Jul 2019, 12:16 1 Let $$x$$ be the total amount. $$\frac{x}{3}= Fruits$$ $$\frac{x}{6}=Vegitables$$ $$12= Pasta$$ $$\frac{1}{2}(x-\frac{x}{3}-\frac{x}{6}-12)=Chocolate$$ {This is half of the remaining amount} $$\frac{x}{6}= Soda$$ $$\frac{x}{3} + \frac{x}{6} + 12 +\frac{1}{2}(x-\frac{x}{3}-\frac{x}{6}-12) + \frac{x}{6} = x$$ $$\frac{x}{3}+\frac{x}{3}+12 + \frac{1}{2} ( x- \frac{x}{2} -12) = x$$ $$\frac{2x}{3}+ 12 + \frac{1}{2}(\frac{x}{2} - 12) = x$$ $$12 + \frac{x}{4}- 6 = \frac{x}{3}$$ $$6= \frac{x}{3} - \frac{x}{4}$$ $$6= \frac{x}{12}$$ Thus, $$x= 12*6 =72$$ Answer is Total Amount= 72. Originally posted by Ajiteshmathur on 26 Jul 2019, 08:49. Last edited by Ajiteshmathur on 26 Jul 2019, 12:16, edited 1 time in total. Senior Manager Joined: 05 Mar 2017 Posts: 256 Location: India Concentration: General Management, Marketing Schools: LBS '22, ISB '20, IE '22 GPA: 3.6 WE: Marketing (Entertainment and Sports) Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:50 Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables,$12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

Take the total money he has is 90.
1/3 is 30
1/6 = 15
12 on pasta
remaining of chocolates and an equal amount in vegetables.

A. 60
B. 66
C. 72
D. 78
E. 84

IMO E.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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26 Jul 2019, 08:51
1
Let total amount be x

on fruits = x/3
on vegetables = x/6
on pasta = $12 on chocolate = (x/2 - 12)/2 on soda = x/3 x/3 + x/6 + 12 + (x/2 - 12)/2 + x/3 = x x = 72 C is correct. Manager Joined: 30 Nov 2016 Posts: 103 Location: India Concentration: Finance, Strategy Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:51 1 total amount=x Amount spent on Fruits=x/3 Amount spent on Vegetables=x/6 Soda=x/6 amount spent on chocolate is (x-(x/3+x/6+12))/2 so the equation boils down to 11x/12+6=x x/12=6 and x=72 Manager Joined: 07 Dec 2018 Posts: 112 Location: India Concentration: Technology, Finance GMAT 1: 670 Q49 V32 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 26 Jul 2019, 08:55 1 Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables,$12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

Let's say the total amount = x
Fruits = x/3
Veggies = x/6
Pasta = 12

How much spent till now?
=x/3+x/6+12
=12+3x/6
=12+x/2

How much remained?
=x-(12+x/2)
=x/2-12

Half the remainder of the money on chocolate.
So, chocolate = (x/2-12) / 2
Soda = Veggies = x/6

Total shall be,
x = x/3+2x/6+(x-24) / 4 + 12
x-12 = 16x+6x - (24*6)
22x - (24*8) = 24x - (12*24)
2x = (12*24) - (8*24)
2x = 24 * (12-6)
2x = 24*6
x=72

Re: Luis spent a certain amount of money in a supermarket. He spent a thir   [#permalink] 26 Jul 2019, 08:55

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