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Math Expert V
Joined: 02 Sep 2009
Posts: 59089
Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 84% (02:14) correct 16% (02:43) wrong based on 200 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  V Joined: 18 Aug 2017 Posts: 5277 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 2 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

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
VP  D
Joined: 20 Jul 2017
Posts: 1076
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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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  G Joined: 10 Aug 2018 Posts: 339 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 1 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. _________________ On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES. " I CAN AND I WILL" GMAT:[640 Q44, V34, IR4, AWA5] 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 V Joined: 24 Aug 2016 Posts: 782 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 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  B 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 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  G Joined: 30 May 2018 Posts: 157 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 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  P Joined: 03 Jun 2019 Posts: 1844 Location: India Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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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Manager  G
Joined: 08 Jan 2018
Posts: 129
Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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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  G Joined: 10 Mar 2019 Posts: 75 Location: Russian Federation Schools: Haas '22 GPA: 3.95 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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  G Joined: 28 Jan 2019 Posts: 126 Location: Peru Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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  P Joined: 27 Aug 2014 Posts: 358 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 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  G Joined: 26 Jan 2016 Posts: 180 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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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Director  P
Joined: 24 Nov 2016
Posts: 778
Location: United States
Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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  S Joined: 24 Jun 2017 Posts: 71 Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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  B Joined: 29 May 2018 Posts: 23 Location: India GMAT 1: 680 Q49 V33 Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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  G Joined: 05 Mar 2017 Posts: 261 Location: India Concentration: General Management, Marketing GPA: 3.6 WE: Marketing (Hospitality and Tourism) Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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.
Manager  G
Joined: 28 Feb 2014
Posts: 180
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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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  S Joined: 30 Nov 2016 Posts: 102 Location: India Concentration: Finance, Strategy Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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 BSchool Moderator G Joined: 07 Dec 2018 Posts: 144 Location: India Re: Luis spent a certain amount of money in a supermarket. He spent a thir [#permalink] ### Show Tags 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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