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# Joseph bought two varieties of rice, costing 5 cents per

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Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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15 Feb 2012, 07:14
2
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12
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Difficulty:

45% (medium)

Question Stats:

70% (01:51) correct 30% (02:30) wrong based on 376 sessions

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Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

What is the level of this one ??? I have problems to set up an equation. Thanks.

Source: GMAT Bible, an excerpt.
[Reveal] Spoiler: OA

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Kudos [?]: 9314 [2], given: 1169

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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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15 Feb 2012, 07:44
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carcass wrote:
Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

What is the level of this one ??? I have problems to set up an equation. Thanks.

Source: GMAT Bible, an excerpt.

Hi, unfortunately cannot advise you on the difficulty level, but as for the equation I would do the following:

1. 20% profit at the price of 7 cents means that cost of the mixture should be 70/12 cents per ounce (7 = 120% and x = 100% => x = 7*100/120)
2. Let the amount of 5 cent rice will be x and the amount of 6 cent one – y. The price of ounce of mixture will be: (5x + 6y)/(x + y), which as we know should equal to 70/12
3. (5x + 6y)/(x + y) = 70/12 => x/y = 1/5

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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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15 Feb 2012, 08:28
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This is a weighted averages question.

Let's suppose Rice A = 5c/ounce... Let quantity of A $$=x$$
Lets suppose Rice B = 6c/ounce...Let quantity of B $$=y$$
Resulting Mixture = 7c/ounce........So quantity of mixture $$=(x+y)$$

Let's setup the equation bearing in mind that right side is $$20%$$ greater:

$$\frac{120}{100}[(Total Cost of x)+(Total Cost of y)]=(Costof Mixture)$$

$$\frac{120}{100}[5(x)+6(y)]=7(x+y)$$
Solve for $$\frac{x}{y}=\frac{1}{5}$$

Hence B
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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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15 Feb 2012, 10:44
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Expert's post
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carcass wrote:
Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

What is the level of this one ??? I have problems to set up an equation. Thanks.

Source: GMAT Bible, an excerpt.

Since 7 cents per ounce made a profit of 20% then the average cost per once was 7/1.2=35/6 cents.

Now, from weighted average formula: $$weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}$$ --> $$\frac{value_1}{value_2}=\frac{weight_2-average}{average-weight_1}$$ --> $$\frac{value_1}{value_2}=\frac{6-\frac{35}{6}}{\frac{35}{6}-5}$$ --> $$\frac{value_1}{value_2}=\frac{\frac{1}{6}}{\frac{5}{6}}=\frac{1}{5}$$.

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Kudos [?]: 133182 [1], given: 12438

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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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16 Feb 2012, 03:28
5
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Expert's post
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carcass wrote:
Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

What is the level of this one ??? I have problems to set up an equation. Thanks.

Source: GMAT Bible, an excerpt.

Actually, the question is not very tricky. Perhaps 650 or so. A couple of things here - If you understand the theory of mixtures, you don't have to set up equations. In most GMAT equations, if you know your theory well, much algebra is not required. Also, the numbers will be a little better. e.g.

"Joseph bought two varieties of rice, costing 4 cents per ounce and 5.5 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 6 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?"

Since a profit of 20% was made, the cost price of the mixture must have been 5. (20% of 5 will be 1 which when added to 5 will give 6)
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (5.5 - 5)/(5 - 4) = 1/2

They were mixed in the ratio 1:2.

For the detailed theory, check out this post: http://www.veritasprep.com/blog/2011/04 ... -mixtures/

Mind you, better numbers doesn't mean no decimals or fractions. It means that the numbers make sense in that scenario. If it is a 20% increase (i.e. 1/5 more), chances are the original number is divisible by 5. If you are dealing with circles, chances are the radius is a multiple of 7 (to cancel off the 7 in $${\pi}$$) etc.
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$6/ounce : Y Ounces Mixture cost + Mixture cost * 0.2 = Total cost {5X + 6Y} * 1.2 = 7(X+Y) Hence (B) _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ Kudos [?]: 919 [0], given: 322 Intern Joined: 19 Oct 2014 Posts: 40 Kudos [?]: 19 [0], given: 35 Location: India Concentration: Finance, Entrepreneurship Schools: WP Carey" 20 GMAT 1: 600 Q48 V25 GMAT 2: 670 Q49 V31 GPA: 3.26 WE: Operations (Manufacturing) Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink] ### Show Tags 23 Mar 2015, 09:29 From 20% profit, we can obtain the cost price(x) of the mixture before profit. 120/100*x=7=>x=35/6. From the answers, we need to find an option that satisfies the above cost price of 35/6 option A)(5+6*10)/11=65/11 B)(5+6*5)/(6)=35/6. Hence option B is the answer Kudos [?]: 19 [0], given: 35 Intern Joined: 03 Jul 2015 Posts: 34 Kudos [?]: 22 [0], given: 27 Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink] ### Show Tags 26 Dec 2015, 11:38 Bunuel wrote: carcass wrote: Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture? A. 1:10 B. 1:5 C. 2:7 D. 3:8 E. 5:7 What is the level of this one ??? I have problems to set up an equation. Thanks. Source: GMAT Bible, an excerpt. Since 7 cents per ounce made a profit of 20% then the average cost per once was 7/1.2=35/6 cents. Now, from weighted average formula: $$weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}$$ --> $$\frac{value_1}{value_2}=\frac{weight_2-average}{average-weight_1}$$ --> $$\frac{value_1}{value_2}=\frac{6-\frac{35}{6}}{\frac{35}{6}-5}$$ --> $$\frac{value_1}{value_2}=\frac{\frac{1}{6}}{\frac{5}{6}}=\frac{1}{5}$$. Answer: B. isnt it possible to do allegation method? i found allegation method is very simple but did not do this one by allegation, Kudos [?]: 22 [0], given: 27 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7750 Kudos [?]: 17874 [0], given: 235 Location: Pune, India Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink] ### Show Tags 27 Dec 2015, 19:39 anik19890 wrote: Bunuel wrote: carcass wrote: Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture? A. 1:10 B. 1:5 C. 2:7 D. 3:8 E. 5:7 What is the level of this one ??? I have problems to set up an equation. Thanks. Source: GMAT Bible, an excerpt. Since 7 cents per ounce made a profit of 20% then the average cost per once was 7/1.2=35/6 cents. Now, from weighted average formula: $$weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}$$ --> $$\frac{value_1}{value_2}=\frac{weight_2-average}{average-weight_1}$$ --> $$\frac{value_1}{value_2}=\frac{6-\frac{35}{6}}{\frac{35}{6}-5}$$ --> $$\frac{value_1}{value_2}=\frac{\frac{1}{6}}{\frac{5}{6}}=\frac{1}{5}$$. Answer: B. isnt it possible to do allegation method? i found allegation method is very simple but did not do this one by allegation, The solution shown above is essentially allegation. We call it the scale method for weighted averages. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Kudos [?]: 17874 [0], given: 235

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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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24 Apr 2016, 21:16
VeritasPrepKarishma wrote:
carcass wrote:
Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?

A. 1:10
B. 1:5
C. 2:7
D. 3:8
E. 5:7

What is the level of this one ??? I have problems to set up an equation. Thanks.

Source: GMAT Bible, an excerpt.

Actually, the question is not very tricky. Perhaps 650 or so. A couple of things here - If you understand the theory of mixtures, you don't have to set up equations. In most GMAT equations, if you know your theory well, much algebra is not required. Also, the numbers will be a little better. e.g.

"Joseph bought two varieties of rice, costing 4 cents per ounce and 5.5 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 6 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?"

Since a profit of 20% was made, the cost price of the mixture must have been 5. (20% of 5 will be 1 which when added to 5 will give 6)
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (5.5 - 5)/(5 - 4) = 1/2

They were mixed in the ratio 1:2.

For the detailed theory, check out this post: http://www.veritasprep.com/blog/2011/04 ... -mixtures/

Mind you, better numbers doesn't mean no decimals or fractions. It means that the numbers make sense in that scenario. If it is a 20% increase (i.e. 1/5 more), chances are the original number is divisible by 5. If you are dealing with circles, chances are the radius is a multiple of 7 (to cancel off the 7 in $${\pi}$$) etc.

Responding to a pm:
Quote:
little question, could i use the allegation cross method to solve this?

The method I have used above is the same as allegation. You can either draw the cross diagram, the scale diagram or use this formula. Everything is just a slightly different presentation of the same concept.
The scale method and the formula are discussed here: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Veritas Prep | GMAT Instructor
My Blog

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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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28 May 2016, 13:10
5x+6y=7(x+y)/1.2
x/y=1/5

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Re: Joseph bought two varieties of rice, costing 5 cents per [#permalink]

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Re: Joseph bought two varieties of rice, costing 5 cents per   [#permalink] 05 Sep 2017, 14:09
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