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A citrus fruit grower receives $15 for each crate of oranges

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A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 30 Jul 2012, 01:20
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A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.
(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

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[Reveal] Spoiler: OA

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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 30 Jul 2012, 01:21
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SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 30 Jul 2012, 19:51
A. 15(2x + 20) + 18x = ???

Insufficient

B. 15x + 18y = 38700

2 variables one equation. Insufficient

Combine them both. Sufficient.
[Reveal] Spoiler:
C
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 31 Jul 2012, 23:08
First what comes to my mind is that it is C, so combining two statements we can figure out:
let say oranges - x and grapefruit -y, combining two statements we have (2y+20)*15+18*20=3870, y=800 and x=1620

Bunuel can you please clarify: How do we know that 800 and 1620 is not the only combination? if it is the only compbination possible then the answer should be B, but how to calculate from the statement 2 alone that there is only one possible solution. I have tried to pick numbers but after few attempts, looking at the watch i said it should be C (just a good feel).
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 01 Aug 2012, 02:35
ziko wrote:
First what comes to my mind is that it is C, so combining two statements we can figure out:
let say oranges - x and grapefruit -y, combining two statements we have (2y+20)*15+18*20=3870, y=800 and x=1620

Bunuel can you please clarify: How do we know that 800 and 1620 is not the only combination? if it is the only compbination possible then the answer should be B, but how to calculate from the statement 2 alone that there is only one possible solution. I have tried to pick numbers but after few attempts, looking at the watch i said it should be C (just a good feel).


if one costs 15 dollars and the other costs 18 dollars
you said one solution is 800 and 1620
then at least you know that 18 crates of orange cost the same price (18*15) than 15 crates of grapefruit (15*18).
So for instance
818 (800+18) and 1605 (1620-15) must be another solution. And there are many others
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 03 Aug 2012, 05:00
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SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 20 Apr 2013, 01:25
Bunuel wrote:
SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.



Hi Bunnel,

I marked this one as B, as i thought that by prime factorization we can get the number of multiples of 15 and 18.
However i later did the prime factorization and now know that their is no way of knowing how many times 15 or 18 goes in to 38,700.

I remembered this technique as I had used it in Problem Solving, so want to know whether this technique can be used in DS questions.
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 20 Apr 2013, 04:20
Expert's post
cumulonimbus wrote:
Bunuel wrote:
SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.



Hi Bunnel,

I marked this one as B, as i thought that by prime factorization we can get the number of multiples of 15 and 18.
However i later did the prime factorization and now know that their is no way of knowing how many times 15 or 18 goes in to 38,700.

I remembered this technique as I had used it in Problem Solving, so want to know whether this technique can be used in DS questions.


What technique are you talking about? Can you please also give PS question for which you've used it?
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 13 Oct 2013, 13:55
Bunuel wrote:
cumulonimbus wrote:
Bunuel wrote:
SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.



Hi Bunnel,

I marked this one as B, as i thought that by prime factorization we can get the number of multiples of 15 and 18.
However i later did the prime factorization and now know that their is no way of knowing how many times 15 or 18 goes in to 38,700.

I remembered this technique as I had used it in Problem Solving, so want to know whether this technique can be used in DS questions.


What technique are you talking about? Can you please also give PS question for which you've used it?


I did the same thing and marked B. How can we tell quickly that there are multiple answers for 5x + 6y = 12900?
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 14 Oct 2013, 04:16
Expert's post
1
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BOOKMARKED
runningguy wrote:
Bunuel wrote:
cumulonimbus wrote:

Hi Bunnel,

I marked this one as B, as i thought that by prime factorization we can get the number of multiples of 15 and 18.
However i later did the prime factorization and now know that their is no way of knowing how many times 15 or 18 goes in to 38,700.

I remembered this technique as I had used it in Problem Solving, so want to know whether this technique can be used in DS questions.


What technique are you talking about? Can you please also give PS question for which you've used it?


I did the same thing and marked B. How can we tell quickly that there are multiple answers for 5x + 6y = 12900?



Trial and error plus some logic and knowledge of basics of number properties should help you to identify this.

For more on this type of questions check:
eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html

Hope it helps.
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 16 Nov 2013, 13:29
Bunuel wrote:
SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.



Hi Banuel,

I get hung up on when i create the equation 15x + 18y = 38700.... When I see a equation like this, should i automatically assume that mutiple combinations of x and y are possible to satisfy the equation or are there instances where I should actually work out the math.... I spend a lot of time contemplating this, although I see the obvious answer in C of two liner equations...

thoughts?

Thanks
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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 16 Nov 2013, 13:35
Expert's post
indiheats wrote:
Bunuel wrote:
SOLUTION

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let x be the # of oranges and y the # of grapefruits. Note that, both x and y must be integers.
Question: x=?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> x=2y+20. Not sufficient to calculate x

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> 15x+18y=38700 --> 5x+6y=12900. Multiple values are possible, for istance: x=180 and y=2000 OR x=60 and y=2100.

(1)+(2) We have two distinct linear equation with two unknowns, hence we can solve for x and y. Sufficient.

Answer: C.



Hi Banuel,

I get hung up on when i create the equation 15x + 18y = 38700.... When I see a equation like this, should i automatically assume that mutiple combinations of x and y are possible to satisfy the equation or are there instances where I should actually work out the math.... I spend a lot of time contemplating this, although I see the obvious answer in C of two liner equations...

thoughts?

Thanks


Generally such kind of linear equations (ax+by=c) have infinitely many solutions for x and y, and we cannot get single numerical values for the variables. But since x and y here represent the # of oranges and the # of grapefruits, then they must be non-negative integers and in this case 15x + 18y = 38700 is no longer simple linear equation, it's Diophantine equation (equations whose solutions must be integers only) and for such kind on equations there might be only one combination of x and y possible to satisfy it. When you encounter such kind of problems you must always check by trial and error whether it's the case.

In my post above there links to several such problems.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 10 Jan 2014, 06:49
Bunuel wrote:
A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.
(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

Practice Questions
Question: 9
Page: 275
Difficulty: 650


We are given this equation: 15*O + 18*6 = Total Revenue, so we have 3 variables.

Statement 1 solves one of our variables, but it's insufficient because we have 2 more.
Statement 2 solves another of our variables, but still on itself it's insufficient.

But if we combine the two statements, we have one equation and one variable, so we can solve for the last variable. The answer is C.
Re: A citrus fruit grower receives $15 for each crate of oranges   [#permalink] 10 Jan 2014, 06:49
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