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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, 02:20
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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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Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink] New post 30 Jul 2012, 02:21
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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, 20:51
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 01 Aug 2012, 00:08
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, 03:35
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, 06:00
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, 02:25
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, 05:20
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?
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


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Re: A citrus fruit grower receives $15 for each crate of oranges   [#permalink] 20 Apr 2013, 05:20
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