Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

87% (01:07) correct 13% (01:05) wrong based on 1317 sessions

HideShow timer Statistics

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

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.

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

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).
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

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

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.

Concentration: General Management, Entrepreneurship

GPA: 3.61

WE: Consulting (Manufacturing)

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

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.

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?
_________________

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

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?

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.

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

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...

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.
_________________

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

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]

Show Tags

05 Oct 2015, 06:20

3

This post received KUDOS

indiheats wrote:

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

Your thought process should be how can we make these numbers more manageable. 15 and 18 both share 3 as a factor, but 38700 looks pretty gnarly. A quick check confirms that 3 is a factor, 3+8+7=18, which is divisible by 3

Now we have the equation in something easier to work with 5x + 6y = 12,900.

It still looks pretty daunting. So here's my thought process, what two values when added give us 12,900, in other words, we're asking what gives us 12,000 + 900

So that equation now becomes, 5x+6y = 12,000 + 900 Can we get an x such that we get 12,000 or 900. Yes. Can we get a y such that we can get 12,000 or 900. Yes. 120 is divisible by 6, and 90 is divisible by 6.

What does that mean for us? Well, we can have a case x=2,400 and G = 150 5*2400 + 6*150 = 12,900

OR We can have a case where x=180 and G= 2000

5*180 + 6*2000 = 12,900

You don't have to actually do the arithmetic. Just do a quick sense check, can we have multiple values for x and y, such that we can get 12000 + 900. Use divisibility rules, if x can give us either 900 or 12000 when multiplied by 5, both are divisible by 5, and if Y can give us either 12000 or 900 when multiplied by 6. Both are divisible by 6. So we can get different values for x and y, and still satisfy 12,900.

Hope that helped someone, I know this post is a bit dated.

A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

24 Nov 2015, 05:22

4

This post received KUDOS

1

This post was BOOKMARKED

malkadhi wrote:

indiheats wrote:

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

Your thought process should be how can we make these numbers more manageable. 15 and 18 both share 3 as a factor, but 38700 looks pretty gnarly. A quick check confirms that 3 is a factor, 3+8+7=18, which is divisible by 3

Now we have the equation in something easier to work with 5x + 6y = 12,900.

It still looks pretty daunting. So here's my thought process, what two values when added give us 12,900, in other words, we're asking what gives us 12,000 + 900

So that equation now becomes, 5x+6y = 12,000 + 900 Can we get an x such that we get 12,000 or 900. Yes. Can we get a y such that we can get 12,000 or 900. Yes. 120 is divisible by 6, and 90 is divisible by 6.

What does that mean for us? Well, we can have a case x=2,400 and G = 150 5*2400 + 6*150 = 12,900

OR We can have a case where x=180 and G= 2000

5*180 + 6*2000 = 12,900

You don't have to actually do the arithmetic. Just do a quick sense check, can we have multiple values for x and y, such that we can get 12000 + 900. Use divisibility rules, if x can give us either 900 or 12000 when multiplied by 5, both are divisible by 5, and if Y can give us either 12000 or 900 when multiplied by 6. Both are divisible by 6. So we can get different values for x and y, and still satisfy 12,900.

Hope that helped someone, I know this post is a bit dated.

Here are two approaches I'd take: 1) 2 sec approach though unscientific - a quick look at the equation will tell you that 12900 is a very large number compared to 5 and 6. Hence it is quite likely to fit in multiple combinations of 5 and 6. INSUF 2) 10 sec approach - let x=0, 12900 is divisible by 6(digits of 12900 add up to 3 and is an even number) so y will be an integer. This will give us one combination. Now let y=0, 12900 is obviously divisible by 5--> second combination. INSUF
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Last edited by NoHalfMeasures on 25 Nov 2015, 09:11, edited 1 time in total.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a 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?

(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.

We get a "2by2" table as below:

Attachment:

GCDS Bunuel A citrus fruit grower receives (20151125).jpg [ 24.76 KiB | Viewed 6492 times ]

There are 2 variables (a,b) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer. If we look at the conditions together,

from a=2b+20, 15a+18b=38,700, we can get the values of a and b, so this is sufficient, and the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

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.

We are given that a citrus grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. We can define some variables for the number of crates of oranges shipped and the number of crates of grapefruit shipped.

Let R = the number of crates of oranges shipped and G = the number of crates of grapefruit shipped.

We need to determine the value of R.

Statement One Alone:

Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.

Using statement one we can set up the following equation:

R = 20 + 2G

We cannot determine the value of R, so statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

From statement two we can set up the following equation:

15R + 18G = 38,700

We cannot determine the value of R, so statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we have the following equations:

1) R = 20 + 2G

2) 15R + 18G = 38,700

We can simplify the second equation by dividing the entire equation by 3:

3) 5R + 6G = 12,900

At this point we substitute (20 + 2G) from equation (1) for R in equation (3), giving us:

5(20 + 2G) + 6G = 12,900

Now, at this point, we know we can determine a value for G and thus determine a value for R. If we were taking the actual test, we could stop at this point and say that the answer is C. However, let’s finish the math to show the steps in evaluating R.

100 + 10G + 6G = 12,900

100 + 16G = 12,900

G = 12,800/16

G = 800

Since R = 20 + 2G, R = 20 + 2(800) = 1,620.

Answer: C
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

12 Dec 2017, 19:55

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: A citrus fruit grower receives $15 for each crate of oranges [#permalink]

Show Tags

15 Dec 2017, 07:27

JeffTargetTestPrep wrote:

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.

We are given that a citrus grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. We can define some variables for the number of crates of oranges shipped and the number of crates of grapefruit shipped.

Let R = the number of crates of oranges shipped and G = the number of crates of grapefruit shipped.

We need to determine the value of R.

Statement One Alone:

Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.

Using statement one we can set up the following equation:

R = 20 + 2G

We cannot determine the value of R, so statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

From statement two we can set up the following equation:

15R + 18G = 38,700

We cannot determine the value of R, so statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we have the following equations:

1) R = 20 + 2G

2) 15R + 18G = 38,700

We can simplify the second equation by dividing the entire equation by 3:

3) 5R + 6G = 12,900

At this point we substitute (20 + 2G) from equation (1) for R in equation (3), giving us:

5(20 + 2G) + 6G = 12,900

Now, at this point, we know we can determine a value for G and thus determine a value for R. If we were taking the actual test, we could stop at this point and say that the answer is C. However, let’s finish the math to show the steps in evaluating R.

100 + 10G + 6G = 12,900

100 + 16G = 12,900

G = 12,800/16

G = 800

Since R = 20 + 2G, R = 20 + 2(800) = 1,620.

Answer: C

Could you explain why the main equation is not [ R + 20 = 2G ] ? [ 20 oranges more than twice of grapefruit]