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:

on p52 of the strategy guide 3 of the MGMAT they give an example

if x and y are nonnegative integers and x+y=25 what is x

1) 20x+10y<300 2) 20x+10y>280

the solution they provide makes sense but 2 things are confusing

a) they say the maximum for 20x + 10y is 250 when x=0 and y=25, why didn't they make the maximum value using x=25 , y=0 since that would give you a larger number?

b) why didn't they use option (1) and solve for Y , then plug that into X=Y=25 from the original problem? wouldn't that solve for x right away?

its probably something simple that I'm missing but any clarity would be appreciated its really bugging me!

Re: If x and y are nonnegative integers and x+y=25 what is x? [#permalink]

Show Tags

12 Feb 2012, 02:47

ooh that makes sense!

not that important but what about for :

a) they say the maximum for 20x + 10y is 250 when x=0 and y=25, why didn't they make the maximum value using x=25 , y=0 since that would give you a larger number?

a) they say the maximum for 20x + 10y is 250 when x=0 and y=25, why didn't they make the maximum value using x=25 , y=0 since that would give you a larger number?

b) why didn't they use option (1) and solve for Y , then plug that into X=Y=25 from the original problem? wouldn't that solve for x right away?

its probably something simple that I'm missing but any clarity would be appreciated its really bugging me!

thanks in advance!

As for your questions (notice that x and y are nonnegative integers):

A. 250 is the smallest possible value of 20x+10y: minimize x, as it has greater multiple (20) and maximize y, as it has smaller multiple (10) --> x=0 and y=25 --> 20x +10y=250. The same way the largest possible value of 20x+10y is for x=25 and y=0 --> 20x +10y=500.

Or another way: 20x+10y=20x+10(25-x)=10x+250 --> to get the smallest possible value minimize x, so make it 0: 10x+250=250, and to get the largest possible value maximize x, so make it 25: 10x+250=500.

B. You can not solve for x or y as you get only the ranges for them from (1), as well as from (2), and not the unique values (refer to the solution above).

Re: If x and y are nonnegative integers and x+y=25 what is x? [#permalink]

Show Tags

12 Aug 2012, 18:06

Bunuel wrote:

c210 wrote:

a) they say the maximum for 20x + 10y is 250 when x=0 and y=25, why didn't they make the maximum value using x=25 , y=0 since that would give you a larger number?

b) why didn't they use option (1) and solve for Y , then plug that into X=Y=25 from the original problem? wouldn't that solve for x right away?

its probably something simple that I'm missing but any clarity would be appreciated its really bugging me!

thanks in advance!

As for your questions (notice that x and y are nonnegative integers):

A. 250 is the smallest possible value of 20x+10y: minimize x, as it has greater multiple (20) and maximize y, as it has smaller multiple (10) --> x=0 and y=25 --> 20x +10y=250. The same way the largest possible value of 20x+10y is for x=25 and y=0 --> 20x +10y=500.

Or another way: 20x+10y=20x+10(25-x)=10x+250 --> to get the smallest possible value minimize x, so make it 0: 10x+250=250, and to get the largest possible value maximize x, so make it 25: 10x+250=500.

B. You can not solve for x or y as you get only the ranges for them from (1), as well as from (2), and not the unique values (refer to the solution above).

Hope it helps.

Hey Bunuel,

You taught me one hard rule, I'll never forget with inequilities. You can only add two inequalities in the same direction, never subtract!!

Ex a<b x<y

a+x<b+y is ok

but a-x<b-y is WRONG!!

Now, does this rule differ if I compare an inequality to an equation? Can I subtract an inequality and an equation in the same direction?

(1) 2x+y<30 (2) x+y=25

Can I simply subtract with confidence to get: x<5? I know that I can solve for y in equation (2) and substitute in equation (1). I would appreciate if you could confirm

Re: If x and y are nonnegative integers and x+y=25 what is x? [#permalink]

Show Tags

12 Aug 2012, 23:19

alphabeta1234 wrote:

Bunuel wrote:

c210 wrote:

a) they say the maximum for 20x + 10y is 250 when x=0 and y=25, why didn't they make the maximum value using x=25 , y=0 since that would give you a larger number?

b) why didn't they use option (1) and solve for Y , then plug that into X=Y=25 from the original problem? wouldn't that solve for x right away?

its probably something simple that I'm missing but any clarity would be appreciated its really bugging me!

thanks in advance!

As for your questions (notice that x and y are nonnegative integers):

A. 250 is the smallest possible value of 20x+10y: minimize x, as it has greater multiple (20) and maximize y, as it has smaller multiple (10) --> x=0 and y=25 --> 20x +10y=250. The same way the largest possible value of 20x+10y is for x=25 and y=0 --> 20x +10y=500.

Or another way: 20x+10y=20x+10(25-x)=10x+250 --> to get the smallest possible value minimize x, so make it 0: 10x+250=250, and to get the largest possible value maximize x, so make it 25: 10x+250=500.

B. You can not solve for x or y as you get only the ranges for them from (1), as well as from (2), and not the unique values (refer to the solution above).

Hope it helps.

Hey Bunuel,

You taught me one hard rule, I'll never forget with inequilities. You can only add two inequalities in the same direction, never subtract!!

Ex a<b x<y

a+x<b+y is ok

but a-x<b-y is WRONG!!

Now, does this rule differ if I compare an inequality to an equation? Can I subtract an inequality and an equation in the same direction?

(1) 2x+y<30 (2) x+y=25

Can I simply subtract with confidence to get: x<5? I know that I can solve for y in equation (2) and substitute in equation (1). I would appreciate if you could confirm

Many thanks!!

YES, you can subtract with confidence, because this operation is equivalent to subtracting the same quantity from both sides, operation allowed when working with inequalities. In the above case, you subtract 25, only that on the left you express it as x + y, and on the right you just simply write it as 25. Therefore, 2x + y - (x + y) < 30 - 25 or x < 5. If you use substitution, replacing x + y in the inequality by 25, you obtain x + 25 < 30, from which by now subtracting 25 from both sides, you get the same conclusion x < 5. So, you do the same thing, just in slightly different forms.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If x and y are nonnegative integers and x+y=25 what is x? [#permalink]

Show Tags

31 Jul 2014, 07:48

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: If x and y are nonnegative integers and x+y=25 what is x? [#permalink]

Show Tags

03 Dec 2016, 07:00

Bunuel wrote:

If x and y are nonnegative integers and x+y=25 what is x

Given: x+y=25 --> y=25-x. Question: x=?

(1) 20x+10y<300 --> 2x+y<30 --> 2x+(25-x)<30 --> x<5. Not sufficient. (2) 20x+10y>280 --> 2x+y>28 --> 2x+(25-x)>28 --> x>3. Not sufficient.

(1)+(2) From (1) and (2) 3<x<5 --> since given that x is an integer then x=4. Sufficient.

Answer: C.

Hope it's clear.

for me ,the right answer is E because the question says that x and y are nonnegative integer means that x and y can be negative fraction and could be positive integer and fraction Therefore when we combine statments we find that x is between 3 and 4 means that x can be 3.5 3.6 3.2 so is insufficient can you please tell me where my reasoning is false ? Thankyou

If x and y are nonnegative integers and x+y=25 what is x

Given: x+y=25 --> y=25-x. Question: x=?

(1) 20x+10y<300 --> 2x+y<30 --> 2x+(25-x)<30 --> x<5. Not sufficient. (2) 20x+10y>280 --> 2x+y>28 --> 2x+(25-x)>28 --> x>3. Not sufficient.

(1)+(2) From (1) and (2) 3<x<5 --> since given that x is an integer then x=4. Sufficient.

Answer: C.

Hope it's clear.

for me ,the right answer is E because the question says that x and y are nonnegative integer means that x and y can be negative fraction and could be positive integer and fraction Therefore when we combine statments we find that x is between 3 and 4 means that x can be 3.5 3.6 3.2 so is insufficient can you please tell me where my reasoning is false ? Thankyou

x and y are nonnegative integers means that x and y are integers greater than or equal to 0: 0, 1, 2, 3, ... This is the only reading of this statement.
_________________

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...