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:

Work with the same base: is \(4^{x+y}=8^{10}\) ? --> is \(2^{2(x+y)}=2^{30}\) ? --> is \(2(x+y)=30\)? is \(x+y=15\)?

(1) x - y = 9. Not sufficient. (2) y/x = 1/4 --> \(x=4y\). Not sufficient.

(1)+(2) We have two distinct linear equation with two unknowns (\(x - y = 9\) and \(x=4y\)), hence we can solve for both of them and get whether \(x+y=15\) is true. Sufficient.

\(4^{x+y}=8^{10}\) ---> \(2^2{x+y}=2^3{10}\)----->\(2^{x+y}=2^{15}\) The question can be restated as Is x+y = 15?

1) x-y = 9 --->Since x & y can assume any value---->Insufficient 2) x= 4y ---> No Absolute value is given for x & y, Only ratio is given-----> Insufficient 1+2) 4y-y = 9 ----> 3y=9---->Sufficient

Thus Answer C
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

From the question is X + Y = 15?

1st Option X - Y = 9 it can be any thing and any no. not necessarly the nos whose sum is equal to 15. Not Sufficient. 2nd Option: Y/x = 1/4 again Y and X can be any thing not necessarly the nos. whose summ is equal to 15. Not sufficient.

Combining Both options: X - X/4 = 9 X = 12 therefore Y = 3.

Work with the same base: is \(4^{x+y}=8^{10}\) ? --> is \(2^{2(x+y)}=2^{30}\) ? --> is \(2(x+y)=30\)? is \(x+y=15\)?

(1) x - y = 9. Not sufficient. (2) y/x = 1/4 --> \(x=4y\). Not sufficient.

(1)+(2) We have two distinct linear equation with two unknowns (\(x - y = 9\) and \(x=4y\)), hence we can solve for both of them and get whether \(x+y=15\) is true. Sufficient.

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________

Ans:C 4^(x+y)=8^(10) =>2^2(x+y)=2^3(10) =>x+y=15? Statement1:x-y=9----Insufficent Statement2:y/x=1/4=>x=4y---Insufficent By combining St1&st2 y=3 and x=12 which gives x+y=15---Sufficient

Hi, could you please help clarify? I'm a little bit confused.

Isn't the answer D?

(1) X-Y=9 ----> X=9+Y We can just put "X=Y+9" in the initial equation X+Y=15 to solve the equation without any help from the 2nd equation, y/x = 1/4.

The same goes to the second equation (2) y/x = 1/4 -------> X=4Y Just put substitute the X in the initial equation, X+Y=15, with the 4Y and then solve the equation for both X and Y.

So, we can actually get the answer using only 1 of statement. So why is the answer C.

Hi, could you please help clarify? I'm a little bit confused.

Isn't the answer D?

(1) X-Y=9 ----> X=9+Y We can just put "X=Y+9" in the initial equation X+Y=15 to solve the equation without any help from the 2nd equation, y/x = 1/4.

The same goes to the second equation (2) y/x = 1/4 -------> X=4Y Just put substitute the X in the initial equation, X+Y=15, with the 4Y and then solve the equation for both X and Y.

So, we can actually get the answer using only 1 of statement. So why is the answer C.

Billion thanks in advance!

Welcome to GMAT Club!

Actually the correct answer is C, not D.

From the stem the question became: is x + y = 15?

Now, (2) says that x - y = 9. Can we tell from this whether x + y = 15? No! Consider x = 10 and y = 1 for a NO answer and x = 12 and y = 3 for an YES answer. Hence, the first statement is NOT sufficient.

The same for the second statement.

The problem with your solution is that you assumed that we have two equations for each statement, whereas we have just one: x - y = 9 for (1) and y/x = 1/4 for (2). The second equation, x + y = 15 is not given to be true, we are asked to find whether it's true.

Now, (2) says that x - y = 9. Can we tell from this whether x + y = 15? No! Consider x = 10 and y = 1 for a NO answer and x = 12 and y = 3 for an YES answer. Hence, the first statement is NOT sufficient.

The same for the second statement.

The problem with your solution is that you assumed that we have two equations for each statement, whereas we have just one: x - y = 9 for (1) and y/x = 1/4 for (2). The second equation, x + y = 15 is not given to be true, we are asked to find whether it's true.

Hope it's clear.

Oh! Thanks a lot! That's clear.

So when a question ask whether an equation is true or not, we cannot use it in solving the problem. Am I right? ^___^

Now, (2) says that x - y = 9. Can we tell from this whether x + y = 15? No! Consider x = 10 and y = 1 for a NO answer and x = 12 and y = 3 for an YES answer. Hence, the first statement is NOT sufficient.

The same for the second statement.

The problem with your solution is that you assumed that we have two equations for each statement, whereas we have just one: x - y = 9 for (1) and y/x = 1/4 for (2). The second equation, x + y = 15 is not given to be true, we are asked to find whether it's true.

Hope it's clear.

Oh! Thanks a lot! That's clear.

So when a question ask whether an equation is true or not, we cannot use it in solving the problem. Am I right? ^___^

Yes, you cannot use it as a given.
_________________

Why do you have to reduce the base to 2? Why cant we just change the base of 8 to 4 so thats it reads X+y=20? That would seem to be easier but mathematically Im not coming out to the correct answer. Can someone help?

Why do you have to reduce the base to 2? Why cant we just change the base of 8 to 4 so thats it reads X+y=20? That would seem to be easier but mathematically Im not coming out to the correct answer. Can someone help?

\(8^{10}\) cannot be written as \(4^{20}\), \(4^{20}=4^{2*10}=16^{10}\neq{8^{10}}\).

Hope it's clear
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Work with the same base: is \(4^{x+y}=8^{10}\) ? --> is \(2^{2(x+y)}=2^{30}\) ? --> is \(2(x+y)=30\)? is \(x+y=15\)?

(1) x - y = 9. Not sufficient. (2) y/x = 1/4 --> \(x=4y\). Not sufficient.

(1)+(2) We have two distinct linear equation with two unknowns (\(x - y = 9\) and \(x=4y\)), hence we can solve for both of them and get whether \(x+y=15\) is true. Sufficient.

Answer: C.

Here's the approach I did, it took me roughly 5 minutes to complete, would you be able to tell me how to get faster, and if i plugged Y into the correct question.

From the Q.Stem I simplified the Question down to, does "x+y=15" Yes/No.

Statement 1) x-y=9 x+y=9+y X=9+Y

I used substation, plugged in X with the original equation, and I got 9+2y=15, reduced down to y=3.

So the question is reduced to "does Y=3, yes or no" from what I know, I'm Not sure. So therefore it's not sufficient.

Statement 2) y/x=1/4 is simplified to 4Y=X,

I Plugged in to the original equation X+Y=15 So now I have 4Y+Y=15 5Y=15, The question is now rephrased as does y equal 3? again, it's not sufficient.

(C) X+Y=15 From Statement 1 & Statement 2, Y=3, I plugged in the following

X+Y=15 X-3=-3 X=12

Banuel, If I went wrong anywhere, can you tell me where I went wrong. Should I test the answer choice to see if it's insufficient, instead of labeling the answer not sufficient?

For statement one, I found myself answering, yes it's sufficient to solve, but X is not given, so I should not assume that the number is automatically "x=12" correct? The simplification is reducing the question still" Does Y=3? and that changes it all, because I don't know if Y=3. So is that enough information to move on? Same reasoning on the second statement. Threw me off for a bit.

Work with the same base: is \(4^{x+y}=8^{10}\) ? --> is \(2^{2(x+y)}=2^{30}\) ? --> is \(2(x+y)=30\)? is \(x+y=15\)?

(1) x - y = 9. Not sufficient. (2) y/x = 1/4 --> \(x=4y\). Not sufficient.

(1)+(2) We have two distinct linear equation with two unknowns (\(x - y = 9\) and \(x=4y\)), hence we can solve for both of them and get whether \(x+y=15\) is true. Sufficient.

Answer: C.

Here's the approach I did, it took me roughly 5 minutes to complete, would you be able to tell me how to get faster, and if i plugged Y into the correct question.

From the Q.Stem I simplified the Question down to, does "x+y=15" Yes/No.

Statement 1) x-y=9 x+y=9+y X=9+Y

I used substation, plugged in X with the original equation, and I got 9+2y=15, reduced down to y=3.

So the question is reduced to "does Y=3, yes or no" from what I know, I'm Not sure. So therefore it's not sufficient.

Statement 2) y/x=1/4 is simplified to 4Y=X,

I Plugged in to the original equation X+Y=15 So now I have 4Y+Y=15 5Y=15, The question is now rephrased as does y equal 3? again, it's not sufficient.

(C) X+Y=15 From Statement 1 & Statement 2, Y=3, I plugged in the following

X+Y=15 X-3=-3 X=12

Banuel, If I went wrong anywhere, can you tell me where I went wrong. Should I test the answer choice to see if it's insufficient, instead of labeling the answer not sufficient?

For statement one, I found myself answering, yes it's sufficient to solve, but X is not given, so I should not assume that the number is automatically "x=12" correct? The simplification is reducing the question still" Does Y=3? and that changes it all, because I don't know if Y=3. So is that enough information to move on? Same reasoning on the second statement. Threw me off for a bit.

5 minutes is too much for this problem.

The question boils down to whether \(x+y=15\).

(1) says x - y = 9. Can we answer whether \(x+y=15\)? No, because infinitely many pairs of (x, y) satisfy x - y = 9, and only one of them yields the sum of 15, namely x=12 and y=3.

(2) says x=4y. Basically the same here: can we answer whether \(x+y=15\)? No, because infinitely many pairs of (x, y) satisfy x=4y, and only one of them yields the sum of 15.

When we combine the statements we have x-y=9 and x=4y. So, we have two two distinct linear equation with two unknowns, hence we can solve for both of them and get whether \(x+y=15\) is true.

As you can see we don't need to solve anything for this question to get the answer.

Thanks Banuel, It really helps. Yeah, 5 Minutes is way too long. I'm having to brush up on linear equations as you can tell. The second time I worked the problem it made more sense, and cut my timing in half.

gmatclubot

Re: Is 4^(x+y)=8^(10) ?
[#permalink]
28 Oct 2013, 14:09

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...