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Question, need some help.

by alex.gellatly » Sun Mar 25, 2012 12:57 am
This is a PS question from Manhattan Cat 3:

If x and y are integers and

(15x + 15x+1) / 4y = 15y,

what is the value of x?

Their solution

(15x + 15x+1) = 15y4y
[15x + 15x(15^1)] = 15y4y
(15x )(1 + 15) = 15y4y
(15x)(16) = 15y4y
(3x)(5x)(24) = (3y)(5y)(22y)

Since both sides of the equation are broken down to the product of prime bases, the respective exponents of like bases must be equal.

2y = 4 so y = 2.
x = y so x = 2.

My question

I might be very stupid now. I understand all the complex parts (prime bases), but how did they go from here [15x + 15x(15^1)] = 15y4y to here (15x )(1 + 15) = 15y4y

Thanks alot
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by seal4913 » Sun Mar 25, 2012 6:31 am
[15x + 15x(15^1)] = 15y4y to here (15x )(1 + 15) = 15y4y

So you factor out 15x and get( 1 + 15) because when you times it out it equal 15x x 1 = 15x plus 15x x 15 = 15x(15) which is the orginal statement[15x + 15x(15^1)]
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by [email protected] » Sun Apr 01, 2012 3:13 am
Please post a proper question as it is posted in the actual test. Kindly post them as it is and not something else... I think there is some problem with the actual question and also the options are also not posted.

Kindly do the same. Thank you...
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by seal4913 » Sun Apr 01, 2012 6:30 am
[email protected] wrote:Please post a proper question as it is posted in the actual test. Kindly post them as it is and not something else... I think there is some problem with the actual question and also the options are also not posted.

Kindly do the same. Thank you...
His question really has nothing to do with the actual test question but with the way to get the answer. If you acutally took the time to read and not criticized the poster like you seem to do a lot you would have noticed this.

He wanted to know about how factoring something out worked. We are all here to try to learn and the biggest part of doing well on the gmat is reading and attention to detial. It seems you still need to work on that.
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by Gmatprep13 » Tue Dec 25, 2012 10:37 pm
I would like to know if there is a better way to solve this. I was wondering if you could plug in the answer choices and if so how to go about doing this.

I have repeated the question and also posted the answer choices as someone mentioned above that there were no answer choices and I am seeking an additional second easier way to solve this that isn't as time consuming.

If x and y are integers and 15^x + 15^(x+1)/ 4^y = 15^y, what is the value of x?

A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
Last edited by Gmatprep13 on Sun Jan 06, 2013 12:41 am, edited 1 time in total.
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by tabsang » Tue Dec 25, 2012 11:45 pm
If x and y are integers and (15^x + 15^x+1)/4^y = 15^y,
what is the value of x?

A. 2
B. 3
C. 4
D. 5
E. Cannot be determined

OA: A
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by tabsang » Wed Dec 26, 2012 12:30 am
Gmatprep13 wrote:I would like to know if there is a better way to solve this. I was wondering if you could plug in the answer choices and if so how to go about doing this.

I have repeated the question and also posted the answer choices as someone mentioned above that there were no answer choices and I am seeking an additional second easier way to solve this that isn't as time consuming.

If x and y are integers and 15^x + 15^(x+1)/ 4y = 15y, what is the value of x?

A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
(Note: The question says 4^y and 15^y. Not 4y and 15y)

(15^x + 15^(x+1))/4^y = 15^y

Expand 15^(x+1)
15^x + 15^x x 15^1 = 15^y x 4^y

Take 15^x common
15^x(1+15)= 15^y x 4^y

15^x(16)= 15^y x 4^y

Now,
15^x x 4^2 = 15^y x 4^y

The above proves two things:
a) x=y (Since 15^x x 4^2 = 15^y x 4^y)
b) x=y=2 (Since 15^x x 4^2 = 15^y x 4^y

I've used the factoring approach too.
I've only tried to bring about more clarity.

Hope this helps.

Cheers,
Taz
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by GMATGuruNY » Wed Dec 26, 2012 5:11 am
Gmatprep13 wrote:I would like to know if there is a better way to solve this. I was wondering if you could plug in the answer choices and if so how to go about doing this.

I have repeated the question and also posted the answer choices as someone mentioned above that there were no answer choices and I am seeking an additional second easier way to solve this that isn't as time consuming.

If x and y are integers and 15^x + 15^(x+1)/ 4y = 15y, what is the value of x?

A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
15^x + 15^(x+1) = (15^y)(4^y).

We can plug in the answers, which represent the value of x.

Answer choice C: 4
15� + 15� = (15^y)(4^y)

15�(1+15) = (15^y)(4^y)

(15�)(4²) = (15^y)(4^y).

The values in red imply that y=2.
Thus, on the left-hand side, 15� needs to decrease to 15², implying that the value of x must be 2 LESS than answer choice C.

The correct answer is A.

Answer choice A: 2
15² + 15³ = (15^y)(4^y)

15²(1+15) = (15^y)(4^y)

(15²)(4²) = (15^y)(4^y).
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