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leovavassori
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Post subject: If 3(x) + 243 = 2 (3(x)), what is the value of x?  Posted: Fri Jan 20, 2012 12:35 pm |
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Posts: 7
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Hello there,
my question relates to the ADVANCED Quant book - Pg 162 - Try it #6-2. It reads:
NOTE: (x) = number raised to "x" exponent.
If 3(x) + 243 = 2 (3(x)), what is the value of x? Solution:
If 3(x) + 243 = (3(x)) (3(x))
x = 5
How did the number 2 on the right side of the equation become (3(x))? I am guessing that its an estimated answer hence the 2 was brought up by 1 unit so that the equation could be manipulated?
Cheers,
Leo
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leovavassori
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Post subject: Re: If 3(x) + 243 = 2 (3(x)), what is the value of x? Posted: Wed Jan 25, 2012 7:37 am |
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Can anyone help please?
cheers,
Leo
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tim
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Post subject: Re: If 3(x) + 243 = 2 (3(x)), what is the value of x? Posted: Thu Feb 02, 2012 7:31 pm |
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| ManhattanGMAT Staff |
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Location: Southwest Airlines, seat 21C
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first, be careful bumping questions. every time you do that it puts the question at the absolute end of the queue for us to answer. bumping a question is the most effective way to cause a delay in getting your question answered..
as for the question, you are missing a plus sign. it should say:
If 3(x) + 243 = 2 (3(x))
3(x) + 243 = (3(x)) + (3(x))
notice that all we've done is take 2 times something and turn it into something plus something. this is always a valid step in algebra; in fact, that's what it means to multiply something by 2..
_________________
Tim Sanders
Manhattan GMAT Instructor
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leovavassori
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Post subject: Re: If 3(x) + 243 = 2 (3(x)), what is the value of x? Posted: Fri Feb 03, 2012 4:05 am |
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First thank you for answering. Second, what is a bumping question? I most certainly would like to know what its so that I can get questions answered quicker.
And with regards to your response:
"as for the question, you are missing a plus sign. it should say:
If 3(x) + 243 = 2 (3(x))
3(x) + 243 = (3(x)) + (3(x))
notice that all we've done is take 2 times something and turn it into something plus something. this is always a valid step in algebra; in fact, that's what it means to multiply something by 2.."
So what you did to the right side of the equation is the following:
i.e. 4 (3(x)) is the same as
(3(x)) + (3(x)) + (3(x)) + (3(x)) !?
Cheers,
Leo
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tim
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Post subject: Re: If 3(x) + 243 = 2 (3(x)), what is the value of x? Posted: Mon Feb 06, 2012 5:06 pm |
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| ManhattanGMAT Staff |
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bumping a question is when you respond to your own post. then your post automatically becomes the newest one, which means it pushes it to the back of the line and you have to wait longer to get a response..
as for your question about the math, you are absolutely correct..
_________________
Tim Sanders
Manhattan GMAT Instructor
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metman82
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Post subject: Re: If 3(x) + 243 = 2 (3(x)), what is the value of x? Posted: Thu Feb 09, 2012 4:03 pm |
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Even if I am still at the beginning with Book 1 and struggling with DS in number properties: I solved this as follows.
If 3^x + 243 = 2(3^x), what is the value of x?
Try to get the 3^x from the left side to the right side
243 = 2(3^x) - 1*3^x
rephrase it (place the 3^x outside the brackets (don't know the english word for this action))
243 = 3^x ( 2 - 1 )
You get
243 = 3^x
You know that 243 is a multiple of 3 ( 2+4+3 = 9).
3x3x3x3x3 = 3^5 = 243
I hope I understood this question correctly.
Maybe its not the best way to solve but I did it in 1 min.
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tim
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Post subject: Re: If 3(x) + 243 = 2 (3(x)), what is the value of x? Posted: Sun Feb 26, 2012 4:44 am |
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| ManhattanGMAT Staff |
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that works!
_________________
Tim Sanders
Manhattan GMAT Instructor
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