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x(x + 7^(1/2)) = 90. In the equation above, x =

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mikemcgarry
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x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   Updated on: 17 Oct 2018, 05:04
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\(x*(5 + \sqrt 7) = 90\). In the equation above, x =


(A) \(5*(5 - \sqrt 7)\)

(B) \(\frac{15}{2}\)

(C) \(15\)

(D) \(90*(5 - \sqrt 7)\)

(E) \(90*(5 + \sqrt 7)\)


For a full discussion of how to divide by radicals and radical expressions, as well as a complete solution to this particular problem, see this blog:
https://magoosh.com/gmat/2013/gmat-math- ... uare-root/

Mike :-)
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A

Originally posted by mikemcgarry on 13 Mar 2013, 11:11.
Last edited by Bunuel on 17 Oct 2018, 05:04, edited 1 time in total.
Renamed the topic and edited the question.
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   15 Mar 2013, 11:54
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\(x*(5+\sqrt{7})=90\)

Just rationalize \(x=\frac{90}{(5+\sqrt{7})}\)

by multiplying and dividing by \((5-\sqrt{7})\)

- The numerator will be: \(90*(5-\sqrt{7})\)

- And the denominator will be: \(25-5*\sqrt{7}+5*\sqrt{7}-7=25-7=18\)

The solution is \(5*(5-\sqrt{7})\)

Solution A
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   13 Mar 2013, 13:08
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It's A.

\(5*(5-\sqrt{7})(5+\sqrt{7})=\)
\(5*(5^2+\sqrt{7}^2)=\)
\(5*18=\)

\(90\)
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   15 Mar 2013, 12:27
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Value of root(7) is close around 2.6, so 5+2.6 is 7.6
hence we can approximate it to be x*7.5= 90
X = 12
Option A is 12.......
I took a non conventional approach.
Moreover the arrangement of options are not in the standard gmat format.......I guess Mike understand, what i m pointing to....

Consider Kudos if my post helps!!!

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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   15 Mar 2013, 12:35
POE

x = \(\frac{90}{(5+\sqrt{7})}\)

\(5 + \sqrt{7}\) will be something between 7 & 8

So, x should be in the range of 11-12.

We can eliminate B,C. D & E will be greater than 90 and hence can also be eliminated. Only A remains.

Answer is A
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   25 Jun 2013, 12:49
mikemcgarry wrote:
\(x*(5 + sqrt(7)) = 90\)
In the equation above, x =

(A) \(5*(5 - sqrt(7))\)
(B) \(\frac{15}{2}\)
(C) \(15\)
(D) \(90*(5 - sqrt(7))\)
(E) \(90*(5 + sqrt(7))\)



Mike :-)


seriously ?? is this a 700+ question ?? its very simple rationalization ..
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   25 Jun 2013, 14:28
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atilarora wrote:
seriously ?? is this a 700+ question ?? its very simple rationalization ..

Dear atilarora
My friend, you are obvious very skilled in mathematics. IF you have the "difference of two squares" at your fingertips, and IF you remember how to square a radical (you'd be surprised how many folks are confused by even that!), and IF you are familiar with the procedure for rationalizing an expression such as this, then yes, this question is very easy. I am guessing that less than 10% of the GMAT taking population meets all of those "IF" conditions.
I was estimating the difficulty based on what most students studying for the GMAT know or don't know. Some people's brains short-circuit as soon as they see a fraction of any kind, and a fraction with radicals send some of them into conniptions. The entire idea of rationalizing a fraction with an expression involving addition of a radical in the denominator --- holy mackerel! For a large swathe of the test-taking population, such a problem might as well be written in Sanskrit! Obviously, you are quite familiar with this. Don't confuse "easy for you" with "easy" in general.

This, in a way, is the paradox of all math --- when you don't know how to do it, it's impossibly difficult, and when you know how to do it, it is often trivially easy, and just one insight or shift in perspective can make the difference between those two.

Does this make sense?
Mike :-)
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   25 Jun 2013, 14:42
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mikemcgarry wrote:
atilarora wrote:
seriously ?? is this a 700+ question ?? its very simple rationalization ..


This, in a way, is the paradox of all math --- when you don't know how to do it, it's impossibly difficult, and when you know how to do it, it is often trivially easy, and just one insight or shift in perspective can make the difference between those two.

Does this make sense?
Mike :-)


Very true.

Quote:
I could not help laughing at the ease with which he explained his process of deduction. “When I hear you give your reasons,” I remarked, “the thing always appears to me to be so ridiculously simple that I could easily do it myself, though at each successive instance of your reasoning I am baffled until you explain your process. And yet I believe that my eyes are as good as yours.”


"A Scandal in Bohemia", Arthur Conan Doyle.
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   25 Jun 2013, 15:55
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mikemcgarry wrote:
atilarora wrote:
seriously ?? is this a 700+ question ?? its very simple rationalization ..

Dear atilarora
My friend, you are obvious very skilled in mathematics.


you wrote later in the post something easy for someone might be difficult for others .. true .. rationalization easy for me does not mean I am very skilled ..

Quote:
IF you have the "difference of two squares" at your fingertips, and IF you remember how to square a radical (you'd be surprised how many folks are confused by even that!)


do you know anyone who is not aware of what is the square of 5 and sqrt(7) ??

Quote:
and IF you are familiar with the procedure for rationalizing an expression such as this, then yes, this question is very easy.


If its easy it should not be in 700+

Quote:
I am guessing that less than 10% of the GMAT taking population meets all of those "IF" conditions.
I was estimating the difficulty based on what most students studying for the GMAT know or don't know. Some people's brains short-circuit as soon as they see a fraction of any kind, and a fraction with radicals send some of them into conniptions. The entire idea of rationalizing a fraction with an expression involving addition of a radical in the denominator --- holy mackerel! For a large swathe of the test-taking population, such a problem might as well be written in Sanskrit! Obviously, you are quite familiar with this. Don't confuse "easy for you" with "easy" in general.


I don't know what GMAT taking population you know, as far as I know some of the students, everyone know how to do this particular question in less then 50 secs. May be because maths comes easy to Indians. and as you are an instructor you must get to know students of very different levels.

Quote:
This, in a way, is the paradox of all math --- when you don't know how to do it, it's impossibly difficult, and when you know how to do it, it is often trivially easy, and just one insight or shift in perspective can make the difference between those two.

Does this make sense?
Mike :-)


truedat .. this makes sense Mike .. you can smile again.
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   03 Jul 2013, 10:25
mikemcgarry wrote:
\(x*(5 + sqrt(7)) = 90\)
In the equation above, x =

(A) \(5*(5 - sqrt(7))\)
(B) \(\frac{15}{2}\)
(C) \(15\)
(D) \(90*(5 - sqrt(7))\)
(E) \(90*(5 + sqrt(7))\)

For a full discussion of how to divide by radicals and radical expressions, as well as a complete solution to this particular problem, see this blog:
https://magoosh.com/gmat/2013/gmat-math- ... uare-root/

Mike :-)



My take::

keep the variable x on one side and move all the other terms to another side of equality.

thus we get 90/ 5+ root 7
now rationalize the denominator to get the answer choice A
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink] New post   26 Oct 2023, 08:38
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Re: x(x + 7^(1/2)) = 90. In the equation above, x = [#permalink]
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