Hi guys! This is my first post in my journey to beat the GMAT! Could you guys please help me understand the below question?
If N is positive, which of the following is equal to 1/(√N+1) - √N?
A. 1
B. (√2N)+1
C. (√N+1)/(√N)
D. (√N)+1-(√N)
E. (√N)+1+(√N)
I can solve most of the equation until I get to {(√N+1)+(√N)}/(N+1)-(√N). The answer is E,but I cannot understand/rationalize how the equation goes from {(√N+1)+(√N)}/(N+1)-(√N) to a result of (√N)+1+(√N). Thank you in advanced!!!
Best,
Jonna!
Power and roots confusion!!
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I have a question about the notation in your question.Jonna89 wrote:Hi guys! This is my first post in my journey to beat the GMAT! Could you guys please help me understand the below question?
If N is positive, which of the following is equal to 1/(√N+1) - √N?
A. 1
B. (√2N)+1
C. (√N+1)/(√N)
D. (√N)+1-(√N)
E. (√N)+1+(√N)
I can solve most of the equation until I get to {(√N+1)+(√N)}/(N+1)-(√N). The answer is E,but I cannot understand/rationalize how the equation goes from {(√N+1)+(√N)}/(N+1)-(√N) to a result of (√N)+1+(√N). Thank you in advanced!!!
Best,
Jonna!
You write 1/(√N+1).
Are we taking the square root of N or N+1?
If we're taking the square root of N+1, it should read: 1/√(N+1).
Cheers,
Brent
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Hi Jonna89,
Has the entire prompt (and the answer choices) been properly transcribed? If you can upload a picture of the original question (and answers), then that would probably make all of this easier.
GMAT assassins aren't born, they're made,
Rich
Has the entire prompt (and the answer choices) been properly transcribed? If you can upload a picture of the original question (and answers), then that would probably make all of this easier.
GMAT assassins aren't born, they're made,
Rich
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You just need to rationalize, by multiplying the numerator and denominator by (√(N+1) + √N) to get option E, as the denominator will be equal to 1 after rationalization i.e.
(√(N+1)-√N)(√(N+1)+√N)= N+1-N = 1.
(√(N+1)-√N)(√(N+1)+√N)= N+1-N = 1.
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Let n = 2.
Then:
1/(√n+1 - √n) = 1/(√3-√2) ≈ 1/(1.7 - 1.4) = 1/.3 = 10/3. This is our target.
Now plug n=2 into the answers to see which comes closest to our target of 10/3.
Only E works:
√(n+1) + √n = √3+√2 ≈ 1.7 + 1.4 = 3.1.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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Better late than never! Keep up the good work.Jonna89 wrote:Wow! That actually made so much sense! You guys are awesome!! Thank you! I wish I would have join the site earlier!!! Cheers!
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In mathematics, it's generally considered poor form to write fractions with roots in the denominator (although having roots in the numerator is acceptable). So, to eliminate the roots in the denominator, we must multiple both numerator and denominator by something that accomplishes this.
Here that something is (√(N+1) + √N).
Aside: (√(N+1) + √N) is known as the "conjugate" of (√(N+1) - √N)
Here's another question that tests this concept: https://www.beatthegmat.com/help-roots-q-t271220.html
Cheers,
Brent
Here that something is (√(N+1) + √N).
Aside: (√(N+1) + √N) is known as the "conjugate" of (√(N+1) - √N)
Here's another question that tests this concept: https://www.beatthegmat.com/help-roots-q-t271220.html
Cheers,
Brent