Is there a faster way to answer this GMAT question?

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SBronson: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Jun 18, 2013 7:48 amFollowed by: 1 member

by SBronson » Tue Jun 18, 2013 10:02 pm

There's gotta be a faster way to answer this question? Can anyone help?

117. If n is positive, which of the following is equal to:

1/(Rad (n+1)âˆ’ Rad n)?
(A) 1
(B) Rad (2n+1)
(C) Rad (n+1)/Rad n
(D) Rad (n+1) âˆ’ rad n
(E) Rad (n+1) + Rad n

The official guide explanation is about half a page long.

Thanks!

-Samantha

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Source: Beat The GMAT — Problem Solving | Tue Jun 18, 2013 10:02 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 18, 2013 11:54 pm

Let n = 2.
Then:
1/(âˆšn+1 - âˆšn) = 1/(âˆš3-âˆš2) â‰ˆ 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:
âˆš(n+1) + âˆšn = âˆš3+âˆš2 â‰ˆ 1.7 + 1.4 = 3.1.

The correct answer is E.

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Raj700: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon Jun 17, 2013 11:02 pm

by Raj700 » Wed Jun 19, 2013 5:38 am

Nice! Thank you Mitch. That's so much easier. It certainly helps though to have rad 2 and rad 3 memorized.

-Raj

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Ashke: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Feb 18, 2013 4:40 pm

by Ashke » Wed Jun 19, 2013 8:11 am

1/(Rad (n+1)- Rad n)

= (Rad (n+1)+ Rad n)/((Rad (n+1)- Rad n))*(Rad (n+1)+ Rad n))

= (Rad (n+1)+ Rad n)

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fcabanski: Master | Next Rank: 500 Posts; Posts: 104; Joined: Fri Oct 07, 2011 10:23 pmFollowed by: 4 members; Thanked: 36 times

by fcabanski » Wed Jun 19, 2013 10:41 pm

Here's an even faster answer:

"OnlyEworks"

Seriously, though, plugging in is often faster than working the algebra. But if you remember how to rationalize the denominator, as Ashke showed, the algebra on this one takes about 10 seconds.

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