a value of f (n)

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jun 18, 2010 4:53 am

If f (n) = n + âˆšn, where n is a positive integer, which of the following would be a value of f (n)?

I. 5
II. 10
III. 12

(A) I, II and III
(B) I and III only
(C) II and III only
(D) III only
(E) None

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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Source: Beat The GMAT — Problem Solving | Fri Jun 18, 2010 4:53 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Fri Jun 18, 2010 5:04 am

n + sqrt(n) shud be an integer.
it will be an integer when sqrt(n) is integer.
so checking for n = 4, 9 , 16..

we get f(n) as 6,12,20...

so answer is 12 only.. D

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Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pmFollowed by: 17 members; Location: New York City; Thanked: 76 times; GMAT Score:770

by Rich@VeritasPrep » Fri Jun 18, 2010 5:16 am

Nice job, kvcpk!

Building on what kvcpk said, since sqrt(n) has to be an integer, that means n has to be a perfect square...

So one sneaky thing you could do is change the equation from f(n) = n + sqrt(n) to:

f(x^2) = x^2 + x

(where n = x^2 and x is a positive integer)

Factor:

f(x^2) = x(x+1)

Notice that x(x+1) denotes the product of two consecutive positive integers. It's easy to see now that the product couldn't be 5 or 10, because no two positive consecutive integers give you those values when multiplied.

But 12 = 3*4, so that works.

Rich Zwelling
GMAT Instructor, Veritas Prep

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Fri Jun 18, 2010 5:23 am

sanju09 wrote:If f (n) = n + âˆšn, where n is a positive integer, which of the following would be a value of f (n)?

I. 5
II. 10
III. 12

(A) I, II and III
(B) I and III only
(C) II and III only
(D) III only
(E) None

lets take n as 4
then f(n) will be 6

let take n as 9
f(n) will be 12

here onwards value of fn will keep on increasing so only (D) III only satisy

Ideation without execution is delusion

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Fri Jun 18, 2010 5:24 am

Thats a kool trick Raz!!

Thanks for sharing!!

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