f is defined by f (n) = k a^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 » Tue Jul 30, 2013 11:51 pm

For all integers n, the function f is defined by f (n) = k a^n where k and a are constants. What is the value of f (3)?

(1) f (0) = 5.

(2) f (2) = 20.

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Source: Beat The GMAT — Data Sufficiency | Tue Jul 30, 2013 11:51 pm

gmatsid: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Jun 21, 2013 2:46 am; Location: India; GMAT Score:740

by gmatsid » Wed Jul 31, 2013 1:33 am

The answer should be E in my opinion.

From the statement: f(n)=ka^n which gives us f(3)=ka^3 So you would need k and a.

Statement 1: f(0)=5=ka^0=k(1)=k.

So k=5, inputting in question stem, f(3)=5a^3
Hence INSUFFICIENT. Cross out options A AND D.

Statement 2: f(2)=ka^2=20 => ka^2=20.

Inputting in question stem, f(3)=ka^3 => f(3) =ka^2.a=20a
Still no value of a. Hence cross out options B.

Checking together, k=5 =>5.a^2=20 =>a^2=4=>a=+2,-2

Inputting in question stem, f(3)=5(2)^3=40 OR f(3)=5(-2)^3=-40

Since two distinct solutions possible, so no unique solution for the question stem. Hence cross out option C. Select E

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rajeshsinghgmat: Master | Next Rank: 500 Posts; Posts: 171; Joined: Tue Jan 08, 2013 7:24 am; Thanked: 1 times

by rajeshsinghgmat » Wed Jul 31, 2013 4:24 am

E

a^2-4=0

a=2,-2

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 31, 2013 6:24 am

sanju09 wrote:For all integers n, the function f is defined by f (n) = k a^n where k and a are constants. What is the value of f (3)?

(1) f (0) = 5.

(2) f (2) = 20.

Target question: What is the value of f(3)?

Given: f (n) = (k)(a^n)

Jump to . . .

Statements 1 and 2 combined:
So, f(0) = 5, and f(2) = 20
There are two sets of values that meet this condition. They are
Case a: a = 2, k = 5, in which case f(3) = (5)(2^3) = 40
Case b: a = -2, k = 5, in which case f(3) = (5)[(-2)^3] = -40
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = e

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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