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# If n is a positive integer, is the value of b a at least

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Director
Joined: 05 Feb 2006
Posts: 904
Followers: 1

Kudos [?]: 33 [0], given: 0

If n is a positive integer, is the value of b a at least [#permalink]  21 Sep 2006, 11:33
00:00

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(N/A)

Question Stats:

100% (01:08) correct 0% (00:00) wrong based on 1 sessions
If n is a positive integer, is the value of b â€“ a at least twice the value of 3^n â€“ 2^n?

1) a=2^n+1 and b=3^n+1
2) n=3
SVP
Joined: 01 May 2006
Posts: 1816
Followers: 8

Kudos [?]: 87 [0], given: 0

For me (A)

The question is : b â€“ a > 2*(3^n â€“ 2^n) (1) ? with n >0

Statment 1:
a=2^n+1 and b=3^n+1

o n=0 <=> b-a = 3^1 - 2^1 = 1 and 2*(3^0 â€“ 2^0) = 2*0 = 0, the equation (1) is verrified
o n=1 <=> b-a = 3^2 - 2^2 = 5 and 2*(3^1 â€“ 2^1) = 2*1 = 2, the equation (1) is verrified
o n=2 <=> b-a = 3^3 - 2^3 = 19 and 2*(3^2 â€“ 2^2) = 2*5 = 10, the equation (1) is verrified

and so on,

SUFF

Statment 2:

INSUFF

Last edited by Fig on 21 Sep 2006, 13:10, edited 1 time in total.
VP
Joined: 02 Jun 2006
Posts: 1270
Followers: 2

Kudos [?]: 36 [0], given: 0

S1:
b = 3^(n+1) = 3.3^n
a = 2^(n+1) = 2.2^n

b-a = 3.3^n - 2.2^n > 2.3^n - 2.2^n

or 3^n > 0

As n is +ve integer this is true for all n.
Sufficient.

S2: b-a > 38?
Not sufficient...

Senior Manager
Joined: 11 Jul 2006
Posts: 385
Location: TX
Followers: 1

Kudos [?]: 6 [0], given: 0

Going with A

(1)
Is it a=2^(n+1) and b=3^(n+1) ?
or a=2^n + 1 and b=3^n + 1

Assuming the latter
b=3^n + 1 (Eq 1)
a=2^n + 1 (Eq 2)

Eq1 - Eq2
b - a = (3^n + 1 ) - (2^n + 1 ) = 3^n - 2^n

(2) Insuff , no value for b and a.
SVP
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 70 [0], given: 39

If n is a positive integer, is the value of b â€“ a at least twice the value of 3^n â€“ 2^n?

1) a=2^n+1 and b=3^n+1
2) n=3

q:

is b-a>= 2(3^n- 2^n)

from one

3^n+1 - 2^n+1 > 2(3^n- 2^n)
3^n+1 - 2^n+1 > 2*3^n - 2^n+1

ie 3^n+1>2*3^n....n is positive intiger least value is = 1

thus 3^2 > 2*3......suff

from two
clearlu insuff

Director
Joined: 05 Feb 2006
Posts: 904
Followers: 1

Kudos [?]: 33 [0], given: 0

The OA is ............... A
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