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# If n is an integer such that 1/6 < 1/(n-1) < 1/3, what

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Senior Manager
Joined: 22 Sep 2005
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If n is an integer such that 1/6 < 1/(n-1) < 1/3, what [#permalink]

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01 Nov 2006, 06:42
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If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of n?

1) (n-6) (n-7) = 0

2) -14>1-3n

Kudos [?]: 239 [0], given: 1

VP
Joined: 25 Jun 2006
Posts: 1161

Kudos [?]: 186 [0], given: 0

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01 Nov 2006, 06:58

1) plug in 6 and 7. u know 6 is the only one. Suff.

2) u get x > 5. from the stem, u get 4 < n < 7. so n can only be 6 here. Suff.

Kudos [?]: 186 [0], given: 0

Senior Manager
Joined: 05 Jun 2005
Posts: 448

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01 Nov 2006, 12:04
tennis_ball wrote:

1) plug in 6 and 7. u know 6 is the only one. Suff.

2) u get x > 5. from the stem, u get 4 < n < 7. so n can only be 6 here. Suff.

for the 2nd statement, can you please show the actual step of how you flipped it and got the range for n?

I know you manipulated it with 1. but just want to make sure that I get this.

thanks

Kudos [?]: 44 [0], given: 0

Manager
Joined: 29 Aug 2006
Posts: 156

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

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01 Nov 2006, 12:17
1/(n-1) >1/6
and
1/(n-1)<1/3

From 1) we know that n can be either 6 or 7, which means (n-1) is +ve

So from the question, we get n-1<6 adnd n-1>3
hence n<7 and n>4 , which means n=6

From 2) -14>1-3n
-14>-(3n-1)

Mutiplying both sides by -1 reverses the inequality sign
hence 3n-1>14
3n>15
n>5
from the question, we know that n<7 and n> 4
so n has to be 6.

Hence D

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SVP
Joined: 05 Jul 2006
Posts: 1742

Kudos [?]: 419 [0], given: 49

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01 Nov 2006, 14:23
If n is an integer such that 1/6 < 1/(n-1) < 1/3, what is the value of n?

1) (n-6) (n-7) = 0

2) -14>1-3n

REPHRASE

6>N-1>3

7>N>3 WHAT IS N? ( IT COULD BE 4,5,6)

FROM ONE N= 6....SUFF

FROM TWO

15<3N THUS N>5 THUS N= 6 SUFF , MY ANSWER IS D

Kudos [?]: 419 [0], given: 49

Director
Joined: 06 Sep 2006
Posts: 736

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01 Nov 2006, 14:32
From stem:
1/6 < 1/(n-1) ==> n-1 < 6 ==> n < 7
1/(n-1) < 1/3 ==> 3 < n-1 ==> n > 4

1) n = 7 or 6 ; n = 6 since n < 7 & a integer. Sufficient.
2) -14 > 1 - 3n ==> 3n > 15 ==> n > 5; n is integer and n < 7 so n = 6. Sufficient

D.

Kudos [?]: 49 [0], given: 0

VP
Joined: 25 Jun 2006
Posts: 1161

Kudos [?]: 186 [0], given: 0

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01 Nov 2006, 19:02
uvs_mba wrote:
tennis_ball wrote:

1) plug in 6 and 7. u know 6 is the only one. Suff.

2) u get x > 5. from the stem, u get 4 < n < 7. so n can only be 6 here. Suff.

for the 2nd statement, can you please show the actual step of how you flipped it and got the range for n?

I know you manipulated it with 1. but just want to make sure that I get this.

thanks

Priyah explained it well.

Kudos [?]: 186 [0], given: 0

01 Nov 2006, 19:02
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# If n is an integer such that 1/6 < 1/(n-1) < 1/3, what

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