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# If k is an integer, what is the value of k?

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Math Expert
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If k is an integer, what is the value of k?  [#permalink]

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24 Mar 2015, 04:44
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35% (medium)

Question Stats:

73% (01:51) correct 27% (01:40) wrong based on 143 sessions

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If k is an integer, what is the value of k?

(1) 1/5 < 1/(k - 1) < 1/2

(2) 3 < (k + 3)/2 < 5

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If k is an integer, what is the value of k?  [#permalink]

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Updated on: 24 Mar 2015, 09:04
Bunuel wrote:
If k is an integer, what is the value of k?

(1) 1/5 < 1/(k - 1) < 1/2

(2) 3 < (k + 3)/2 < 5

(1) 1/5 < 1/(k - 1) < 1/2
Since K is integer (k-1) will be an integer so there are two possible values
k-1=4; K=5
k-1=3; K=4
Not Sufficient.

(2) 3 < (k + 3)/2 < 5
(K+3)/2 , we can find multiple values of K from this inequality.
eg: (K+3)/2=3.5 so K = 4
(K+3)/2=4 so K = 5
(K+3)/2=4.5 so K = 6

Combining A and B , still insufficient.

Originally posted by Lucky2783 on 24 Mar 2015, 05:54.
Last edited by Lucky2783 on 24 Mar 2015, 09:04, edited 1 time in total.
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Re: If k is an integer, what is the value of k?  [#permalink]

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24 Mar 2015, 08:52
1

k has to be an integer so

(1) 1/5 < 1/(k-1) < 1/2

Then k = 5 or k = 4

1/5 < 1/4 < 1/2 -OR- 1/5 < 1/3 < 1/2

(2) 3 < (k + 3)/2 < 5

Then k = 4, k = 5, or k = 6

3 < 3.5 < 5 -OR- 3 < 4 < 5 -OR- 3 < 4.5 < 5

From (1) we know k is 5 or 4 and from (2) we know it's 4, 5, or 6 and therefore insufficient - E
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Re: If k is an integer, what is the value of k?  [#permalink]

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24 Mar 2015, 09:06
MechEGMAT wrote:

k has to be an integer so

(1) 1/5 < 1/(k-1) < 1/2

Then k = 5 or k = 4

1/5 < 1/4 < 1/2 -OR- 1/5 < 1/3 < 1/2

(2) 3 < (k + 3)/2 < 5

Then k = 4, k = 5, or k = 6

3 < 3.5 < 5 -OR- 3 < 4 < 5 -OR- 3 < 4.5 < 5

From (1) we know k is 5 or 4 and from (2) we know it's 4, 5, or 6 and therefore insufficient - E

Right .
i overlooked k as 4 and 3 when it is 5 and 4 actually.
k-1=4
k-1=3
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Re: If k is an integer, what is the value of k?  [#permalink]

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24 Mar 2015, 12:09
1
St 1:
1/5 <1/(k-1) < 1/2
therefore, 5>k-1>2
6>k>3 So k could be 4 or 5 as k is an integer. Not Sufficient.

St 2:
3 <(k+3)/2 < 5
therefore, 6 <(k+3) < 10
3<k < 7 So k could be 4 or 5 or 6 as k is an integer.Not Sufficient.

Ans: E
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Re: If k is an integer, what is the value of k?  [#permalink]

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24 Mar 2015, 19:26
1
Bunuel wrote:
If k is an integer, what is the value of k?

(1) 1/5 < 1/(k - 1) < 1/2

(2) 3 < (k + 3)/2 < 5

Statement 1:
1/5 < 1/4 < 1/2
1/5 < 1/3 < 1/2
k= 4 or 5
Insufficient

Statement 2:
k could be 4,5,6
Insufficient

Combined, still insufficient since k could be 4 or 5

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Re: If k is an integer, what is the value of k?  [#permalink]

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25 Mar 2015, 00:15
1
K is int, K=?

1. To satisfy this equation k can be 5 or 4, Not sufficient
2. To satisfy (K+3)/2 can be 3.5,4,4.5; so k can be 4,5,6, Not sufficient

1+2. K can still be 4 or 5 so not sufficient.

Thanks,
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Re: If k is an integer, what is the value of k?  [#permalink]

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30 Mar 2015, 04:28
Bunuel wrote:
If k is an integer, what is the value of k?

(1) 1/5 < 1/(k - 1) < 1/2

(2) 3 < (k + 3)/2 < 5

MAGOOSH OFFICIAL SOLUTION:
Attachment:

kwithinequalities_explanation.png [ 39.25 KiB | Viewed 1604 times ]

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Re: If k is an integer, what is the value of k?  [#permalink]

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24 Dec 2015, 15:11
agree on E.

1 -> k can be 4 or 5. not sufficient.
2 -> k can be 4,5, or 6. not sufficient.

1+2 - k can be 4 or 5. not sufficient.
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Re: If k is an integer, what is the value of k?  [#permalink]

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20 Dec 2017, 20:11
Bunuel niks18

How do we simplify St1 as in FightToSurvive approach ?

Quote:
St 1:
1/5 <1/(k-1) < 1/2
therefore, 5>k-1>2
6>k>3 So k could be 4 or 5 as k is an integer. Not Sufficient.

Can we simplify flip the ratios ? Or since numerator is same, we can associate denominators
with same inequality?
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Re: If k is an integer, what is the value of k?  [#permalink]

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25 Dec 2017, 09:28
Bunuel niks18

How do we simplify St1 as in FightToSurvive approach ?

Quote:
St 1:
1/5 <1/(k-1) < 1/2
therefore, 5>k-1>2
6>k>3 So k could be 4 or 5 as k is an integer. Not Sufficient.

Can we simplify flip the ratios ? Or since numerator is same, we can associate denominators
with same inequality?

here you can cross multiply the ratios because we know k-1>0 i.e positive. so on cross-multiplying sign will not be impacted.

so 1/(k-1)<1/2 =>k-1>2=>k>3

and 1/5<1/(k-1)=>k-1<5=>k<6

Or directly take the reciprocal and invert the inequality sign so 1/5<1/(k-1)<1/2 on reciprocating will become 5>k-1>2 =>6>k>3

All you need to realize is k-1 is positive here
Re: If k is an integer, what is the value of k?   [#permalink] 25 Dec 2017, 09:28
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