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I'm getting answer choice E.

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
Answer E.
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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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Bunuel
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

Answer: E
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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.
Hence answer is E

Thanks,
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Bunuel
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
kwithinequalities_explanation.png [ 39.25 KiB | Viewed 4841 times ]
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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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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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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?

Hi adkikani,

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
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