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James' age is between that of Gwen and Lucille and Is closer

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James' age is between that of Gwen and Lucille and Is closer [#permalink] New post 03 Jun 2020, 05:47
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James' age is between that of Gwen and Lucille and is closer to Gwen's age than to Lucille's. Gwen is between 30 and 40 years old, inclusive. Lucille is less than 70 years old, and her age In years has exactly three prime factors. Which of the following could be James' age, in years?


Indicate all such ages.


❑ 15

❑ 18

❑ 22

❑ 37

❑ 42

❑ 52

❑ 65
[Reveal] Spoiler: OA

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Re: James' age is between that of Gwen and Lucille and Is closer [#permalink] New post 03 Jun 2020, 05:48
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Re: James' age is between that of Gwen and Lucille and Is closer [#permalink] New post 03 Jun 2020, 20:32
How can be answer 22, if the problem states that James age is between Gwen and Lucille's?
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Re: James' age is between that of Gwen and Lucille and Is closer [#permalink] New post 05 Jun 2020, 09:23
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James' age is minimized if both Gwen and Lucille's ages are minimized, making Lucille the youngest and Gwen the oldest. If Gwen is 30 and Lucille is 8, James is closer in age to Gwen if he is more than \(\frac{30+8}{2} =19\) years old. James' age is maximized if both Gwen and Lucille's ages are maximized, making Lucille the oldest and Gwen the youngest. If Gwen is 40 and Lucille is 68, James is closer in age to Gwen if he is less than \(\frac{40+68}{2}=54 \) years old. James must be between 19 and 54 years old (not inclusive, by the way, or else James could be the same difference in age with both Gwen and Lucille, not closer in age to Gwen as required).

The correct answers are 22, 37, 42, and 52.
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Re: James' age is between that of Gwen and Lucille and Is closer [#permalink] New post 24 Jun 2020, 22:35
@Carcass what I understand from this problem is that the tricky part is Lucille's age bracket is not mentioned except the limit that is less than 70. So Lucille could be between 1-69
The bracket of Gwen age is 30-40.
so we have to find max and min age.
if we take min age, say L=2 and G=30 so 30+2/2= 16
max age bracket, L=68 and G=40 so 68+40/2 = 108/2 = 54
Final age bracket we got is from 16 to 54

why we wont consider 18? Also why are you considering 22? if he more closer to age bracket 30-40 then both 18 and 22 should not be considered?
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Re: James' age is between that of Gwen and Lucille and Is closer   [#permalink] 24 Jun 2020, 22:35
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