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Manager  P
Joined: 03 Mar 2018
Posts: 204
Every member of a local chess club is assigned one of two skill levels  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 24% (03:01) correct 76% (03:10) wrong based on 57 sessions

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Every member of a local chess club is assigned one of two skill levels: A or B. At the beginning of the month, there were 'a' level A members and 'b' level B members. The ratio of a to b was 5:4. At the end of the month, the ratio of level A members to level B members has changed to 7:8. If nobody left the club and no new members joined during the month, how many total members are in the club?

1) 49<a<79
2) 29<b<59

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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1417
Location: India
Every member of a local chess club is assigned one of two skill levels  [#permalink]

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itisSheldon wrote:
Every member of a local chess club is assigned one of two skill levels: A or B. At the beginning of the month, there were 'a' level A members and 'b' level B members. The ratio of a to b was 5:4. At the end of the month, the ratio of level A members to level B members has changed to 7:8. If nobody left the club and no new members joined during the month, how many total members are in the club?

1) 49<a<79
2) 29<b<59

Total number of A and B level people is not changing here, while the individual values of A level people and B level people are definitely changing. Since 5+4 = 9 and 7+8 = 15, lets assume the total members to be 45x (because 45 is LCM of 9 and 15).

Initially, number of A level members = 5/9 * 45x = 25x, and number of B level members = 4/9 * 45x = 20x
At the end of month, number of A level members = 7/15 * 45x = 21x, and number of B level members = 8/15 * 45x = 24x.

We need to find the value of 45x, or if we can get x we have the answer.

(1) Given 25x lies between 49 and 79. But there are two possibilities; x can be 2, which makes 25x as 50 or x can be 3 which makes 25x as 75. Thus there is no unique answer here. Not sufficient.

(2) 20x lies between 29 and 59. Only multiple of 20 lying between 29 and 59 is 40, that means x can only be 2. Sufficient.

Intern  S
Joined: 12 Jul 2017
Posts: 33
Re: Every member of a local chess club is assigned one of two skill levels  [#permalink]

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Since no one left and there are no newcomers then there must've been a redistribution of members and since the ratio of a:b decreased (5:4 to 7:8) then some people left A to join B leading us to:
a/b=5/4 (a-x)/(b+x)=7/8 => b=5x and a=(25/4)x. b must be a multiple of 5 and x must be a multiple of 4 leading to "a" being a multiple of 25. To summarize we have b=5x and a=(25/4)*4k=25k
1) for k=2 and k=3, a=50 and 75 respectively. Not sufficient.
2) b is multiple of 5 thus leading us to the following values: 30, 35, 40, 45, 50, 55. Also a=5/4*b meaning b must also be a multiple of 4. Among the values only 4 is both a multiple of 4 and 5. Answer (B). Re: Every member of a local chess club is assigned one of two skill levels   [#permalink] 29 May 2018, 07:18
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