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cloudz9
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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 02:08
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A total of 70 chairs are currently placed in a room, in rows (each row has an equal number of chairs). In order to accomodate for new equipment, 2 chairs are removed from the end of each row and are placed at the back of room, creating 4 new rows. All 70 chairs are once again in equal-sized rows. How many rows had the chairs originally been placed in?

A) 5
B) 6
C) 7
D) 10
E) 14



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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 04:52
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i think it is D

70=Rows*Chairs
70=(Rows+4)(Chairs-2)

10 rows 7 chairs

14 rows 5 chairs
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rxs0005
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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 05:32
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oops my bad its 10 rows with 7 chairs in each row
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ashkg
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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 11:40
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R rows N seats

1. RN = 70
2. (R+4)(N-2) = 70

simplifying

2N-R = 4

Now N,R can take only following values. 2,5,7.

The only values of N,R that fits this equation is 7,10.
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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 18:28
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cloudz9
A total of 70 chairs are currently placed in a room, in rows (each row has an equal number of chairs). In order to accomodate for new equipment, 2 chairs are removed from the end of each row and are placed at the back of room, creating 4 new rows. All 70 chairs are once again in equal-sized rows. How many rows had the chairs originally been placed in?

A) 5
B) 6
C) 7
D) 10
E) 14
Show more


70 = 2*5*7

possible # of rows 1,2,5,7,10,14,35,70

B) is out

A) 5 rows of 14 => 5X12 + 5X2 = 5X12 + 10 => out
C) 7 rows of 10 => 7X8 + 7X2 = 7X8 + 14 => out
D) 10 rows of 7 => 10X5 + 10X2 => correct
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HIMALAYA
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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 19:29
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cloudz9
A total of 70 chairs are currently placed in a room, in rows (each row has an equal number of chairs). In order to accomodate for new equipment, 2 chairs are removed from the end of each row and are placed at the back of room, creating 4 new rows. All 70 chairs are once again in equal-sized rows. How many rows had the chairs originally been placed in?

A) 5
B) 6
C) 7
D) 10
E) 14
Show more


imo, the best approach to the question like this is POE:

Using POE, we can easily find that the answer is 10 rows of 7 charirs in each row. after taking out 2 from each, there are 20 chairs and are sufficient to creat 4 more rows, each with 5 chairs.
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cloudz9
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A total of 70 chairs are currently placed in a room, in rows 07 Jun 2005, 21:50
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10 Rows is correct! :)
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HongHu
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A total of 70 chairs are currently placed in a room, in rows 09 Jun 2005, 23:33
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You could also think this way if you don't want to write any algebra equations

70=2*5*7
seat>2
seat=5 or seat=7
row=14 or row=10

3*18<>70
5*14=10

So take solution set two.
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krisrini
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A total of 70 chairs are currently placed in a room, in rows 10 Jun 2005, 03:21
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cloudz9
A total of 70 chairs are currently placed in a room, in rows (each row has an equal number of chairs). In order to accomodate for new equipment, 2 chairs are removed from the end of each row and are placed at the back of room, creating 4 new rows. All 70 chairs are once again in equal-sized rows. How many rows had the chairs originally been placed in?

A) 5
B) 6
C) 7
D) 10
E) 14
Show more


I fit in the answer choices to get the answer D



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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