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16 Sep 2014, 00:34
Kudos
Bookmarks
In a conference room, there are a total of 45 chairs, which can be either metal or wooden. Out of these chairs, 14 are reclining chairs and 10 of the reclining chairs are wooden. If 20% of the metal chairs are reclining, what is the number of non-reclining wooden chairs in the conference room?
A. 31
B. 25
C. 15
D. 14
E. 10
A. 31
B. 25
C. 15
D. 14
E. 10
16 Sep 2014, 00:34
Kudos
Bookmarks
Official Solution:
In a conference room, there are a total of 45 chairs, which can be either metal or wooden. Out of these chairs, 14 are reclining chairs and 10 of the reclining chairs are wooden. If 20% of the metal chairs are reclining, what is the number of non-reclining wooden chairs in the conference room?
A. 31
B. 25
C. 15
D. 14
E. 10
We have the following information:
• There are 45 chairs in total.
• 14 are reclining chairs.
• 10 of the reclining chairs are wooden.
• 20% of the metal chairs are reclining.
Since 10 out of the 14 reclining chairs are wooden, the remaining 4 reclining chairs must be metal.
Since these 4 reclining metal chairs represent 20% of all metal chairs, we can find that the total number of metal chairs is 20 (4 is 20% of 20).
Therefore, the number of wooden chairs is 45 - 20 = 25.
Finally, since out of these 25 wooden chairs 10 are also reclining, the remaining 15 chairs are non-reclining wooden chairs.
Answer: C
In a conference room, there are a total of 45 chairs, which can be either metal or wooden. Out of these chairs, 14 are reclining chairs and 10 of the reclining chairs are wooden. If 20% of the metal chairs are reclining, what is the number of non-reclining wooden chairs in the conference room?
A. 31
B. 25
C. 15
D. 14
E. 10
We have the following information:
• There are 45 chairs in total.
• 14 are reclining chairs.
• 10 of the reclining chairs are wooden.
• 20% of the metal chairs are reclining.
Since 10 out of the 14 reclining chairs are wooden, the remaining 4 reclining chairs must be metal.
Since these 4 reclining metal chairs represent 20% of all metal chairs, we can find that the total number of metal chairs is 20 (4 is 20% of 20).
Therefore, the number of wooden chairs is 45 - 20 = 25.
Finally, since out of these 25 wooden chairs 10 are also reclining, the remaining 15 chairs are non-reclining wooden chairs.
Answer: C
09 Nov 2019, 12:39
Kudos
Bookmarks
This problem is easily solved using the table method:
From the prompt:
__________l_Metal_l_Wood_l_Total_
Recline____l__.2M__l__10__l__14__
No Recline_l_______l___*__l______
Total______l___M__l______l___45_
We're asked to find the number of wood, non-reclining chairs (indicated by a star in the table above)
We can subtract 10 wood reclining chairs from the total of 14 reclining chairs to get 4 metal reclining chairs. Since 20% of the total metal chairs recline, the total number of metal chairs is 20:
.2M=4
M=20
__________l_Metal_l_Wood_l_Total_
Recline____l_.2M=4_l__10__l__14__
No Recline_l_______l___*__l______
Total______l_M=20_l______l___45_
We can now subtract 20 metal chairs from 45 total chairs to get 25 wood chairs:
45-20=25
And we can subtract the 10 wood reclining chairs from the 25 total wood chairs to get 15 wood, non-reclining chairs:
25-10=15
__________l_Metal_l_Wood_l_Total_
Recline____l_.2M=4_l__10__l__14__
No Recline_l_______l__15__l______
Total______l_M=20_l__25__l___45_
The correct answer is (C).
From the prompt:
__________l_Metal_l_Wood_l_Total_
Recline____l__.2M__l__10__l__14__
No Recline_l_______l___*__l______
Total______l___M__l______l___45_
We're asked to find the number of wood, non-reclining chairs (indicated by a star in the table above)
We can subtract 10 wood reclining chairs from the total of 14 reclining chairs to get 4 metal reclining chairs. Since 20% of the total metal chairs recline, the total number of metal chairs is 20:
.2M=4
M=20
__________l_Metal_l_Wood_l_Total_
Recline____l_.2M=4_l__10__l__14__
No Recline_l_______l___*__l______
Total______l_M=20_l______l___45_
We can now subtract 20 metal chairs from 45 total chairs to get 25 wood chairs:
45-20=25
And we can subtract the 10 wood reclining chairs from the 25 total wood chairs to get 15 wood, non-reclining chairs:
25-10=15
__________l_Metal_l_Wood_l_Total_
Recline____l_.2M=4_l__10__l__14__
No Recline_l_______l__15__l______
Total______l_M=20_l__25__l___45_
The correct answer is (C).
