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by GmatKiss » Sat Oct 15, 2011 2:32 pm
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

OA: 4
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by n@resh » Sat Oct 15, 2011 4:05 pm
GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

OA: 4
cook / waiter = 3/13 and cook / waiter + 12 = 3/16
solve it waiter, you endup 52 and cooks 12.
Hence D!
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by GMATGuruNY » Sat Oct 15, 2011 7:24 pm
GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

OA: 4
Here's an efficient non-algebraic approach:

The original ratio of cooks to waiters = 3:13, so the original number of waiters is a multiple of 13:
13,26,39,52,65...

When 12 waiters are added, the new ratio = 3:16, so the increased number of waiters is a multiple of 16:
16,32,48,64,80...

The values in red are 12 apart.
Thus, the original number of waiters = 52.
Since 3:13 = 12:52, the original number of cooks = 12.

The correct answer is D.
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by Abhishek009 » Sun Oct 16, 2011 3:36 am
GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

OA: 4
Cooks to the number of waiters is 3 to 13

c/w = 3a/13a { Let a be the common factor }

When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16

So , 3a/(13a + 12 ) = 3/16

So, 48a = 39a + 36

Or , 9a = 36

So , a = 4


We know , c/w = 3a/13a

So total number of cooks is 3*4 => 12
Abhishek
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by HeyArnold » Sun Oct 16, 2011 6:23 am
Use the unknown variable here, since it's a ratio...

Cooks: 3x
Waiters: 13x

so if you add 12 waiters then...

3x / (13x + 12) = 3 / 16

Cross multiply

3(13x + 12) = 3x(16)

39x + 36 = 48x

36 = 9x

x = 4, plugging back into 3x = 3(4) = 12
Answer is [spoiler]D
[/spoiler]
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by saketk » Mon Oct 17, 2011 9:44 pm
GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

OA: 4
C/w = 3/13

this means C = 3x and W= 13x

now the new count of W = 13x+12

the corresponding ratio is

3x/(13x+12) = (3/16)
48x = 39x+36
this gives x= 4

So the number of Cooks = 4*3 = 12

Option D
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