Each of the dinners served at a banquet was either chicken or beef or

Question

Each of the dinners served at a banquet was either chicken or beef or fish. The ratio of the number of chicken dinners to the number of beef dinners to the number of fish dinners served at the banquet was 7:5:2, respectively. If there were more than 5 fish dinners served at the banquet, what was the total number of dinners served at the banquet ?

(1) The total number of beef dinners and fish dinners served at the banquet was less than 30.
(2) The number of chicken dinners served at the banquet was less than 25.

AntrikshR · Answer

C:B:F ::: 7k:5k:2k
Total dinners: 14k where k is a positive integer.
14k = ?
Given: 2k>5 or k>2.5
1) Beef+fish = 7k
7k<30
=>k<4.2 and we know k>2.5
=> k = 3 or 4
Not sufficient.
2) 7k<25
=>k<3.5 and we know k>2.5
=> k = 3
=> 14k = 52 dinners sufficient.
B) IMO

IanStewart · Answer

The ratio of chicken to beef to fish is 7 to 5 to 2. Notice then that the number of chicken dishes equals the total number of beef and fish dishes, so Statement 2 is a stronger restriction (and thus gives more information) than Statement 1 -- the answer could never be A or C.

We have 7x chicken, 5x beef and 2x fish dishes, where x must be an integer. If more than 5 fish dishes were served, then x is at least 3. Statement 1 tells us that 7x is less than 30, so x can be 3 or 4. Statement 2 tells us 7x is less than 25, so x must be 3, and Statement 2 is sufficient alone.

alwaysHP · Answer

Each of the dinners served at a banquet was either chicken or beef or fish. The ratio of the number of chicken dinners to the number of beef dinners to the number of fish dinners served at the banquet was 7:5:2, respectively. If there were more than 5 fish dinners served at the banquet, what was the total number of dinners served at the banquet ?

(1) The total number of beef dinners and fish dinners served at the banquet was less than 30.
5x+2x<30
7x<30
 X= cannot be 1 or 2 as more than 5 fish dinners served but it can be 3, 4... 
  hence incorrect
(2) The number of chicken dinners served at the banquet was less than 25.
 
7x= 25
X cannot be 1 or 2 as more than 5 fish dinners served
But can be 3. 
Only one value is possible which is 7*3= 21 
hence we can get other values as 5*3 & 2*3

Its B

MBAB123 · Answer

Bunuel , this is a GMAT prep question.

Bunuel · Answer

_____________________
Added the tag. Thank you!

Equanimity · Answer

Why should k be an integer here?? All the answers mentioned are considering this. Not sure how this is arrived at! 7k,5k,2k should be integers, not k itself, right?

Bunuel  , Please help here!

Bunuel · Answer

The ratio of the number of chicken dinners to beef dinners to fish dinners served at the banquet was 7:5:2, respectively. This implies C : B : F = 7k : 5k : 2k, for some positive integer k. Hence, for the values of k from 1 onwards, we get all possible values of C, B, and F:

C : B : F = 7k : 5k : 2k = 7 : 5 : 2 = 14 : 10 : 4 = 21 : 15 : 6, and so on.

This is a standard method for expressing ratios that yield integer values.

bumpbot · Answer

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Each of the dinners served at a banquet was either chicken or beef or

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