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14 Oct 2020, 00:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:09) correct
35%
(02:24)
wrong
based on 953
sessions
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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.
(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.
14 Oct 2020, 05:52
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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
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
General Discussion
14 Oct 2020, 07:30
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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.
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.
