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01 Feb 2022, 02:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
51% (02:13) correct
49%
(02:01)
wrong
based on 147
sessions
History
Date
Time
Result
Not Attempted Yet
The average of five number is 16. Is the sum of the two largest numbers in the set greater than 34?
(1) The largest number in the set is greater than 20.
(2) The median of the set is 16.
(1) The largest number in the set is greater than 20.
(2) The median of the set is 16.
01 Feb 2022, 03:07
Kudos
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Pre-thinking
Sum of the five numbers are 16 * 5 = 80.
(1) Only
It is possible that the sum of the two largest numbers in the set greater than 34. Say, 20.01+19 = 39.01. The other three numbers add up to 80-39.01=40.99. So they can be 13, 13.99, 14.
Now, is it possible for the sum of the two largest numbers smaller than or equal to 34? Let's try 20.01+13.99=34. The other three numbers add up to 80-34 = 46. But 46/3>15, which means at least one number should be larger than 15, which is > 13.99. So, it is not possible for the sum of the two largest numbers to be smaller than or equal to 34.
We can definitely answer the question. The answer is "Yes". (1) is sufficient.
(2) Only
In 16, 16, 16, 16, 16, the sum of the two largest numbers in the set is 32 < 34.
In 14, 15, 16, 17, 18, the sum of the two largest numbers in the set is 35 > 34. (The sum of the two largest numbers can be much higher: 100, 1000, 100000, etc.)
Not sufficient.
The answer is (A).
Sum of the five numbers are 16 * 5 = 80.
(1) Only
It is possible that the sum of the two largest numbers in the set greater than 34. Say, 20.01+19 = 39.01. The other three numbers add up to 80-39.01=40.99. So they can be 13, 13.99, 14.
Now, is it possible for the sum of the two largest numbers smaller than or equal to 34? Let's try 20.01+13.99=34. The other three numbers add up to 80-34 = 46. But 46/3>15, which means at least one number should be larger than 15, which is > 13.99. So, it is not possible for the sum of the two largest numbers to be smaller than or equal to 34.
We can definitely answer the question. The answer is "Yes". (1) is sufficient.
(2) Only
In 16, 16, 16, 16, 16, the sum of the two largest numbers in the set is 32 < 34.
In 14, 15, 16, 17, 18, the sum of the two largest numbers in the set is 35 > 34. (The sum of the two largest numbers can be much higher: 100, 1000, 100000, etc.)
Not sufficient.
The answer is (A).
01 Feb 2022, 08:24
Kudos
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Bunuel
1) If average is 16 and largest number is greater than 20. Then, in worst case scenario the 2nd largest number will be 15. 20+15 = 35. So it will be greater than 34. Sufficient.
2) The median is 16. It is possible that all numbers are 16. Then, sum of two largest numbers will be 32.
Another scenario can be where smallest two numbers are 0. then largest two numbers will be 32 and 32. So, Sum will be 64.
Thus Insufficient.
Answer. A
