VJesus12 wrote:For a lottery ticket, Emily chose six numbers that average to 10. Did more than half the numbers have 2 digits?
(1) One of the numbers was 10.
(2) Three of the numbers added up to 40.
The OA is E.
Experts, how can I conclude that each statement alone is not sufficient. May you help me?
We have the average of six numbers = 10, thus the sum of the six numbers = 60.
(1) One of the numbers was 10.
Case 1: Say the six numbers are 10 each. The answer is yes, more than half the numbers have 2 digits.
Case 2: Say the six numbers are 50, 10, 0, 0, 0, 0. The answer is no, less than half the numbers have 2 digits.
Insufficient
(2) Three of the numbers added up to 40.
Since three of the numbers added up to 40, the other three numbers would add 60 - 40 = 20.
Case 1: Say the six numbers are [30, 10, 0], [20, 0, 0]. The answer is no, more than half the numbers do not have 2 digits.
Case 2: Say the six numbers are [17, 13, 10], [20, 0, 0]. The answer is yes, more than half the numbers have 2 digits.
Insufficient
(1) and (2) combined:
Cases discussed in Statement 2 are applicable here too. Thus, even after combining the two statements, we cannot conclude.
The correct answer:
E
Hope this helps!
-Jay
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