DavidTutorexamPAL wrote:
The Logical approach to this question will use the logic behind average.
Statement (1) tells us that the median is 70, which means that (since the integers are all different from one another) the two largest number are each larger than 70, and thus their average is also larger than 70. That's enough information!
Statement (2) tells us that the average is 70. Imagine that all numbers were 70. Now, even in the extreme example that the smaller for of them are negative, the largest one must 'make up for the deficit' of the others. Thus, the average of the two larger ones must be larger than 70.
And if this is too theoretical to grasp, using extreme numeric examples can help: 68,69,70,71,72 vs. -100,-90,-80,-70,410. In both cases the average is 70, but the smaller the second largest number, the greater the largest one, and their average only becomes further from 70.
So the second statement is also enough on its own.
The correct answer is (D).
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Hi David,
Tiny doubt regarding statement 2. Say we start from all the 5 numbers being equal to 70, in that case the average of the 2 greatest integers in the set be equal to 70 and not greater. The other values that could be assigned to the integers within the constraints of the statement would give us an average greater than 70 for the greatest two digits. Wouldn't that render statement 2 insufficient? Considering there are two possibilities and the question specifically asks for an average greater than 70.