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27 Oct 2018, 22:31
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E
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Question Stats:
47% (02:18) correct
53%
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If x, y, a, and b are positive integers less than 20, is the average of x and y greater than the average of a and b?
1) x = 3a
2) The range of x and y> the range of a and b.
1) x = 3a
2) The range of x and y> the range of a and b.
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28 Oct 2018, 04:58
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Question whether \(\frac{x+y}{2} > \frac{a+b}{2}\)
From statement 1:
x = 3a.
Clearly no info about y and b. Insufficient.
From statement 2:
Range of x & y > Range of a & b.
A range is just the difference between x and y or between a and b.
If x = 3 and y = 5. and if a = 18 and b =19.
Range of x&y > Range of a&b. But the average of x&y < a&b.
If x = 19 and y = 17. and a = 3 and b = 2.
Range of x&y > Range of a&b. And also the average of x&y > a&b.
Insufficient.
Combining also gives no extra info.
E is the answer.
From statement 1:
x = 3a.
Clearly no info about y and b. Insufficient.
From statement 2:
Range of x & y > Range of a & b.
A range is just the difference between x and y or between a and b.
If x = 3 and y = 5. and if a = 18 and b =19.
Range of x&y > Range of a&b. But the average of x&y < a&b.
If x = 19 and y = 17. and a = 3 and b = 2.
Range of x&y > Range of a&b. And also the average of x&y > a&b.
Insufficient.
Combining also gives no extra info.
E is the answer.
28 Oct 2018, 18:28
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Wouldn't combining both A and B give us the required info to solve this question.
It is given that (y-x) > (b-a) and x = 3a
-> y-3a > b-a
-> y> b+2a
for (y+x)/2 > (b+2a+3a)/2
-> (y+x)/2 > (b+5a)/2 > (b+a)/2
It is given that (y-x) > (b-a) and x = 3a
-> y-3a > b-a
-> y> b+2a
for (y+x)/2 > (b+2a+3a)/2
-> (y+x)/2 > (b+5a)/2 > (b+a)/2
