lheiannie07 wrote:If m is an integer greater than 9 but less than 20, is n greater than the average (arithmetic mean) of m and 20?
(1) n = 3m
(2) The distance on the number line between n and 20 is less than the distance on the number line between n and m.
I am confused in this, can some experts help me?
OA D
We have 9 < m < 20.
We have to determine whether n > (m + 20)/2.
(1) n = 3m
Case 1: The minimum value of m = 10, thus at m = 10, n = 30.
Thus, n > (m + 20)/2 => 30 ? (10 + 20)/2 => 30 > 15. The answer is Yes.
Case 1: The maxmum value of m = 19, thus at m = 19, n = 57.
Thus, n > (m + 20)/2 => 57 ? (19 + 20)/2 => 57 > 19.5. The answer is Yes.
Sufficient.
(2) The distance on the number line between n and 20 is less than the distance on the number line between n and m.
Case 1: The minimum value of m = 10.
Thus, the distance on the number line between n and 20 = |n - 20|; the distance on the number line between n and m (= 10) = |n - 10|.
We have |n - 20| < |n - 10|.
=> n - 20 < n - 10. Since n vanished, let's ignore this.
|n - 20| < |n - 10| can also mean n - 20 > 10 - n => 2n > 30 => n > 15
We see that m = 10 and n = 15.1 (a littel greater than 15), n > (m + 20)/2. Let's check it. n > (m + 20)/2 => 15.1 ? (10 + 20)/2 => 15.1 > 15. The answer is Yes.
Case 2: The maximum value of m = 19.
Thus, the distance on the number line between n and 20 = |n - 20|; the distance on the number line between n and m (= 19) = |n - 19|.
We have |n - 20| < |n - 19|.
=> n - 20 < n - 19. Since n vanished, let's ignore this.
|n - 20| < |n - 19| can also mean n - 20 > 19 - n => 2n > 39 => n > 19.5
We see that m = 19 and n = 19.51 (a littel greater than 19.5), n > (m + 20)/2. Let's check it. n > (m + 20)/2 => 19.51 ? (19 + 20)/2 => 19.51 > 19.5. The answer is Yes.
Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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