uptowngirl92 wrote:The average of three distinct positive integers x,y and z is 64.If a new number d is added,will the percent increase exceed 13%?
1. d is twice the value of one of the original numbers
2.d is half the value of the largest of the original numbers
[spoiler]Ans:d[/spoiler]
What's the source of this question? As written, it's unanswerable. "Percent increase" without reference is ambiguous; you have to have a percent increase of something specific.
In any case, no matter how you slice it, D certainly isn't the correct answer.
Let's use our secret bad question decoder rings and postulate that the question should read:
The average of three distinct positive integers x,y and z is 64. If a new number d is added to the set, will the average increase by more than 13%?
(1) d is twice the value of one of the original numbers
Picking numbers quickly shows us that (1) is insufficient. Let's choose extreme values (often a good strategy).
We know that x, y and z sum to 192 (sum = avg*# of terms), so let's pick 1, 2 and 189.
If d = 2 (nothing says that d must also be distinct), then our average actually goes down.
If d = 378, then our average more than doubles.
Therefore, the answer to the original question could be "yes" or "no"... insufficient.
(2) d is half the value of the largest of the original numbers
Again, let's look at the most extreme case.
If x, y and z are 1, 2 and 189, then d = 94.5 (nothing says d must be an integer). Our new sum is 192 + 94.5 = 286.5 and our new average is 286.5/4 = 71.625.
Is 71.625/64 > 1.13? What an annoying question! However, long division (we don't need to finish the problem, as soon as we see that the answer starts with 1.11 we know that it's going to be less than 1.13) shows us that the answer is "no".
So, we made d as big as we possibly could and we got a "no" answer. Smaller values of d will lead to a smaller increase. Therefore, the increase will NEVER be greater than 13%... sufficient.
(2) is sufficient, (1) is not: choose B.
