averages

[me]

if x and y are points on the number line, what is the value of x + y?

1. 6 is the halfway between x and y.

2. y=2x

got this from the GMAT software.

i answered C. can you explain why it's A and why you couldn't use many numbers for x and y to make A true?

thanks

[RonPurewal]

whenever you see a statement about AVERAGES (of which 'halfway' is one), you should automatically associate averages with SUMS. in other words, if you ever see a statement about an average, you should immediately translate that statement into the language of sums. to do so, just use the following equation:
average = sum / # of data points
or, equivalently,
sum = (average) x (# of data points)

statement (1):
this tells you that 6 is the average of x and y (or, (x + y)/2 = 6).
therefore,
sum of x + y = (average)(# of data points) = 6 x 2 = 12.
you can also do good old fashioned algebra to get this result: multiply both sides of (x + y)/2 = 6 by 2 to yield x + y = 12. in fact, that's probably easier on this problem, but it's important that you learn the average/sum formula so that you can apply it effortlessly to other situations (such as sums of 10, 20, or more numbers) on which an algebraic solution would be awkward or just plain impossible in a reasonable amount of time.

in any case, x + y = 12, so this is sufficient.

statement (2):
clearly insufficient by itself, since x and y could be huge (1 million and 2 million) or tiny (0.0001 and 0.0002).

--

in answer to your query about number plugging, yes, you could plug in numbers to your heart's content: 0 and 12, 3 and 9, 4 and 8, ... heck, even 6 and 6. in every case, you'd find that x + y = 12, so sooner or later you'd become convinced that the statement is sufficient.

[abedinbhuiyan]

draw a line in between!!

BR

[ChrisB]

Hi Abed,

Interesting strategy. What do you mean by drawing a line in between? In this problem we don't ever need to know what x and y are, and instead care about the sum, x + y. In that case it may be helpful to visualize 6 as marking the the halfway point between x and y but that may prove limiting.

For example, if x were to equal 5 and y were to equal 7 the midpoint would be 6 just as it would be if x=-100 and y = 112. In either case, the important take away is the sum, x+y.

Thanks,
Chris