A certain list consists of five different integers

[arielle.bertman]

A certain list consists of five different integers. Is the average o fthe two greatest integers in the list greater than 70?

(1) The median of the integers in the list is 70
(2) The average of the integers in the list is 70

OA:D

Can you explain the best way to prove stmnt 2 is sufficient. I quickly identified stmnt 1 as sufficient and then by selecting numbers that for stmnt 2, eventually figured it out but I think there must be a faster way.

Thanks!

[RonPurewal]

A certain list consists of five different integers. Is the average o fthe two greatest integers in the list greater than 70?

(1) The median of the integers in the list is 70
(2) The average of the integers in the list is 70

OA:D

Can you explain the best way to prove stmnt 2 is sufficient. I quickly identified stmnt 1 as sufficient and then by selecting numbers that for stmnt 2, eventually figured it out but I think there must be a faster way.

Thanks!

let's look at specific numbers. remember, when you pick numbers, you should TRY FOR INSUFFICIENT.
since this is a yes/no question, that means that you should try to get at least one "yes" and at least one "no".

it's easy to get a "yes": just take any equally spaced list, such as
68 69 70 71 72
or
50 60 70 80 90

so we're trying to get a "no".
* if we can find a list of 5 different numbers whose average is 70, and whose HIGHEST two numbers average 70 or less, then, insufficient.
* if we can't, then, sufficient.

let's try to find such a list.
since the average is 70, the sum must be 350.
now remember, the average of the HIGHEST two numbers must be 70 or less to get a "no".
this means that:
- the sum of those two numbers is 140 or less, AND
- the lower of the two (i.e., the second-highest number out of the five) is LESS than 70.
...but then the three other numbers, which are even lower, are also less than 70 each.
so we have (at most 140) + 3*(less than 70)
this is less than 350. that's a contradiction (the sum is supposed to be 350), so there can be no such set.

therefore, SUFFICIENT

--

you can build a similar argument with "overs" and "unders" (see the mgmat strategy guide, word translations, chapter on statistics, for more on this).

--

finally, note that the condition stipulating that the numbers be DIFFERENT is crucially important.
if you remove that condition, then the answer goes all the way to (e), since you can now use the set 70, 70, 70, 70, 70 to achieve a "no" even with both statements.

[NinaP494]

every once in a while in seemingly easy questions like these I keep forgetting conditions in the question stem. in this question I forgot by the time I was in st2 that the number should be different and thought that the avg for the two greatest numbers could be equal to 70 also {70,70,70,70,70} any suggestions to avoid such silly mistakes? thanks

[RonPurewal]

if you forget stated conditions, there are two ways to go about fixing that.

1/
SLOW DOWN.

2/
WRITE DOWN the conditions on your scratch paper, where you will see them.

that's really it. "SLOW DOWN" is so important that perhaps there should be 3 numbered points, of which both #1 and #2 are "SLOW DOWN".