Data Sufficiency

In a recent survey, twenty families reported their incomes for 1995. Was the range of reported 1995 incomes for these families greater than $60,000?

1) Thirteen of the reported incomes were between $20,000 and $35,000.

2) Seven of the reported incomes were between $80,000 and $95,000.

I had C

Original answer is E

Can someone explain why?

lazarogb wrote:In a recent survey, twenty families reported their incomes for 1995. Was the range of reported 1995 incomes for these families greater than $60,000?

1) Thirteen of the reported incomes were between $20,000 and $35,000.

2) Seven of the reported incomes were between $80,000 and $95,000.

I had C

Original answer is E

Can someone explain why?

Try EXTREMES.

Case 1: 13 incomes of 34,000 and 7 incomes of 81,000
Range = 81,000 - 34,000 = 47,000.

Case 2: 13 incomes of 21,000 and 7 incomes of 94,000
Range = 94,000 - 21,000 = 73,000.

Since in the first case the range is less than 60,000, and in the second case the range is greater than 60,000, the two statements combined are INSUFFICIENT.

The correct answer is E.

Hi Mitch,

I got your point about the extremes and understood the explanation.

But I had a few questions:

1. When the question says the range is between 20K and 35K, aren't we supposed to assume that at least one family has an income of 20K and at least one family has income of 35K?

2. Is it not necessary for the range to actually include those extreme values or is it just sufficient for all the 13 values to be in that range - for that matter all could be 30K? I assumed F1 = 20K, F13 = 35K, all others within this range but irrelevant

Could you please clarify? Just wanted to be crystal clear about this.
Thanks in advance...

Thanks T.

That's true. The statements don't specify the incomes to be in a "range", just that they are between x and y.

Another lesson "read the question and given information carefully"!

See image.

Read other explanation before leaving this link!!

Hi,

Could someone help to explain this one, if the information given were
(1) Thirteen of the reported incomes were FROM $20,000 TO $35,000.
could we infer that in this group, there were at least one family whose income was exactly $20,000 and at least one family whose income was exactly $35,000? I mean will the meaning change if we use "FROM .. TO.." instead of "BETWEEN.. AND.." in this context?

Thanks for response

thuyduong91vnu wrote:Hi,

Could someone help to explain this one, if the information given were
(1) Thirteen of the reported incomes were FROM $20,000 TO $35,000.
could we infer that in this group, there were at least one family whose income was exactly $20,000 and at least one family whose income was exactly $35,000? I mean will the meaning change if we use "FROM .. TO.." instead of "BETWEEN.. AND.." in this context?

Thanks for response

Not necessarily. Between 20 and 35 would be 20 < all incomes < 35, and "from 20 to 35" would be 20 ≤ all incomes ≤ 35.

You're on the right track, though! 20 ≤ x means that x COULD be 20, while 20 < x means that x CANNOT be 20. So incomes of $20,000 and $35,000 become possible, though not necessary.