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.



OAE

Please explain.

Needgmat 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.

Test 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.

The wording here is deceptive! "Between $20,000 and $35,000" doesn't necessarily mean that we had an income of exactly $20,000! They could have all been $34,050, for all we know.

Same issue with S2: everything could've been $80,001.

So on some level, all we can say is the range is greater than ($80,000 - $35,000), and less than ($95,000 - $20,000). But that doesn't give us our answer, so E.

This is a great Q, since it features the VERY EASY C. On test day, DO EVERYTHING YOU CAN TO AVOID THIS ANSWER! If C seems too obvious in DS, it is too obvious: it's probably the most common trap on the entire exam.