In a recent survey, twenty families reported their incomes for \(1995.\) Was the range of reported \(1995\) incomes for

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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 \(\$95,000.\)

Answer: E

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Gmat_mission wrote:
Fri Jan 28, 2022 11:48 am
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 \(\$95,000.\)

Answer: E

Source: GMAT Prep
Statement 1 is insufficient as it only provides the lower bound.
Statement 2 is insufficient as it only provides the upper bound.

Now let's combine both statements, and try the 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 \(= 94,000 - 21,000 = 73,000.\)

In case 1, the range is less than \(60,000\) and in case 2 the range is greater than \(60,000.\)

Therefore, E