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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Fri Jan 28, 2022 11:48 am

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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

Source: GMAT Prep

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 28, 2022 11:48 am

swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: In a recent survey, twenty families reported their incomes for $1995.$ Was the range of reported $1995$ incomes

by swerve » Fri Jan 28, 2022 12:41 pm

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

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