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Apartment Carpeting

GMAT-N25DEL

An apartment building has 25 floors with four apartments on each floor. The landlord wants to install new carpeting in twelve apartments to see how well the new​ carpet resists stains and tearing before he decides whether to replace the carpet in the entire building.

The following table shows the four apartments on each floor (identified A, B, C and D), as well as which apartments currently have children in residence (identified with “yes” in the appropriate cell). The landlord knows that carpeting typically experiences more stress in apartments with children.

Floor Unit A Unit B Unit C Unit D
1 yes
2 yes yes
3
4
5 yes
6 yes
7 yes yes
8 yes
9
10
11 yes yes yes
12
13 yes
14 yes yes
15
16
17 yes
18
19
20 yes yes
21
22
23
24 yes
25

Decide whether the following statements are true or false about this scenario.

True

False

True

False

In order to have an effective trial of the new carpeting, the landlord should select 12 of the 100 apartments completely at random to be the apartments which receive the new carpeting.

True

False

In order to have an effective trial of the new carpeting, the landlord should select 3 of the 25 floors completely at random, and then have all four apartments on each of those floors be the apartments which receive the new carpeting.

True

False

In order to have an effective trial of the new carpeting, the landlord should guarantee that two or three of the 12 apartments selected to receive new carpeting have children in residence.