**11. Correct answer: (B) **

Given:

Z W Y X

Two adjacent may be interchanged

The entire sequence can be reversed

To find:

The least number of changes needed to put the letters into alphabetical order from left to right

Solution:

We need to change the sequence from Z W Y X to W X Y Z.

The least steps needed would involve changing from

Z W Y X to Z Y X W and then reverse the entire sequence.

Swap W and Y; Z W Y X → Z Y W X

Swap W and X; Z Y W X → Z Y X W

Reverse entire sequence: Z Y X W → W X Y Z

The least number of changes needed is 3.

**Answer: (B) 3**

**12. Correct answer: (D) **

Given:

A cube with edges of length 4 cm

A rectangular box 20 cm by 24 cm by 32 cm

To find:

The number of cubes needed to fill the rectangular box

Solution:

Volume of cube = 4 × 4 × 4 = 64

Volume of rectangular box = 20 × 24 × 32 = 15360

Divide volume of rectangular box by volume of cube

= 15360 ÷ 64 = 240

Note that you should only divide the volumes when you are sure that the smaller shape can fit into the larger shape without any leftover space.

**Answer: (D) 240**

**13. Correct answer: (E) **

Given:

0 < *n* < 1

To find:

Find the correct ordering of

Solution:

**Answer: (E) n 2 < n < √n **

**14. Co****rrect answer: (C) **

Given:

The figure

To find:

Median of the slopes

Solution:

Topic(s): Coordinate geometry, statistics

**Answer: (C) **

**15. Correct answer: (A) **

Given:

When it is noon (EST) in New York City, it is 9.00 a.m. (PST) in San Francisco

A plane took off from New York City at noon EST and arrived in San Francisco at 4.00 p.m. on the same day

A second plane left San Francisco at noon PST and took exactly the same amount of time for the trip

To find:

The second plane’s arrival time (EST) in New York City

Solution:

When it is 9:00 a.m. PST, it is 12:00 noon EST.

The time difference from PST to EST is +3 hours.

A plane took off at 12:00 noon EST and arrived at 4:00 p.m. PST.

4:00 p.m. PST would be 4 + 3 = 7:00 p.m. EST.

The time taken would be from 12:00 noon to 7:00 p.m., which is 7 hours.

A second plane took off at 12:00 noon PST and took the same amount of time as the first plane, which is 7 hours. It would then be arriving at 7:00 p.m. PST.

7:00 p.m. PST would be 7 + 3 = 10.00 p.m. EST

**Answer: (A) 10.00 p.m. EST**

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