11. Correct answer: (B)
Z W Y X
Two adjacent may be interchanged
The entire sequence can be reversed
The least number of changes needed to put the letters into alphabetical order from left to right
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)
A cube with edges of length 4 cm
A rectangular box 20 cm by 24 cm by 32 cm
The number of cubes needed to fill the rectangular box
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)
0 < n < 1
Find the correct ordering of
Answer: (E) n 2 < n < √n
14. Correct answer: (C)
Median of the slopes
Topic(s): Coordinate geometry, statistics
15. Correct answer: (A)
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
The second plane’s arrival time (EST) in New York City
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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