4.5 Answer ExplanationsAlgebra
Given that the sum of the first n even numbers is
n(n + 1), the sum is equal to 110 when
110 = n(n + 1). To find the value of n in this case,
we need to find the two consecutive integers
whose product is 110. These integers are 10 a nd
11; 10 x 11 = 110. The smaller of these numbers
is n.Th e correct answer 1s A.＃ (^1) 寸Td上
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(A) #7
(8) #8
(C) #9
(D) #10
(E) #11
harbor
North
West+East
South
#5 #6 #7 #8 #9 #10 #11
south dock
PS08375
- A certain harbor has docking stations along its west
and south docks, as shown in the figure; any two
adjacent docking stations are separated by a uniform
distance d. A certain boat left the west dock from
docking station #2 and moved in a straight line
diagonally until it reached the south dock. If the boat
was at one time directly east of docking station #4 and
directly north of docking station #7, at which docking
station on the south dock did the boat arrive?
Geometry
The boat traveled in a straight line from docking
station #2 on the west dock to one of the docking
stations on the south dock, passing through a
single point that is both due east of docking
station #4 and due north of docking station #7.
Call this point P. Having traveled to P, the boat
was both 2d south of its starting point and 2d
east of its starting point. Therefore, traveling in a
straight line, the boat traveled one unit south for
every one unit traveled east. And because at point
P the boat was a distance d north of the south
dock, the boat must have reached the south dock
at a point which is a distance of d east of dockingstation #7 (which is due south of point P). This
point is the position of doc如ngstation^ #8. The
boat therefore arrived at docking^ station^ #^8.Th e correct answer 1 s B.
PS03887- 6(87.30 + 0.65)—5(87.30) =
(Al 3.90
(Bl 39.00
(C) 90.90
(D) 9 1.20
(El 91.85
Arithmetic
This question is most efficiently answered by
distributing the 6 over 87.30 and 0.65, and then
combining the terms that contain a factor of
87.30, as follows:6(87.30 + 0.65) - 5(87.30) = 6 (87.30) + 6 (0.65)- 5 (87.30) = (6 - 5) 87.30 + 6(0.65) = 87.30 +
3.90 = 91.20
The correct answer is D.
PS13800- Points A, B, C, and D, in that order, lie on a line. If
AB= 3 cm, AC= 4 cm, and BD = 6 cm, what is CO, in
centimeters?
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4
6
3A .B C DThe figure shows points A, B, C, and D as well as
the given measurements. Since AC= AB+ BC, it
follows that 4 = 3 + BC, and so BC= l. Then,
since BD =BC+ CD, it follows that 6 = 1 +
CD, and so CD= 5.Alternately, AD = AB + BD = 3 + 6 = 9. Also,
AD=AC+ CD,so 9=4+ CD and CD=5.1h e correct answer 1s E.