5.5 Answer Explanationsdividing both 12 and 48 by 48, it follows
1 2 1
that an area of—= -m^2 is represented
48 4
48 1
by an area of—= 1 cm^2 and so x2 =—or
l(^48 4)
X = -; SUFFICIENT.
2
(2) This indicates that a length of 15 mis
represented by a length of 30 cm. Then,
dividing both 15 and 30 by 30, it follows
15 1
that a length of—= -mis represented
30 2
30 1
by a length of—= 1 cm and so x = -;
(^30 2)
SUFFICIENT.
Th e correct answer 1s D·
each statement alone is sufficient.
y
p
。
R
Q s
x
DS03939
- In the rectangular coordinate system above, if !!:,OPQ
and l!:,QRS have equal area, what are the coordinates
of point R?
(1) The coordinates of point Pare (0,12).
(2) OP = OQ and QS = RS.Geometry
Since the area of�OPQ is equal to the area of6 1
QRS, it follows that - (OQ)(OP) =
1 2- (QS)(SR), or (OQ)(OP)= (QS)(SR). Also, if
2
both OS and SR are known, then the coordinates
of point R will be known.
(1) Given that they-coordinate of Pis
12, it is not possible to determine the
coordinates of point R. For example, if OQ
= QS = SR= 1 2 , then the equation
(OQ)(OP) = (QS)(SR) becomes
(^12 )(^12 ) = (^12 )(^12 ), which^ is^ true,^ and^ the
x-coordinate of R is OQ + QS = 24 and the
y-coordinate of R is SR= 12. However, ifOQ = 12, QS = 24, and SR= 6, then the
equation (OQ)(OP) = (QS)(SR) becomes
(^12 )( 12 ) = (^24 )(^6 ),^ which^ is^ true,^ and^ the
x-coordinate of R is OQ + QS = 36 and the
y-coordinate of R is SR= 6; NOT sufficient.(^2 ) Given that OP= OQ and QS = RS, it is not
possible to determine the coordinates of
point R, since everything given would still
be true if all the lengths were doubled, but
doing this would change the coordinates of
point R; NOT sufficient.
Taking (1) and (2) together, it follows that
OP= OQ = 12. Therefore, (OQ)(OP)= (QS)(SR)becomes (^) ( (^12) )( (^12) ) = (QS)(SR), or (^144) = (QS)(SR).
Using QS = RS in the last equation gives
144 = (QS)气or 12 = QS. Thus, OQ = QS = SR=
12 and point R has coordinates (24,12).
Th e correct answer 1s C;
both statements together are sufficient.
DS07258
- In a school that had a total of 600 students enrolled in
the junior and senior classes, the students contributed
to a certain fund. If all of the」uniors but only half of the
seniors contributed, was the total amount contributed
more than $ 7 40?
(1) Each junior contributed $1 and each senior who
contributed gave $3.
(2) There were more juniors than seniors enrolled in
the school.Arithmetic
The task in this question is to determine whether
the respective statements are sufficient for
answering the question of whether the total
amount contributed was more than $740. In
making this determination, it is important to
remember that we are to use only the information
that has been given. For example, it may seem
plausible to assume that the number of seniors at
the school is roughly equal to the number of
juniors. However, because no such information
has been provided, we cannot assume that this
assumption holds. With this in mind, consider
statements 1 and 2.(1) If it were the case that half of the 600
students were seniors, then, given that half
of the 300 seniors would have contributed