Lesson 8
208
w w w . p e t e r s o n s . c o m / a r c o
ARCO
■
SAT II Subject Tests
7. The correct answer is (D). Using
the distance formula
8. The correct answer is (D). This is a good exercise in problem solving. Since “Cannot be deter-
mined” is not an answer choice, we can be certain that we have sufficient
information to find RS. We
already know:
And the figure shows:
QS +
RT =
QR +
RS +
RS +
ST
All we have to do is find a way to manipulate these symbols until we isolate
RS:
(
QR +
RS) + (
RS +
ST) =
QS +
RT
RS + (
QR +
RS +
ST) = (
QS +
RT)
RS = (
QS +
RT) – (
QR +
RS +
ST)
Since
QR +
RS +
ST =
QT:
RS = (
QS +
RT) –
QT
And, using the values provided:
If you tend to reason spatially, you might just have looked at the figure and seen:
Then you
would see that the length of QS and
RT together exceeds that of
QT by the length of
RS. So,
just add
QS and
RT and
subtract QT.
Mathematics Level IC/IIC Subject Tests
209
ARCO
■
SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o
9. The correct answer is (E). There are several ways of reaching the correct answer here. One, since
the line that bounds the lower portion of the shaded area includes the points (0,0) and (5,5), it is the
graph
of the equation x =
y. For a point to be in the shaded region, the
y coordinate must be greater
than the
x coordinate. Only (E) meets this requirement. Or, you might reason
less formally that the
line contains points in which the “rise” is equal to the “run.” So you are looking for a point for which
the “rise” is greater than the “run.” Or you might just choose to plot the points on the diagram.
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