The Official SAT Online Course39
Transcript of The Official SAT Online Course39
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1
Explanation for Correct Answer C :
Choice (C) is correct. Converting from feet to inches, the length of
the rope is inches. Therefore, the maximum number of
pieces, each inches long, that can cut from the rope is
Explanation for Incorrect Answer A :
Choice (A) is incorrect. Converting from feet to inches, the length of
the rope is inches. A total of pieces (not ), each
inches long, can be cut from the -inch-long rope.
Explanationfor IncorrectAnswer B :
Choice (B) is incorrect. Converting from feet to inches, the length of
the rope is inches. A total of pieces (not ), each
inches long, can be cut from the -inch-long rope.
Explanation for Incorrect Answer D :
Choice (D) is incorrect. Converting from feet to inches, the length of
the rope is inches. To cut a total of pieces, each
inches long, would require inches of rope.
Explanation for Incorrect Answer E :
View Answers and Explanations
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Online - Practice Test #3
A r ope is feet long . Wha t is th e m ax im um nu m ber of pieces, each inch es
long, that can be cut from the rope? ( foot inches)
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
Test Sections
Section 1
Section 3
Section 4
Section 5
Section 6
Section 7
Section 8
Section 9
Sect ion 1 0
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Choice (E) is incorrect. Converting from feet to inches, the length of
the rope is inches. To cut a total of pieces, each
inches long, would require inches of rope.
2
Explanation for Correct Answer C :
Choice (C) is correct. When two lines intersect, vertical angles areformed. Since vertical angles have equal measures and since is a
line, then Since we have
which simplifies to so
Explanation for Incorrect Answer A :
Choice (A) is not correct. If were then we would have
Solving this equation for gives
However, not Therefore, cannot be
Explanation for Incorrect Answer B :
Choice (B) is not correct. If were then we would have
Solving this equation for gives
However, not Therefore, cannot be
Explanation for Incorrect Answer D :
Choice (D) is not correct. If were then we would have
Solving this equation for gives
However, not Therefore, cannot be
Lines and intersect at a point as shown above. If wha t is the v alue
of
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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Explanation for Incorrect Answer E :
Choice (E) is not correct. If were then we would have
Solving this equation for gives
However, not Therefore, cannot be
3
Explanation for Correct Answer D :
Choice (D) is correct. If is the average of the three numbers
and then From this it follows that
Solving this equation for gives
and
Explanation for Incorrect Answer A :
Choice (A) is not correct. It is given that is the average of the three
numbers and Therefore, if were equal to then
would be equal to However, is equal to not
It follows that cannot be equal to
Explanation for Incorrect Answer B :
Choice (B) is not correct. It is given that is the average of the three
numbers and Therefore, if were equal to then
would be equal to However, is equal to
not It follows that cannot be equal to
Explanation for Incorrect Answer C :
Choice (C) is not correct. It is given that is the average of the three
numbers and Therefore, if were equal to then
would be equal to However, is equal to
The av erage (arit hm etic mean ) of the num bers shown above is What is the
v alue of
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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Explanation for Incorrect Answer E :
Choice (E) is not correct. It is given that is the average of the three
numbers and Therefore, if were equal to then
would be equal to However, is equal to not
It follows that cannot be equal to
4
Explanation for Correct Answer C :
Choice (C) is correct. The familys average daily use of electricity for
a month was less than kilowatt-hours if and only if the point
representing that month on the line graph lies below the horizontal
grid line at There are three such points: July, August, and May.
Explanation for Incorrect Answer A :
Choice (A) is not correct. T he familys average daily use of electricity
for a month was less than kilowatt-hours if and only if the point
representing that month on the line graph lies below the horizontal
grid line at There are three such points, not one.
The line graph above shows the av erage daily use of electricit y , in kilowat t-hours,
by a fa mily for ea ch m onth of a y ear, sta rt ing i n J uly . For how man y m onths of
the y ear was the familys av erage daily use of electricity less than kilowatt-
hours?
(A) One
(B) Two
(C) Three
(D) Fiv e
(E) Eight
ANSWERS ANDEXPLANATIONS
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Explanation for Incorrect Answer B :
Choice (B) is not correct. T he familys average daily use of electricity
for a month was less than kilowatt-hours if and only if the point
representing that month on the line graph lies below the horizontal
grid line at The two leftmost points on the graph lie below the
horizontal grid line at but the point for May is a third such point.
Explanation for Incorrect Answer D :
Choice (D) is not correct. There are five months for which the
familys average daily use of electricity was between and
kilowatt-hours, but this is not what the question asked.
Explanation for Incorrect Answer E :
Choice (E) is not correct. There are eight months for which the
familys average daily use of electricity was less than kilowatt-
hours, but in only three of these months was the familys average
daily use less than kilowatt-hours.
5
Explanation for Correct Answer A :
Choice (A) is correct. The equation means that is equal
to the sum of and which is equivalent to the statement is
more than
Explanation for Incorrect Answer B :
Choice (B) is not correct. The equation represents thestatement is times as great as
Explanation for Incorrect Answer C :
Choice (C) is not correct. The equation represents the
statement the sum of and is equal to
Explanation for Incorrect Answer D :
Choice (D) is not correct. The inequality represents the
statement the sum of and is greater than
Which of the following r epr esents t he sta tem ent, is m ore than ?
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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Explanation for Incorrect Answer E :
Choice (E) is not correct. The inequality represents the
statement the sum of and is greater than
6
Explanation for Correct Answer D :
Choice (D) is correct. At Middletown High School, of juniors
are members of the marching band. This means that of the
juniors are members of the band. The fraction of the number of
seniors who are members of the band is equal to the fraction of the
number of juniors who are members of the band. Therefore, since
there are seniors, the number of seniors in the band is
Explanation for Incorrect Answer A :
Choice (A) is not correct. If there were seniors in the band, then
the fraction of the number of seniors who are members of the band
would be The fraction of the number of seniors who are
members of the band is equal to the fraction of the number of juniors
who are members of the band, so of the juniors would be
members of the band. However, the fraction of the number of juniors
who are members of the band is not
Explanation for Incorrect Answer B :
Choice (B) is not correct. If there were seniors in the band, then
the fraction of the number of seniors who are members of the band
would be The fraction of the number of seniors who are
members of the band is e ual to the fraction of the number of uniors
At Middletown Hig h Sch ool, of ju ni ors are mem ber s of the m ar ch ing
band. T he fraction of the nu m ber of seniors who are m em ber s of the ba nd is equ alto the fraction of the n um ber of juniors who are m embers of the band. How m any
of the seniors are in the band?
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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who are members of the band, so of the juniors would be members
of the band. However, the fraction of the number of juniors who are
members of the band is not
Explanation for Incorrect Answer C :
Choice (C) is not correct. If there were seniors in the band, then
the fraction of the number of seniors who are members of the band
would be The fraction of the number of seniors who are
members of the band is equal to the fraction of the number of juniors
who are members of the band, so of the juniors would be
members of the band. However, the fraction of the number of juniors
who are members of the band is not
Explanation for Incorrect Answer E :
Choice (E) is not correct. If there were seniors in the band, then
the fraction of the number of seniors who are members of the band
would be The fraction of the number of seniors who are
members of the band is equal to the fraction of the number of juniors
who are members of the band, so of the juniors would be members
of the band. However, the fraction of the number of juniors who are
members of the band is not
7
Line intersects at point so tha t as shown above. If and
(not shown) are the midpoints of and respectiv ely , which of the
following mu st be true?
I. an d ar e on th e sam e side of
II. an d ar e on th e same side of
III. an d ar e on opposite sides of
(A ) I on ly
(B) II on l
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Explanation for Correct Answer E :
Choice (E) is correct. Consider each one of the statementsindependently to determine whether it must be true.
Statement I concerns points and Point is the midpoint of
so both and are to the left of point on It follows
that and are on the same side of so statement I must be true.
Statement II concerns points and Point is the midpoint of
and so must lie to the right of on It follows
that and are on the same side of so statement II must be
true.
Statement III concerns points and We know that is to the
left of point on Point is the midpoint of so must lie
to the right of on It follows that and are on opposite
sides of so statement III must be true.
Therefore, all three of the statements I, II, and III must be true.
Explanation for Incorrect Answer A :
Choice (A) is not correct. Statement I must be true, but statements II
and III must also be true.
Explanation for Incorrect Answer B :
Choice (B) is not correct. Statement II must be true, but statements I
and III must also be true.
Explanation for Incorrect Answer C :
Choice (C) is not correct. Statement III must be true, but statements
I and II must also be true.
Explanation for Incorrect Answer D :
Choice (D) is not correct. Statements I and III must be true, but
statement II must also be true.
8
(C) III only
(D) I and III only
(E) I, II, and III
ANSWERS ANDEXPLANATIONS
Georg e collected tokens worth a total of point s. If each of th e tokens has a
v alue of either point s or point s, h ow m an y -point tokens did George
collect?
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Explanation for Correct Answer E :
Choice (E) is correct. Let be the number of -point tokens
George collected, and let be the number of -point tokens he
collected. Since George collected a total of tokens, it follows that
Since these tokens are worth a total of points, it
follows that Multiplying the first equation by
( ) and subtracting from the second gives
and so Therefore, George collected tokens of value
points.
Explanation for Incorrect Answer A :
Choice (A) is not correct. George collected tokens of value
points, but the question asked for the number of -point tokens he
collected.
Explanation for Incorrect Answer B :
Choice (B) is not correct. If George had collected only tokens of
value points, he would then have tokens of value points.
Then the total value of Georges tokens would be only
points, not points.
Explanation for Incorrect Answer C :
Choice (C) is not correct. If George had collected only tokens of
value points, he would then have tokens of value points.
Then the total value of Georges tokens would be only
points, not points.
Explanation for Incorrect Answer D :
Choice (D) is not correct. If George had collected only tokens of
value points, he would then have tokens of value points.Then the total value of Georges tokens would be only
points, not points.
9
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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Explanation for Correct Answer B :
Choice (B) is correct. The equation is equivalent to
From the table, only when
Explanation for Incorrect Answer A :
Choice (A) is incorrect. From the table,
not
Explanation for Incorrect Answer C :
Choice (C) is incorrect. From the table, not
Explanation for Incorrect Answer D :
Choice (D) is incorrect. From the table, not
Explanation for Incorrect Answer E :
Choice (E) is incorrect. From the table, not
10
The function is defined by the table above. For wha t v alue of does
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
The figure a bov e shows a tr apezoid divided into three tria ngles. What is the area of
the shaded trian gle?
(A)
(B)
(C)
(D)
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Explanation for Correct Answer D :
Choice (D) is correct. We can find the area of the shaded triangle by
subtracting the sum of areas of two unshaded triangles from the area
of the trapezoid. The area of a trapezoid can be calculated by
multiplying the average of the lengths of the bases by the altitude ofthe trapezoid. The length of bases of the trapezoid are and and
so their average is The altitude of the trapezoid is so
the area of trapezoid is The two unshaded triangles are
congruent right triangles with legs of length and so the area of
each unshaded triangle is The sum of the areas of the
two unshaded triangles is then It follows that the area
of the unshaded triangle is
Explanation for Incorrect Answer A :
Choice (A) is not correct. If the area of the shaded triangle was
then the sum of the areas of the three triangles would be
The sum of the areas of the three triangles is
equal to the area of the trapezoid. However, the area of the trapezoid
is not Therefore, the area of the shaded triangle cannot be
Explanation for Incorrect Answer B :
Choice (B) is not correct. If the area of the shaded triangle was
then the sum of the areas of the three triangles would beThe sum of the areas of the three triangles is
equal to the area of the trapezoid. However, the area of the trapezoid
is not Therefore, the area of the shaded triangle cannot be
Explanation for Incorrect Answer C :
Choice (C) is not correct. The sum of areas of two unshaded triangles
is However, the question is asking for the area of
shaded triangle, not the sum of the areas of the unshaded triangles.
Explanation for Incorrect Answer E :
Choice (E) is not correct. If the area of the shaded triangle was
then the sum of the areas of the three triangles would be
The sum of the areas of the three triangles is
equal to the area of the trapezoid. However, the area of the trapezoid
is not Therefore, the area of the shaded triangle cannot be
(E)
ANSWERS ANDEXPLANATIONS
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11
Explanation for Correct Answer E :
Choice (E) is correct. In the -plane, the graph of
is a parabola that intersects the -axis at
and at When so
the graph of is above the -axis for values less
than below the -axis for values between and and
above the -axis for values greater than It follows that all the
values of for which are those values between
and Of these, the smallest integer value is
Explanation for Incorrect Answer A :
Choice (A) is not correct. If then
Therefore, is not a value of
for which
Explanation for Incorrect Answer B :
Choice (B) is not correct. If then
Therefore, is not a value of
for which
Explanation for Incorrect Answer C :
Choice (C) is not correct. If then
Therefore, is not a value of
for which
Explanation for Incorrect Answer D :
Choice (D) is not correct. If then
Therefore, is not a value of for
which
12
What is the smal lest possible int eger v alue of for w hich
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
In the -plane, thr ee of the v ertices of a square are and If
the square is reflected about the line which of the following is one v ertex of
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Explanation for Correct Answer A :
Choice (A) is correct. Since three vertices of the square are
and the fourth vertex is To find the reflection of
across one can recall that the reflection of any point
about is given by Therefore, the reflection
of about the line is the point
Alternatively, since has slope any line perpendicular to
must have slope (the negative reciprocal of ). The line
with slope that passes through is Thus the
perpendicular from to intersects at
Following this perpendicular an equal distance beyond shows
that the reflection of about the line is
Explanation for Incorrect Answer B :
Choice (B) is not correct. The point lies on the line
Thus is the reflection of itself, about the line
The point is not one of the vertices of the original square and,
thus, not a vertex of the resulting square.
Explanation for Incorrect Answer C :
Choice (C) is not correct. The point is the reflection of
about the line The point is not one of the vertices of
the original square, and so is not a vertex of the resulting
square.
Explanation for Incorrect Answer D :
Choice (D) is not correct. The point lies on the line
Thus is the reflection of itself, about the line
The point is not one of the vertices of the original
square and, thus, not a vertex of the resulting square.
Explanation for Incorrect Answer E :
Choice (E) is not correct. The point is the reflection of
about the line The point is not one of the vertices of
the resulting square?
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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the original square, and so is not a vertex of the resulting
square.
13
Explanation for Correct Answer B :
Choice (B) is correct. Since of the campers could swim, then
there were swimmers among the campers and who couldnt
swim; and since of the campers took climbing lessons, there were
campers who took climbing lessons.
Each of the campers who took climbing lessons either could swim
or couldnt swim. Since a total of campers at the summer camp
couldnt swim, at most of the campers who took climbing
lessons couldnt swim. Therefore, the least possible number ofcampers taking climbing lessons who could swim is
Explanation for Incorrect Answer A :
Choice (A) is not correct. If were the least possible number of
campers taking climbing lessons who could swim, then there could be
campers who couldnt swim and also took climbing lessons. But
there are only campers at the summer camp who couldnt swim.
Explanation for Incorrect Answer C :
Choice (C) is not correct. There were campers who took climbing
lessons, but it need not be true that all of these campers could swim.
Explanation for Incorrect Answer D :
Choice (D) is incorrect. Since only campers took climbing
lessons, there cannot be campers who took climbing lessons and
also could swim.
Explanation for Incorrect Answer E :
Of the cam pers at a summ er cam p, could swim. If of the cam pers took
climbing lessons, wha t w as the least possible num ber of cam pers taking clim bing
lessons who could swim ?
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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Choice (E) is incorrect. There were swimmers among the
campers, but the question asks for the least possible number of
campers taking climbing lessons who could swim. Since only
campers took climbing lessons, there cannot be campers who
took climbing lessons and also could swim.
14
Explanation for Correct Answer E :
Choice (E) is correct. Let be the point on for which
Then triangle and triangle are both righttriangles. Since the measure of is and the hypotenuse of
triangle has length the length of the side opposite is
of so By the Pythagorean Theorem, it follows that
The measure of is so
triangle is an isosceles right triangle. We have so
is also The length of segment is then
Explanation for Incorrect Answer A :
Choice (A) is not correct. Let be the point on for which
We have and If the length
of was then the length of would be
However, the length of must be less than because is one
leg of a right triangle with hypotenuse Therefore, the length of
cannot be
Explanation for Incorrect Answer B :
Choice (B) is not correct. Let be the point on for which
In above, the measur e of is and the measure of is
What is the len gt h of seg ment
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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We have Also
so
Therefore, the length of cannot be
Explanation for Incorrect Answer C :
Choice (C) is not correct. Let be the point on for which
We have and so
Therefore, the length of cannot be
Explanation for Incorrect Answer D :
Choice (D) is not correct. Let be the point on for which
The length of is but the length of is
15
Explanation for Correct Answer A :
Choice (A) is correct. Taking the power of each side of
gives This simplifies to
Explanation for Incorrect Answer B :
Choice (B) is not correct. equals not
Explanation for Incorrect Answer C :
Choice (C) is not correct. equals not
Explanation for Incorrect Answer D :
If an d wh at does equal in term s of
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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Choice (D) is not correct. equals not
Explanation for Incorrect Answer E :
Choice (E) is not correct. equals not
16
Explanation for Correct Answer A :
Choice (A) is correct. In each equation, is expressed in terms of
two other variables; in all, a total in three variables appear in the
right-hand sides of the three equations: and However, each
variable appears in exactly two of the equations, once with acoefficient of and once with a coefficient of Hence if all three
equations are added, all the variables on the right will cancel:
It follows that and so the value of is
Explanation for Incorrect Answer B :
Choice (B) is not correct. Adding the three given equations yields
which simplifies to
not Therefore, the value of is not
Explanation for Incorrect Answer C :
Choice (C) is not correct. Adding the three given equations yields
Based on th e system of equations abov e, wh at is th e v alue of
(A)
(B)
(C)
(D)
(E)
ANSWERS ANDEXPLANATIONS
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which simplifies to
not Therefore, the value of is not
Explanation for Incorrect Answer D :
Choice (D) is not correct. Adding the three given equations yields
that the value of is but the value of is
Explanation for Incorrect Answer E :Choice (E) is not correct. Adding the three given equations yields
which simplifies to
Therefore, the value of is not
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