SECTION 6
1. B The best way to approach this problem is to plug in the answers. Start with C. When
6 is subtracted from 10, the result is 4. Divide 4 by 2 to see if it equals 3. It does not,
so C can’t be correct. Because our answer was too small, you need to subtract a
smaller number from 10. Try B. When 4 is subtracted from 10, the result is 6. Divide
by 2 to get 3; this is correct.
2. C The number of degrees in a line is 180. Therefore, b + c = 180. And since a + 90 =
180, a = 90. So a + b + c = 270. Note that E is the Joe Bloggs choice—“it cannot be
determined” is rarely the correct answer.
3. E Use the formula for distance: distance = rate × time.
Steve runs 12 miles at 8 miles per hour, which means that he runs for 1
hours (or
1.5 if you’re using your calculator). Adam runs the same 12 miles at 6 miles per
hour, which means that he runs for 2 hours. Adam takes half an hour longer to
complete the race, and half an hour is 30 minutes.
4. D Because there are variables in the answers, try Plugging In! If a = 2, then
www.cracksat.net
. Plug a = 2 into the answers to find that only D is 32. Another
option is to rewrite the problem as
. Reduce before you multiply by dividing
the denominator of the first term and the numerator of the second term by 3 to get
.
5. E To solve this problem, you need to figure out the ratio between the x- and y-values
on line segment
. Looking at the figure,
is the hypotenuse of a right triangle
with a side of 12. You can see this is a multiple of one of ETS’s favorite right
triangles: 3:4:5. This is a 9:12:15 triangle, and the coordinates of point B are (9, 12).
All the points on line segment
are in a ratio of 9:12. Only E has a similar ratio.
6. B Because you aren’t given the cost of any book, you can plug in your own values.
Let’s say that the average cost of the textbooks, excluding the anatomy textbook,
is $10. You can make all the books cost $10 each to make the problem easier. The
anatomy textbook would cost $30. The total cost of all the textbooks would be
$130. The anatomy textbook would be
of the total cost.
7. A The trick is to notice that this parallelogram is actually made of two equal triangles.
By finding the area of the triangles, you can find the area of the parallelogram. The
triangles are both right triangles, and the two sides given in the figure follow the
3:4:5 pattern. If you look at triangle ACD with
as the base, the base is 3 and the
height is 4. Now use the formula for area of a triangle:
www.satpanda.com
That means the parallelogram is 2 × 6 = 12.
Also, if you estimate the area, the base is 5 and the height is less than 3, so the area
is less than 15. The only answer less than 15 is A!
8. D Plug in a value for b, the number of minutes the pie is baked. Let’s say 52 minutes,
because 52 is greater than 50, less than 60, and not 55 (which is in all the answer
choices). The only answer choice that works is D: |52 – 55| = |–3| = 3, which is less
than 5.
9.
2
Just simplify and solve for x:
Remember that the first grid-in question returns the difficulty meter to easy!
10.
19, 39, 59, 79, or 99
The simplest way to solve this problem would be to find values of n that satisfy the
first condition, and then to check which of those also satisfies the second condition.
So, let’s find some numbers that leave a remainder of 4 when divided by 5: {9, 14,
19, 24, 29}.
www.cracksat.net
That should be enough. Now let’s check which of these leaves a remainder of 3
when divided by 4:
9 ÷ 4 = 2 R1
14 ÷ 4 = 3 R2
19 ÷ 4 = 4 R3
19 is one acceptable response.
11.
145
Because the two lines are parallel, 110 + 2x = 180. Solving this equation for x, you
get x = 35. Looking at the triangle, the missing angle (m) can be found by solving
the equation 110 + x + m = 180. If x = 35, m = 35. If m + y = 180 and m = 35, y =
145.
12.
36
If x2 = 16 then x = ± 4. If y2 = 4 then y = ± 2. To maximize (x – y)2, you need to
maximize the difference. The greatest difference is (–4) – 2 = –6 or 4 – (–2) = 6, and
both 62 and (–6)2 equal 36.
13.
130
First use a Ratio Box to find the number of males and females. If the ratio is 2 to 3,
www.satpanda.com
the total ratio is 5. The actual is 250, so the multiplier is 50. That means there are 50
× 2 = 100 males and 50 × 3 = 150 females. Set up a group grid (the bolded
numbers are information from the problem):
You find that 20 females must be taking French, and because there 150 females
total, 130 must be taking Spanish.
14.
8
In the diagram, you can assume that the shorter ticks are evenly spaced, so each
one must be 0.25 units long. Plugging the coordinates of the points into the given
. As you can see, canceling works
expression gives you
well: The two negatives cancel each other out, and two of the numbers in the
numerator are double the size of two of the numbers in the denominator. This
leaves you with
. You can also just plug the whole thing into your
www.cracksat.net
calculator, but make sure you use enough parentheses: You need to enclose the
entire numerator in parentheses, and then the entire denominator in parentheses.
15.
12
Start with the most restricted spots. There are 2 tools that can go in the first spot.
Once you put 1 there, only 1 tool can go in the second spot. Once you’ve used
these 2 tools, there are only 3 that can go in the third spot, then 2 in the fourth spot
and 1 in the fifth spot. So, there are 2 × 1 × 3 × 2 × 1 = 12 ways to arrange the
tools.
16.
4
This question looks tough, so work it one step at a time, and start with what you
know. Sector AOB is a quarter-circle (it covers an angle of 90 out of 360 degrees), so
multiplying its area (π) by 4 gives you the area of the whole circle (4π). Plugging this
into the equation for the area of a circle, A = πr2, gives you 4π = πr2, and the radius
must be a positive value, so r = 2. This means that the coordinates of point A must
be (−2, 0). Because A is on both the circle and the parabola, you can plug its xand y-coordinates into the given equation of the parabola, y = x2 – b. This becomes
0 = (–2)2 – b, so b = 4.
17.
3
The first step is to draw a diagram:
www.satpanda.com
You should notice that BD is part of one of ETS’s favorite right triangles: a 3:4:5
triangle. So BD = 3.
18.
or 1.2
Inversely proportional means x1y1 = x2y2 where x represents hours of sleep
and y represents the number of errors: (2 hours)(3 errors) = (5 hours)(y errors). 6 =
5y, so y =
www.cracksat.net
www.satpanda.com
www.cracksat.net
Digital SAT Test Resource
Digital SAT Reading and Writing Practice Tests
https://www.cracksat.net/digital/reading-writing/
https://www.satpanda.com/sat/reading-writing/
Digital SAT Math Practice Tests
https://www.cracksat.net/digital/math/
https://www.satpanda.com/sat/math/
More SAT Math Tests
https://www.cracksat.net/sat/math-multiple-choice/
https://www.satpanda.com/sat/math/
SAT Grammar Tests
https://www.cracksat.net/sat/grammar/
Digital SAT Practice Tests Download
https://www.cracksat.net/sat-downloads/new-sat.html
Mock Digital SAT Exams
https://exam.satpanda.com
www.satpanda.com
www.cracksat.net
ACT Online Practice Tests:
https://www.actexam.net
https://www.crackab.com
Mock ACT Exams Online
https://exam.actexam.net
AP Exams Practice Tests:
https://www.crackap.com
https://www.apstudy.net
www.satpanda.com