SECTION 4
1. B This simple equation should present you with little difficulty, but beware: It is on
precisely such questions that your guard might come down and you can become
careless! Using Plugging In The Answers is safest. Only B works:
2 + (0) = 2 – (0)
2=2
2. B As the directions at the beginning of every math section remind us, the area of a
triangle is given by this formula: A =
area is 2. A =
bh. If the base is 4 and the height is 1, the
× 4 × 1 = 2.
3. E If the area of square A is 16, the length of each side is 4, and the perimeter is 16. You
are told that this is
of B’s perimeter, which you can calculate:
www.cracksat.net
Now that you know the perimeter of B, you can calculate the perimeter of C:
If the perimeter of C is 36, each side is 9, and the area of C is 92, or 81. If you chose
B, you need to read the question more carefully.
4. E According to the ratios given, you know that the mixture contains more wheat than
rye; there must be more than 5 pounds of wheat. So let’s eliminate A and B. Use
the Ratio Box.
Because there is a total of 5 pounds of rye, the multiplier is 2.5. This allows you to
solve for 12.5 pounds for the wheat.
5. C Because 135° is one of the middle angles of the circle, the triangles must each have a
45° angle, and are therefore both identical 45°-45°-90° triangles. Remember (or
www.satpanda.com
check the front page of the test) that the ratio of the sides in such a triangle is x:x:
x. You know that the diameter of the circle is 12, so the hypotenuse (which is equal
to the radius of the circle) of each triangle is 6. If 6 is the long side, the other side of
each triangle must be
. Now you can find the area of one of the triangles and
double it. The area of a triangle is
. So
bh, and both the base and height are equal to
= 9. You have found the area for one of the triangles, so
double it to get 18, or C. Another way to solve this is to use the side of your answer
sheet as a ruler and ballpark. If XZ = 12, the hypotenuse of each triangle is 6. Now
mark off the length of 6 with your homemade ruler and compare that to a side of
one of the triangles. You can guesstimate that the side is about 4. Using that
approximation, calculate that since the base and height of both triangles is 4, the
area of each triangle is
× 4 × 4 = 8. The area of both triangles together is 16,
which is closest to 18, or C. ETS wants you to do complicated geometry, but all you
care about is finding the answer.
6. A Translate each statement, piece by piece. The first part tells us that “ the product
of x and y is 76.” Since product means multiplication, then the first equation must
be xy = 76, so you can eliminate answers C and D. The second part says that “x is
twice the square of y,” which translates to x = 2y2, so eliminate answers B and E,
and A is the only answer left. Notice that only the y needs to be squared, which is
why B is wrong. The second equation for B would be written as “the square of
twice y,” which is not what the problem stated.
www.cracksat.net
7. A Try roughly plotting the data points, and then look at your graph. Find the answer
that best fits your graph. Alternatively, notice that the number of customers
increases as the temperature increases. The line of best fit will go up as you follow
the graph from left to right, so eliminate B, D, and E. Notice that the number of
customers does not increase by the same number for each 10-degree temperature
increase. This is an exponential increase, not a linear increase. So, the graph will be
curved. Eliminate C. Only A fits the data in the chart.
8. E Plug in 6 for c. The question is now asking what percent of 18 is 9. The answer would
be 50. Which-ever choice gives you 50 when 6 is plugged in for C is the answer.
Therefore, E is the answer. Remember: Plugging in good numbers will make your life
much easier!
9. D Draw the missing figures. When you sketch this out, you’ll see that it’s a right
triangle with legs of lengths 4 and 5. Use the Pythagorean theorem: 42 + 52 = c2.
Now solve for c. c2 = 41 and c =
. Remember that the question asked for
perimeter, so add up the sides: 4 + 5 +
=9+
, which is choice D.
www.satpanda.com
10. B If 20% of the coins are either nickels or dimes, 80% are neither. 80% of 220 equals
176. Use your calculator or write it out and solve:
11. D Take out your calculator:
216,000 + 20% of 216,000 = 259,200
204,000 + 20% of 204,000 = 244,800
259,200 – 244,800 = 14,400
Another route to the answer is to take the difference immediately (216,000 –
204,000 = 12,000) and then increase that by 20%.
Watch out for partial answers. E is 20% of Springfield’s population, and A is the
difference between 20% of Springfield’s population and 20% of Rockville’s
population.
12. E With algebraic answer choices, you should plug in numbers. Let’s let x = y = 2,
which makes z = 4. Plugging these values into the choices, you’d get the following:
(A) 2(2) + 2(2) = 2(4) [Yes]
(B) 2 – 2 = 0 [Yes]
(C) 2 – 4 = 2 – 4 [Yes]
(D) 2 -
www.cracksat.net
[Yes]
(E) 4 – 2 = 2(2) [No]
The correct answer is E. Don’t forget the EXCEPT!
13. A Do NOT try to figure out the seven numbers in the original list! The median is the
middle number in a list of numbers. Because 8 is lower than every other number,
and 43 is higher, they won’t change the value of the median. This means that
option II is wrong, so you can eliminate B, D, and E. Because A and C both include I,
you know it must be true without even checking it. Let’s focus on option III. The
mode is the number repeated most often. Because 8 and 43 weren’t in the original
list, they can’t change the mode. Eliminate C and pick A.
14. D There are variables in the answer choices, and the question asks you what must
be true. This indicates that you will need to plug in values for x, possibly more than
once. Try both –2 and 3. Only D remains true for both. Remember that the square of
any nonzero number, either positive or negative, is always positive.
15. E Here’s the relationship: The smaller the shoes, the greater the difficulty. This is an
inverse relationship. So, look for an inverse function. Only E is an inverse function. If
you weren’t sure, try plugging in 8 and 10 for the s. The function should yield a
greater D for 8 than it does for 10. Only E has D(8) > D(10).
www.satpanda.com
16. D Note first that this is an EXCEPT question. Now, since a2b = 122, and b is an odd
integer, let’s see what you can come up with. Let’s make b equal 1, so you get the
following: a2 × 1 = 122 = 144, so a = 12. If a equals 12, it is divisible by 1, 2, 3, 4, 6,
and 12. The only choice that remains is D.
17. D Since each side is a mysterious “x long,” let’s make up a value for x to make our
lives a little easier. Let’s use 10, just because it’s nice and round. To find the area
of the first triangle, you’ll have to find the height, which is the middle side of a
30°-60°-90° triangle. If the entire base is 10, then the height is 5
then A =
bh =
10(5
) = 25
. The area is
. The second triangle has side lengths of 2x, which
means each side is 20 long. We can find the area in the same way as the first one.
We’ll end up with a height of 10
, and the area is
20(10
) = 100
. Since the
area of the second triangle is four times the area of the first one, the answer is D, 1 :
4.
18. A Keep in mind that this figure is not drawn to scale. Because
, you know that
the following angles are equal: ∠DCE, ∠CEA, ∠BCA, ∠CAE. Because triangle ACE has
two equal angles, it is isosceles and the sides opposite those angles are also equal.
Therefore, CE = AC = 3.
www.cracksat.net
19. C Plug in numbers. If a = 10 and b = 10, then the inequality doesn’t work: (10 – 5)(10
+ 5) = (5)(15) = 75, which is larger than 0, so eliminate answers D and E. If a = –5
and b = –10 then the inequality also doesn’t work: (–5 – 5)(–10 + 5) = (–10)(–5),
which is larger than 0, so eliminate answers A and B, and C is the only answer left.
20. D Because 61 is the value of the second term in the sequence, plug in 2 for n: a3(2) – 3
= 61. Therefore, a6 = 64, and a must be equal to ±2. Make sure you read carefully; III
would work if 61 were the value of the first term.
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