Percent; Ratio&Proportion

1. [March US 2023] 4. [June 2023]

If x > 0 and p% of x is 13, which expression The ratio of green tiles to blue tile in a
represents x in terms of p piece of artwork is 5 to 2. If there are 16
blue tiles in the piece of artwork, how many
100p green tiles are there?
A) 13p C) 13
13p (100)(13)
B) 100 D) p

5. [August US 2023]

If
2. [March US 2023] g 1 10g 1
= and = ,
h 100 kh 100
What is the 90% of 80? what is the value of k?

A) 10 C) 88 A) 0.1 C) 100
B) 72 D) 152 B) 10 D) 1,000

3. [June 2023] 6. [August US 2023]

A scientist analyzed a soil sample with a The positive quantity r is increased by 20%,
mass of 900 grams and determined that it and then the resulting quantity is decreased
contained 189 grams of water. What is the by 25%. Which expression represents the
percentage of water, by mass, in this soil result of these two changes?
sample?
A) 0.90r C) 1.05r
A) 9% C) 18.9% B) 0.95r D) 15.0r
B) 9.9% D) 21%

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7. [November 2023] 11. [March 2024]

Julia purchased 600 feet of fencing. She A real estate company offers a series of three
used 70% of this fencing to surround a veg- webinars. 1,250 people attended the first
etable garden. How many feet of fencing did webinar. 68% of the people who attended
Julia use to surround the vegetable garden? the first webinar attended the second webi-
nar, and 32% of the people who attended
A) 14 C) 420 the first and second webinars attended the
third webinar. How many people attended
B) 35 D) 530
all three webinars?

12. [March 2024]

8. [November 2023]
The speeds of particles A, B, and C are
The ratio 36 to m is equivalent to the ratio a meters per second, b meters per second,
2 to 12. What is the value of m? and c meters per second, respectively. If the
speed of particle A is 7, 900% of the speed
of particle C and the speed of particle C
is 0.008% of the speed of particle B, which
expression represents the value of a + b in
terms of c?

A) 12, 579c C) 7, 908c

9. [December 2023] B) 8, 025c D) 2, 040c

A clothing store buys shirts at a wholesale

price of 5.00 dollars each and resells them
each at a price that is 270% of the wholesale
price. At the end of the season, any remain-
ing shirts are marked at a discounted price
that is 70% of the retail price. What is the
discounted price of each remaining shirt, in 13. [May 2024]
dollars?
For a certain rectangular region, the ratio
of its length to its width is 10 : 4. If the
width of the rectangular region increases
by 7 units, how must the length change to
maintain this ratio?

A) It must decrease by 7 units.

10. [March 2024]
B) It must increase by 7 units.
2a a
If = 5.8 and = 23.2, what is the C) It must increase by 17.5 units.
b bn
1
value of ? D) It must decrease by 17.5 units.
n

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14. [May 2024] 17. [May US 2024]

The composition of an animal is defined as After 20% of the original number of objects
the muscles, bones, and fat of the animal. in a group were removed from the group, 180
A scientist studied the composition of one objects remained in the group. How many
young swamp buffalo and determined the objects were removed from the group?
buffalo had 133 kilograms of muscle, which
made up approximately 65.9% of its com-
A) 36 C) 225
position. Of the remaining composition of
this buffalo, approximately 46.2% was bone, B) 45 D) 900
and the remainder was fat. Based on these
approximations, to the nearest tenth, how
many kilograms of this buffalo’s composition
was bone?

18. [May 2024]

15. [May 2024] When a collection of books is sorted, 52%

are nonfiction and the remaining books are
The positive number a is 2, 800% of the fiction. Of those that are fiction, 75% are
number c, and c is 20% of the number b. westerns and the remaining fiction books are
What is the value of a − b in terms of c? romance. If there are 933 romance books in
this collection, what is the total number of
A) 23c C) 560c books in the collection?
B) 140c D) 2, 240c

19. [May 2024]

16. [May 2024]
For each of two rectangles, the ratio of the
The combined original price for a towel and rectangle’s length to its width is 10 to 5.
chair is $36. After a 45% discount to the The width of rectangle X is 16.5 times the
chair and a 25% discount to the towel are width of rectangle Y . How does the length
applied, the combined sale price for the two of rectangle X compare to the length of
items is $25. Which system of equations rectangle Y ?
gives the original price t in dollars of the
towel and c in dollars of the chair?
A) The length of rectangle X is 0.5 times
A) t + c = 36 the length of rectangle Y .
0.45t + 0.25c = 25
B) The length of rectangle X is 2 times
B) t + c = 36 the length of rectangle Y .
0.55t + 0.75c = 25
C) t + c = 36 C) The length of rectangle X is 16.5 times
0.25t + 0.45c = 25 the length of rectangle Y .

D) t + c = 36 D) The length of rectangle X is 33 times

0.75t + 0.55c = 25 the length of rectangle Y .

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20. [June 2024] 23. [August US 2024]
√
The mass of object A is 498% of the mass Which expression is equvalent to x153 ,
of object B, and the mass of object A is where x > 0?
0.830% of the mass of object C. If the mass
2
of object C is p% of the mass of object B, A) x 153 C) x151
what is the value of p? 153
B) x 2 D) x306

21. [June 2024]

There is a proportional relationship between 24. [August US 2024]

p and t. If p = 2, 340 when t = 3, 120, then
what is the value of p when t = 2, 496? For the positive quantities h,j, and k. 94%
of h is equivalent to 47% of j, and j is equiv-
A) 1, 716 C) 3, 276 alent to 30% of k. What percentage of k is
h? (Disregard the % sign when entering
B) 1, 872 D) 3, 328
your answer. For example, if you answer is
39%, enter 39)

22. [August 2024]

A square map has a side length of 35 inches, 25. [August 2024]

and 1 inch on the map represents an actual
distance of 17 miles. A smaller version of A company studied a random sample of 20
the same map is printed as a square with lawns in a small town. The company found
the side length 55% shorter than the side that 4 of these lawns contain fertilizer. If
length of the previous map. On the smaller there are 260 lawns in the town, which of the
map, which of the following is closest to the following is the best estimate of the number
actual distance, in miles, represented by 1 of lawns that contain fertilizer?
inch?
A) 3 C) 13
A) 7.65 C) 19.25 B) 5 D) 52
B) 10.97 D) 37.78

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26. [August 2024] 29. [August US 2024]

Each side of square A has a length of 24 A clothing store buys shirts at a whole-
inches. Each side of square A is multiplied sale price of 7.00 dollars each and resells
by a scale factor of 2 to create square B. them each at a retail price that is 260% of
What is the length, in inches, of each side the wholesale price. At the end of the sea-
of square B? son, any remaining shirts are marked at a
discounted price that is 75% off the retail
A) 22 C) 26 price. What is the discounted price of each
remaining shirt, in dollars?
B) 24 D) 48

27. [August 2024] 30. [June 2024]

The table summarizes the number of ob- The mass of object A is 483% of the mass
jects in each group. of object B, and the mass of object A is
0.069% of the mass of object C. If the mass
Group Number of objects of object C is p% of the mass of object B,
p
A 325 what is the value of ?
1, 000
B 68
C 572
D 102
Total 1067

The number of objects in group C is p% of

the number of objects in group A. What is
the value of p?

31. [October 2024]

A clothing store buys shirts at a whole-

sale price of 5.00 dollars each and resells
them each at a retail price that is 270% of
the wholesale price. At the end of the sea-
son, any remaining shirts are marked at a
28. [August 2024]
discounted price that is 70% off the retail
price. What is the discounted price of each
A clothing store buys shirts at a whole-
remaining shirt, in dollars?
sale price of 4.00 dollars each and resells
them each at a retail price that is 280% of
the wholesale price. At the end of the sea-
son, any remaining shirts are marked at a
discounted price that is 80% off the retail
price. What is the discounted price of each
remaining shirt, in dollars?

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32. [October US 2024] 35. [November 2024]

The positive number a is 3, 700% of the A researcher surveyed undergraduate stu-

number c, and c is 20% of the number b. If dents, graduate students, and postgraduate
a − b = wc, where w is a constant, what is students. The number of undergraduate
the value of w? students surveyed was 7450% of the num-
ber of postdoctoral students surveyed and
the number of graduate students surveyed
was 24% of the undergraduate students sur-
veyed. If there were 3576 graduate students
surveyed, what was the sum of the number
of undergraduate students and postdoctoral
students surveyed?
33. [October 2024]

The positive number a is 2, 352% of the

sum of the positive numbers b and c, and b
is 84% of c. What percent of b is a?

A) 5,152% C) 51.52%
36. [October US 2024]
B) 2,436% D) 24.36%
The ratio of 12 to x is equal to the ratio
of 156 to y. Which expression represents y
in terms of x?

1 1
A) x C) x
13 12
B) 13x D) 12x

34. [October US 2024]

The composition of an animal is defined as

the muscles, bones, and fat of the animal.
A scientist studied the composition of one
young swamp buffalo and determined that
the buffalo had 139.2 kilograms of muscle, 37. [October US 2024]
which made up approximately 67.7% of its
composition. Of the remaining composition For the positive quantities h, j, and k, 27%
of this buffalo, approximately 51.4% was of h is the equivalent of 24% of j, and j is
bone, and the remainder was fat. Based on equivalent to 45% of k. What percentage of
these approximations, to the nearest tenth, k is h?(Disregard the % sign when entering
how many kilograms of this buffalo’s com- your answer. For example, if your answer is
position was bone. 39%, enter 39)

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38. [November US 2024] 41. [December US 2024]

A chemist mixed x liters of a 2% saline solu- Julia purchased 800 feet of fencing. She
tion with y liters of a 5% saline solution to used 60% of this fencing to surround a veg-
produce a 3% saline solution. Which equa- etable garden. How many feet of fencing did
tion best represents this situation? (Assume Julia use to surround a vegetable garden?
the volumes of the solutions are additive.)

A) 0.02x + 0.05y = 3(x + y) A) 12 C) 480

B) 0.02x + 0.05y = 0.03(x + y) B) 30 D) 740

C) 0.2x + 0.5y = 3(x + y)

D) 0.2x + 0.5y = 0.3(x + y)

42. [December US 2024]

39. [November US 2024]
The value of an autographed baseball in-
The ratio 5 to x is equivalent to the ra- creased by 178% from the end of 2012 to
tio y to 8. Which equation represents x in the end of 2013 and then decreased by 21%
terms of y? from the end of 2013 to the end of 2014.
What was the net percentage increase in
5y y the value of the autographed baseball from
A) x = C) x =
8 40 the end of 2012 to the end of 2014?
8y 40
B) x = D) x =
5 y A) 119.62% C) 157.00%
B) 140.62% D) 236.38%

40. [November US 2024]

The mass of object A is 416% of the mass

of object B, and the mass of object A is 43. [December 2024]
0.064% of the mass of object C. If the mass
of object C is p% of the mass of object B, On a plot of land, 52.0% of the square
p
what is the value of ? footage is farmland and the remaining
1, 000
square footage is pasture. There are build-
ings on exactly 21.5% of the square footage
of the farmland, and there are buildings on
exactly 14.0% of the square footage of the
pasture. If there are buildings on exactly
p% of the square footage of the plot of land,
what is the value of p?

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44. [December 2024] 47. [December 2024]

The speeds of particles A, B, and C are Levi and Marissa each have stamp collec-
a meters per second, b meters per second, tions. The number of stamps in Levi’s col-
and c meters per second, respectively. If the lection is 200% of the number of stamps in
speed of particle A is 6, 000% of the speed Marissa’s collection. If there are 460 stamps
of particle C and the speed of particle C in Marissa’s collection, how many stamps
is 0.008% of the speed of particle B, which are in Levi’s collection?
expression represents the value of a + b in
terms of c? A) 230 C) 920
B) 460 D) 1,380
A) 12, 560c C) 6, 008c
B) 6, 125c D) 1, 850c

48. [March 2025]

The positive number a is 2, 047% of the

45. [December 2024] sum of the positive numbers b and c, and b
If x > 0 and x is 33% of y, which expression is 89% of c. What percent of b is a?
represents y in terms of x?
A) 21.36% C) 2, 300%
100 1 B) 36.69% D) 4, 347%
A) x C) x
33 33
10 67
B) x C) x
33 100

49. [March 2025]

A square map has a side length of 55 inches,

and 1 inch on the map represents an actual
46. [December 2024] distance of 13 miles. A smaller version of
the same map is printed as a square with
Jasmin grows bean pods in her garden. This the side length 70% shorter than the side
year, she harvested 330 bean pods and saved length of the previous map. On the smaller
10% of them to plant next year. How many map, which of the following is closest to the
of the harvested bean pods did Jasmin save actual distance, in miles, represented by 1
to plant next year? inch?

A) 23 C) 41 A) 3.90 C) 38.50
B) 33 D) 43 B) 7.65 D) 43.33

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50. [March US 2025] 53. [March 2025]

A furniture company is selling all tables A square map has a side length of 35 inches,
with a 20% discount off their original price and 1 inch on the map represents an actual
for the month of October. What is the dis- distance of 13 miles. A smaller version of
count, in dollars, on a table with an original the same map is printed as a square with
price of $130? the side length 70% shorter than the side
length of the previous map. On the smaller
A) $110 C) $52 map, which of the following is closest to the
B) $90 D) $26 actual distance, in miles, represented by 1
inch?

A) 3.90 C) 24.50
B) 7.65 D) 43.33

51. [March US 2025]

In a collection of items, 10% are red, 25%

are green, 35% are blue, and 30% are yellow.
If there are 40 green items, how many blue
items are in the collection?
54. [May 2025]

A) 14 C) 48 If 350% of n is 35, what is the value of

n?
B) 16 D) 56

A) 12,250 C) 1,000
B) 1,225 D) 10

52. [March US 2025]

A square map has a side length of 30 inches,

and 1 inch on the map represents an actual
distance of 17 miles. A smaller version of
55. [May 2025]
the same map is printed as a square with
the side length 65% shorter than the side
A number f is 120% greater than a posi-
length of the previous map. On the smaller
tive number g. A number h is 90% less than
map, which of the following is closest to the
the number f. The number h is how many
actual distance, in miles, represented by 1
times the number g?
inch?

A) 5.95 C) 19.50 A) 0.12 C) 1.08

B) 10.30 D) 48.57 B) 0.22 D) 1.98

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56. [May 2025] 59. [June US 2025]

A researcher surveyed undergraduate stu- While the mass of an object is the same
dents, graduate students, and postdoctoral everywhere, the weight of an object is not
students. The number of undergraduate the same on different planets. An object
students surveyed was 7, 150% of the num- has a weight of 170.00 pounds on Earth
ber of postdoctoral students surveyed and and a weight of 186.32 pounds on Neptune.
the number of graduate students surveyed The object’s weight on Jupiter is 252.8% of
was 45% of the number of undergraduate its weight on Earth. If the object’s weight
students surveyed. If there were 6, 435 grad- on Neptune is x% of its weight on Jupiter,
uate students surveyed, what was the sum which of the following is closest to the value
of the number of undergraduate students of x?
and postdoctoral students surveyed?

A) 43.35 C) 277.07
B) 71.73 D) 429.76

57. [June 2025]

The table summarizes the number of ob-

jects in each group.

Group Number of objects

A 325
B 64
C 611
D 96
Total 1,096
60. [June 2024]

The number of objects in group C is p% of A proposal for a construction project was

the number of objects in group A. What is included on a city election ballot. A TV
the value of p? news report stated that 8 times as many
people voted in favor of the proposal as peo-
ple who voted against it. An internet article
reported that 24, 500 more people voted in
favor of the proposal than voted against
it. Based on these data, how many people
voted against the proposal?
58. [June US 2025]

A scientist analyzed a soil sample with a

mass of 900 grams and determined that it
contained 189 grams of water. What is the
percentage of water, by mass, in this soil
sample?

A) 9% C) 18.9%
B) 9.9% D) 21%

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61. [November 2023] 64. [November 2024]

In a random sample of 276 residents in a A gallery had x artifacts in a collection.

certain building, 9 residents reported that When more artifacts were added to the col-
they take the train to work. If there are lection, number of artifacts increased by
a total of 1,380 residents in this building, 149%. What is the number of artifacts in
which of the following is the best estimate the collection in terms of x?
of the number of building residents who take
the train to work? A) 5.10x C) 1.49x
B) 0.51x D) 2.49x
A) 9 C) 276
B) 45 D) 1,095

65. [August 2024]

If 380% of n is 38, what is the value of

n?
62. [June US 2025]
A) 14,440 C) 1,000
A researcher investigated two species of B) 1,444 D) 10
mites: a predator and its prey. At the start
of a week, there was an equal number of the
two species. At the end of the week, the
number of prey had increased by 2,700% of
the number of prey at the start of the week,
and the number of predators had increased
by 180% of the number of predators at the
start of the week. The number of prey at
the end of the week was p% greater than the
number of predators at the end of the week.
What is the value of p?

63. [August 2024]

The result of increasing the quantity x by

600% is 126. What is the value of x?

A) 18 C) 474
B) 21 D) 756

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 Questions 66 and 67 refer to the following information

Candidate 1 Candidate 2 Other candidates Total

County A 35,954 34,777 1,640 72,371
County B 165,973 77,837 6,862 250,672
County C 46,475 54,235 2,026 102,736
Total 248,402 166,849 10,528 425,779

For three counties, the table summarizes the number of residents who voted, by county and by
candidate, during a 2016 US gubernatorial election. In 2016, the total number of residents in all
three of these counties was 960000, and the total area of these three counties was 1949 square
miles.

66. [August US 2023] 67. [August US 2023]

To the nearest whole percent, the total For these three counties, which of the fol-
number of residents who voted for Candi- lowing is closest to the number of residents
date 1 is what percent of the total number who voted per square mile?
of residents who voted for Candidate 2?

A) 67% C) 103% A) 650 C) 218

B) 86% D) 149% B) 493 D) 127

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 Answers: Percent, Ratio & Proportion

Number Answer Number Answer

1 D 2 B
3 D 4 40
5 B 6 A
7 C 8 216
9 9.45 10 8
11 272 12 A
13 C 14 31.8
15 A 16 D
17 B 18 7775
19 C 20 60000
21 B 22 D
23 B 24 15
25 D 26 D
27 176 28 2.24
29 4.55 30 700
31 4.05 32 32
33 A 34 34.1
35 15100 36 B
37 40 38 B
39 D 40 650
41 C 42 A

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 Number Answer Number Answer
43 17.9 44 A
45 A 46 B
47 C 48 D
49 D 50 D
51 D 52 D
53 D 54 D
55 B 56 14500
57 188 58 D
59 A 60 3500
61 B 62 90
63 A 64 D
65 D 66 D
67 B

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