The document provides information on various arithmetic topics including order of operations, fractions, decimals, percentages, ratios, and proportional reasoning. It includes definitions, examples, and multi-step word problems to solve. The document would help prepare for a test on fundamental arithmetic concepts and their applications.

1. Arithmetic

3. PEDMAS:
Order of Operations: If an expression has parentheses within parentheses,
work from the innermost out.
P- Parentheses,
E- Exponents,
M- Multiplication,
D- Division,
A- Addition,
and S- Subtraction
This mnemonic will help you remember the order of operations: Please
Excuse My Dear Aunt Sally (PEMDAS).

4. Example:
30 – 5 × 4 + (7 – 3)2 ÷ 8

5. Fractions:
4 ← numerator (also known as the dividend)
— ← fraction bar (means divided by)
5 ← denominator (also known as the divisor)

6. Equivalent Fractions:
When you multiply the numerator and denominator by the same
number (any number other than zero), the fraction is unchanged. You
simply get an equivalent fraction.
Example:
1
2
=
1𝑋2
2𝑋2
=
2
4
The GMAT often uses this technique to change the form of fractions
that have radicals in the denominator.
Example:
9
√2
=
9𝑋√2
√2𝑋√2
=
9√2
2

7. Reduce
15
35
to lowest terms.

8. Adding and Subtracting Fractions
Example:
3
5
+
2
3
-
1
2

9. Multiplying Fractions
Example:
10
9
x
3
4
x
8
15

10. Dividing Fractions
Example:
10
9
÷
5
6

11. Complex Fractions
7
9
−
1
6
1
3
+
1
2

12. Comparing Positive Fractions
10
9
5
6

13. Comparing Positive Fractions
8
9
5
6

14. Mixed Numbers
Convert
50
7
to a mixed number.

15. Convert 5
1
4
to a fraction.

16. Decimals
Decimals can be converted to common fractions with a power of 10 in
the denominator.
Example: 0.037 =
37
1000

17. Comparing Decimals
Arrange in order from smallest to largest: 0.7, 0.77, 0.07, 0.707, and 0.077.

18. Adding and Subtracting Decimals
0.506 + 0.78 +0.002
0.255 - 0.01 + 0.78 - 0.894

19. Multiplying and Dividing Decimals
0.4 x 0.67
0.25
0.625

20. Simplify:
1
3
+ ( 2
3 )
2
(A) 1
2
9
(B) 1
1
9
(C)
7
9
(D)
8
9
(E) 1

21. If x and y are positive numbers, is
𝑥2
𝑦
>
𝑥
𝑦2?
(1)
𝑥
𝑦
> 1
(2) xy > 1

22. If a and b are positive numbers, is 8a < 3b?
(1)
𝑎
𝑏
< 0.374 (2) b > 2.671a

23. The equation
5𝑎
2𝑏
+
10
3
= 5 is equivalent to each of the
following EXCEPT:
(A) 3a = 2b
(B) 5a – 2b =
4𝑏
3
(C)
5𝑎
2𝑏
+ 1 =
8
3
(D) 3a + 2b – 1 = 2a + 3b
(E)
𝑎
2𝑏
=
1
3

24. Does a = b?
(1) a2 − b2 = 0 (2) 1-
𝑎3
𝑏3 = 0

25. What is the value of integer n?
(1) n = n4
(2) 1n ≠ n

26. Each of the 600 elements of Set X is a distinct
integer. How many of the integers in Set X are
positive odd integers?
(1) Set X contains 150 even integers.
(2) 70 percent of the odd integers in Set X are positive.

27. Is z an integer?
(1) 2z is an even integer.
(2) 4z is an even integer.

28. If each of d, q, and r is a positive integer such that
dq+r=3, what is the value of d?
(1) The number r/d is less than 2/3.
(2) The integer q/r is less than 2.

29. If f and g are positive integers, is
𝑓+𝑔
𝑓
an integer?
(1) g = 5f−4 (2) f =
𝑔
3

30. If n is a positive integer, is
𝑛
3
an integer?
(1)
𝑛
3
is an integer.
(2) 14𝑛 is NOT an integer.

31. ODD / EVEN
Even ± Even = Even Even * Even = Even
Even ± Odd = Odd Even * Odd = Even
Odd ± Odd = Even Odd * Odd = Odd
EvenPositive integer= Even
OddPositive Integer = Odd

32. If x is an integer, is x odd?
(1) x + 4 is an odd integer.
(2)
𝑥
3
is NOT an even integer.

33. Set S contains 5 integers, labeled A, B, C, D, and E. If the
sum of all of the elements of set S is odd, how many of
the elements of set S are even?
(1) The sum of A and B is odd.
(2) The product of B, C, and D is odd.

34. If a and b are integers and a is odd, is b even?
(1) (a3+1)∗b is even. (2)
𝑎2
𝑏
= b−4

35. If m is an odd number and p is a prime number,
which of the following must be odd?
(A) mp (B) m(m+p) (C) m − p
(D) m2+ 2p2+1 (E) m2(m + 2p)

36. Is x – 2y + z greater than x + y – z?
(1) y is positive. (2) z is negative.

37. If x – y = 8, which of the following must be true?
I. Both x and y are positive.
II. If x is positive, y must be positive.
III. If x is negative, y must be negative.
(A) I only (B) II only (C) III only (D) I and II (E) II and III

38. Is
𝑠−𝑡
𝑠𝑡
< 0 ?
(1) t < 0 < s (2)
𝑠𝑡
𝑠−𝑡
< −1

39. If b≠0 and -1 <
𝑎
𝑏
< 1, which of the following CANNOT be
true?
(A) a + b < 0 (B) (a + b)(a − b) > 0 (C) a − b > 0
(D) (a + b)(a − b) < 0 (E) a + b > 0

40. Factors and Multiples

41. If p, q, and r are positive integers such that q is a factor
of r, and r is a multiple of p, which of the following
must be an integer?
A)
𝑝+𝑞
𝑟
B)
𝑞+𝑟
𝑝
C)
𝑝
𝑞
D)
𝑝𝑞
𝑟
E)
𝑟(𝑝+𝑞)
𝑝𝑞

42. If p, q, and r are positive integers such that q is a factor
of r, and r is a multiple of p, which of the following
must be an integer?
A)
𝑝+𝑞
𝑟
B)
𝑞+𝑟
𝑝
C)
𝑝
𝑞
D)
𝑝𝑞
𝑟
E)
𝑟(𝑝+𝑞)
𝑝𝑞

43. If a certain number is divisible by 18 and 24, it must
also be divisible by which of the following?
(A) 30 (B) 38 (C) 72 (D) 216 (E) 432

44. What is the greatest positive integer x such that
96x is a factor of 8110+x?
(A) 2 (B) 4 (C) 5 (D) 6 (E) 15

45. What is the greatest positive integer x such that
96x is a factor of 8110+x?
(A) 2 (B) 4 (C) 5 (D) 6 (E) 15

46. How many positive integers less than 70 are multiples
of either 3 or 4 but not both?
(A) 17 (B) 18 (C) 23 (D) 30 (E) 35

47. Primes

48. Divisibility Rules:

49. Remainders

50. If a and b are prime numbers, which of the
following CANNOT be the value of ab?
A) 9 B) 14 C) 21 D) 23 E) 25

51. If n is an integer such that 12 ≤ n ≤ 24, is n a prime
number?
(1) The remainder when n is divided by 4 is 1.
(2) The remainder when n is divided by 6 is 1.

52. If x = 12, y = 35, and x2y2 = 21×28×30×z, what is
the value of z?
(A) 10 (B) 12 (C) 15 (D) 21 (E) 30

53. If a=5m+2 and b=5n+13, and m and n are positive
integers, what is the remainder when a + b is divided by 5?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

54. If a and b are positive integers, is 3a2b divisible by 60?
(1) a is divisible by 10.
(2) b is divisible by 18.

55. A baseball team won 45 percent of the first 80 games it
played. How many of the remaining 82 games will the
team have to win in order to have won exactly 50
percent of all the games it played?
(A) 36 (B) 45 (C) 50 (D) 55 (E) 81

56. The ratio of domestic sales to foreign sales of a certain
product is 3:5. What fraction of the total sales are the
domestic sales?

57. Given that the ratio of men to women to children in a
room is 4:3:2, what other ratios can be determined?
Ratio of men : total people =
Ratio of women : total people =
Ratio of children : total people =
Ratio of women : men =
Ratio of men : children =
Ratio of children : women =

58. A movie buff stores movies on the internet and on her personal
computer in a ratio of 7:2. If she purchases 6 new movies and
downloads them to her personal computer, that ratio would
change to 11:4. If she stores movies in no other locations, what
was the original number of movies she owned before the
purchase of new movies?
A) 22 B) 28 C) 77 D) 99 E) 105

59. The ratio of two quantities is 2:3. If each of the quantities
is increased by 6, what is the ratio of the new quantities?
A) 2:3 B) 6:7 C) 8:9 D) 8:3 E) cannot be determined

60. At a certain university, the football program receives 4 times
more funding than does the basketball program. Together, the
football and basketball programs receive 3 times as much
funding as do all other sports programs combined. What is the
ratio of funding for the basketball program to funding for all
other sports programs, not including the football program?
(A) 1:5 (B) 1:4 (C) 3:5 (D) 3:4 (E) 5:3

61. If
𝑎
𝑏
=
𝑐
𝑑
, what is the numerical ratio of b to d?
(1)
𝑎
2𝑏
=
1
3
(2) a = 2 and d = 4.

62. If the ratio of a to b is 4 to 3 and the ratio of b to c is
1 to 5, what is the ratio of a to c?
(A)
4
15
(B)
15
4
(C)
4
5
(D)
5
4
(E)
3
5

63. After 360 liters of fuel were added to a container, the
amount of fuel in the container was
5
8
of the tank’s
capacity. What is the capacity of the container?
(1) After the 360 liters were added, the container had
108 liters less than of the tank’s capacity.
(2) Before the 360 liters were added, there were 180
liters of fuel in the container.

64. The weight of a certain type of cable is always directly
proportional to its length. If 560 meters of this cable
weighs 84 kilograms, what is the weight, in kilograms, of
110 meters of the same cable?
(A) 11.5 (B) 16.5 (C) 22 (D) 24.5 (E) 26

65. The ratio of the cost of a wooden plank to the length of a
wooden plank is constant. A plank measuring 6 feet long
costs $96. Jordan wants to buy planks that measure 10
feet in length, and Kristen wants to buy planks that are
7.5 feet in length. How much more, in dollars, will Jordan
pay per plank?
(A) 40 (B) 45 (C) 120 (D) 135 (E) 160

66. There are chips of four different colors distributed in
stacks as follows: 1/2 are white, 1/6 are green, 1/5 are
blue, and the remaining 12 chips are red. What is the
total number of chips in the four stacks?
A. 60 B. 75 C. 90 D. 100 E. 125

67. What is 25 percent of 36?

68. 13 is 33
1
3
percent of what number?

69. 18 is what percent of 3?

70. If n is 15 percent less than 60, what is the value of n?

71. What is the price of a television that costs 28
percent more than a $50 radio?

72. Percent Increase and Decrease
Percent decrease =
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑊ℎ𝑜𝑙𝑒
x 100%
Percent increase =
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑊ℎ𝑜𝑙𝑒
x 100%

73. If a dress is offered for a discounted price of $120, what
is the percent discount if the regular price is $150?

74. The price of an antique is reduced by 20 percent, and
then this discount price is further reduced by 10 percent.
If the antique originally cost $200, what is its final price?

75. A pet store regularly sells pet food at a discount of 10
percent to 30 percent from the manufacturer’s suggested
retail price. If during a sale, the store discounts an
additional 20 percent from the discount price, what would
be the lowest possible price of a container of pet food that
had a manufacturer’s suggested retail price of $20.00?
A) $10.00 B) $11.20 C) $14.40
D) $16.00 E) $18.00

76. Four different batches of concrete are combined in a large mixing vat.
Batch A, which weighs 1,000 kilograms, contains 30 percent gravel by
weight. Batch B, which is twice the weight of batch A, is made up of 40
percent gravel. Batch C weighs 25 percent less than batch B and contains
50 percent gravel. Finally, batch D, which is half the weight of batch A,
contains 60 percent gravel. What is the percentage of gravel in the
concrete when the four batches are mixed together?
(A) 40% (B) 43% (C) 45% (D) 50% (E) 55%

77. In the first quarter of the year, a certain entrepreneur sold
36 percent of the 75 crafts that she put for sale online. In
the second quarter of that year, she sold one-fourth of the
remaining crafts. What was the percent decrease from the
first quarter to the second in the number of crafts the
entrepreneur sold?
(A) 12% (B) 25% (C) 43
1
5
% (D) 61% (E) %

78. In the first quarter of the year, a certain entrepreneur sold 36
percent of the 75 crafts that she put for sale online. In the second
quarter of that year, she sold one-fourth of the remaining crafts.
What was the percent decrease from the first quarter to the
second in the number of crafts the entrepreneur sold?
A. 12% B. 25% C. 55 5/9% D. 61% E. 66 2/3%

79. The administration of a certain school surveys all 120 students to plan a
field trip. Each student can express a preference for only one destination:
the science museum, the art museum, or neither. The results of the
student survey are shown above. Assuming that the maximum number of
students who are allowed to visit their preferred museum visit that
museum for the field trip, how many students who have a preference do
not visit their preferred museum?
(1) Due to transportation constraints, the maximum number of students
who can take a field trip to the science museum is 55.
(2) Due to high demand, the art museum can accommodate a maximum
of 50 students.

80. Two brands of detergent are to be combined. Detergent X
contains 20 percent bleach and 80 percent soap, while
Detergent Y contains 45 percent bleach and 55 percent
soap. If the combined mixture is to be 35 percent bleach,
what percent of the final mixture should be Detergent X?
A) 10% B) 32
1
2
% C) 35% D) 40% E) 60%

81. A display case contains a certain number of donuts,
some chocolate, some jelly filled, and the rest plain. One-
sixth of the donuts are chocolate. How many chocolate
donuts must be added so that one-fourth of the total
donuts are chocolate?
(1) There are 40 plain donuts in the case.
(2) The ratio of plain donuts to jelly-filled donuts is 2:1.

82. A farmer who grows only two crops, corn and soybeans, has the
same combined target output by weight every year. This year,
corn makes up 40 percent of the crop and weighs 24 tons. Next
year, however, the farmer wants corn to be only 15 percent of
the total tonnage. How many more tons of soybeans must the
farmer grow next year to maintain the same target output?
(A) 9 (B) 15 (C) 25 (D) 36 (E) 51

83. If an amount of a solution containing 10 percent Chemical
A is combined with twice as much of a solution that is 30
percent Chemical A and four times as much of a solution
that is 35 percent Chemical A, what is the concentration
of Chemical A in the resulting solution?
(A) 17.5% (B) 20% (C) 25% (D) 27.5% (E) 30%

84. The price of a certain car this year is $42,000, which is 25
percent greater than the cost of the car last year. What
was the price of the car last year?
(A) $27,000 (B) $28,000 (C) $31,500
(D) $33,600 (E) $34,500

85. If the average (arithmetic mean) of x, 25, y, and 30 is
x + y, which of the following equals the value of x?
A) 18
1
3
y B) 18
1
3
+ y C) 18 -
3
𝑦
D) y - 18
1
3
E) 18
1
3
- y

86. If each of the bowlers in a tournament bowled an equal
number of games, what is the average (arithmetic mean)
score of all the games bowled in the tournament?
(1) Of the bowlers, 70 percent had an average (arithmetic
mean) score of 120, and the other 30 percent had an
average score of 140.
(2) Each of the 350 bowlers in the tournament bowled 3
games.

87. Bradley’s grade in his science class is determined by his scores
on 5 tests that each count an equal amount toward his grade.
He has received scores of 67, 76, 78, and 94 on the 4 science
tests thus far. If the last test consists of 20 equally weighted
questions and is graded out of 100 points, how many questions
does he need to answer correctly on the last test in order to
average an 80 in his science class?
(A) 15 (B) 16 (C) 17 (D) 18 (E) 19

88. The average price of Emily’s 5 meals was $20. Meals with
a price of $25 or more include a free dessert. How many
of Emily’s 5 meals included a free dessert?
(1) The most expensive of the 5 meals had a price of $50.
(2) The least expensive of the 5 meals had a price of $10.

89. If José reads at a constant rate of 2 pages every 5 minutes,
how many seconds will it take him to read N pages?
A)
3
8
N B) 2N C)
5
8
N D) 24N E) 150N

90. If the city centers of New York and London are 3,471
miles apart, which of the following is closest to the
distance between the city centers in inches? (There are
5,280 feet in a mile.)
A) 1.75×107 B) 1.83×107 C) 2.10 × 108
D) 2.10 × 109 E) 2.20×1010

91. A group of friends rent a small bus to go sightseeing. The
rate for the bus and driver is $90 per hour, and the total
distance of the sightseeing tour is 112 miles. If the total
charge for the trip is $420, what is the average speed of
the bus in miles per hour?
(A) 16.7 (B) 21.0 (C) 22.5 (D) 24.0 (E) 25.8

92. Pierre’s European car measures fuel economy in terms
of liters per kilometer. If the car averages
1 𝑙𝑖𝑡𝑟𝑒
10 𝐾𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟𝑠
on a trip, what is the car’s approximate fuel economy in
terms of the standard U.S. measurement of miles per
gallon? (Note: 1 gallon is approximately 3.78 liters, and 1
mile is approximately 1.61 kilometers.)
(A) 4 (B) 16 (C) 24 (D) 30 (E) 40

93. A student can complete x homework questions in h hours.
According to his calculations, it will take him 4 days to
complete his latest assignment if he works m minutes a
day. How many questions are on his latest assignment?
(A)
𝑚𝑥
60ℎ
(B)
15𝑥
𝑚ℎ
(C)
4𝑥ℎ
𝑚
(D)
𝑚𝑥
15ℎ
(E)
4𝑚𝑥
15ℎ

94. John travels 30 miles per hour in 2 hours and then 60
miles per hour in 3 hours. What is his average speed in
miles per hour?
A) 16 B) 32 C) 48 D) 64 E) 80

95. A powerboat crosses a lake at 18 miles per hour and
returns at 12 miles per hour. If the time taken turning
the boat around was negligible and it returns by the
same route, then what was the boat’s average speed for
the round trip, in miles per hour?
A) 7.2 B) 14.4 C) 21.6 D) 28.8 E) 36

96. What was the average speed of a runner in a race from
Point X to Point Z?
(1) The runner’s average speed from Point X to Point Y
was 10 miles per hour.
The runner’s average speed from Point Y to Point Z was
8 miles per hour.

97. A motorcyclist started riding at highway marker A, drove 120 miles to
highway marker B, and then, without pausing, continued to highway
marker C, where she stopped. The average speed of the motorcyclist,
over the course of the entire trip, was 45 miles per hour. If the ride from
marker A to marker B lasted 3 times as many hours as the rest of the ride,
and the distance from marker B to marker C was half of the distance from
marker A to marker B, what was the average speed, in miles per hour, of
the motorcyclist while driving from marker B to marker C?
(A) 40 (B) 45 (C) 50 (D) 55 (E) 60

98. Did Jon complete a journey of 40 kilometers in less time than it
took Ann to complete the same journey?
(1) Jon traveled at an average speed of 30 kilometers per hour
for the first 10 kilometers and then at an average speed of 15
kilometers per hour for the rest of the journey.
(2) Ann traveled at an average speed of 20 kilometers per hour
for the entire journey.

99. A hiker walks three sections of a trail that are of equal
length. The first section of the trail is flat, and on this
section the hiker travels at 3 miles per hour for 1.5 hours.
The second section is uphill, and on this section the
hiker’s pace slows by 25 percent. The third section is
downhill, and here his speed doubles. What was the
hiker’s average speed for the entire three-section hike?
(A) 1.5 (B) 3 (C) 3.25 (D) 4.5 (E) 9.75

100. A truck driver drove for 2 days. On the second day, she
drove 3 hours longer and at an average speed of 15 miles
per hour faster than she drove on the first day. If she
drove a total of 1,020 miles and spent 21 hours driving
during the 2 days, what was her average speed on the
first day, in miles per hour?
(A) 25 (B) 30 (C) 35 (D) 40 (E) 45

101. Working together, John, David, and Roger require 2
1
4
hours to
complete a certain task, if each of them works at his respective
constant rate. If John alone can complete the task in 4
1
2
hours
and David alone can complete the task in 9 hours, how many
hours would it take Roger to complete the task working alone?
A) 2
1
4
B) 4
1
2
C) 6
3
4
D) 9 E) 12

102. Working alone, machine X can manufacture 1,000 nails in
12 hours. Working together, machines X and Y can
manufacture 1,000 nails in 5 hours. How many hours
does it take machine Y to manufacture 1,000 nails
working alone?
A. 3
9
17
B. 5
1
3
C. 7 D. 7
1
5
E. 8
4
7

103. Working at its usual constant rate, Pump A can empty a
water storage tank in 3 hours. Pump B, also working at
its usual constant rate, can empty half of the same
tank in 4 hours. How many hours will it take both
pumps working together at their usual respective
constant rates to empty half of the tank?
A.
12
11
B.
24
11
C.
24
7
D.
7
2
E.
36
7

104. Machine 1 and Machine 2 working together can produce
12,000 meters of steel cable per hour. Each machine
works at a constant rate. Machine 1 by itself can produce
5,000 meters of cable per hour. How many hours would it
Machine 2 working alone to produce 12,000 meters of
cable?
A.
7
12
B.
67
40
C.
12
7
D.
11
5
E.
5
2

105. If $100 were invested at 12 percent simple annual
interest, what would be the total value of the investment
after 3 years?

106. If $100 were invested at 12 percent interest compounded
annually, what would be the total value of the investment
after 3 years?

107. If $100 were invested at 12 percent annual interest,
compounded quarterly, what would be the total value
of the investment after 3 years?

108. The number of bacteria in a petri dish increased by 50 percent
every 2 hours. If there were 108 million bacteria in the dish at
2:00 p.m., at what time were there 32 million bacteria in the
dish?
A) 6:00 p.m. B) 8:00 pm. C) 6:00 a.m. D) 8:00 a.m. E) 10:00 a.m.

109. A certain account pays 1.5 percent compound interest
every 3 months. A person invested an initial amount and
did not invest any more money in the account after that. If
after exactly 5 years, the amount of money in the account
was T dollars, which of the following is an expression for
the original number of dollars invested in the account?
(A) (1.015)4T (B) (1.015)15T (C) (1.015)20T
(D) T/(1.015)15 (E) T/(1.015)20

110. Binh invested $1,000 in a certificate of deposit (CD) that matured in 4
years. The certificate paid 4 percent annual interest compounded
quarterly for the original 4-year term and then 2 percent simple annual
interest on the compounded amount after that until the CD was
redeemed by the holder. If Binh held his CD for exactly 6 years, how
much money did he receive when he redeemed it?
(A) 1,000×(1.01)16×1.04 (B) 1,000×(1.01)16×(1.02)2
(C) 1,000×(1.04)6 (D) 1,000×(1.01)24 (E) 1,000×(1.04)16×(1.02)2

111. The amount of an investment will double in approximately 70/ p years,
where p is the percent interest, compounded annually. If Thelma invests
$ 40,000 in a long-term CD that pays 5 percent interest, compounded
annually, what will be the approximate total value of the investment
when Thelma is ready to retire 42 years later?
A. $ 280,000 B. $ 320,000 C. $ 360,000
D. $ 450,000 E. $ 540,000

112. A polling company surveyed a certain country, and it found that 35
percent of that country’s registered voters had an unfavorable
impression of both of that state’s major political parties and that 20
percent had a favorable impression only of Party A. If 1 registered voter
has a favorable impression of both parties for every 2 registered voters
who have a favorable impression only of Party B, then what percentage
of the country’s registered voters have a favorable impression of both
parties (assuming that respondents to the poll were given a choice
between favorable and unfavorable impressions only)?
A) 15 B) 20 C) 30 D) 35 E) 45

113. Of the 65 books released last year by a particular
publishing house, 25 were no more than 200 pages. The
publisher released 35 fiction books, of which 20 were
more than 200 pages, and it also published nonfiction
books. How many nonfiction books of no more than 200
pages did the publishing house release last year?
(A) 5 (B) 10 (C) 20 (D) 30 (E) 35

114. Three hundred students at College Q study a foreign language. Of these,
110 of those students study French and 170 study Spanish. If at least 90
students who study a foreign language at College Q study neither French
nor Spanish, then the number of students who study Spanish but not
French could be any number from
(A) 10 to 40 (B) 40 to 100 (C) 60 to 100 (D) 60 to 110 (E) 70 to 110

115. The Financial News Daily has 25 reporters covering Asia, 20 covering Europe, and
20 covering North America. Four reporters cover Asia and Europe but not North
America, 6 reporters cover Asia and North America but not Europe, and 7
reporters cover Europe and North America but not Asia. How many reporters
cover all three continents (Asia, Europe, and North America)?
(1) The Financial News Daily has 38 reporters in total covering at least 1 of the
following continents: Asia, Europe, and North America.
(2) There are more Financial News Daily reporters covering only Asia than there
are Financial News Daily reporters covering only North America.

116. In an election, candidate Smith won 52 percent of the
total vote in Counties A and B. He won 61 percent of the
vote in County A. If the ratio of people who voted in
County A to County B is 3:1, what percent of the vote did
candidate Smith win in County B?
(A) 25% (B) 27% (C) 34% (D) 43% (E) 49%