100% GMAT Î¼Îµ ÏŒÎ»Î± Ï„Î± Î¼ÎÏÎ·: Math, Verbal, Integrated Reasoning, and Writing.
100% GMAT Î¼Îµ ÏŒÎ»Î± Ï„Î± Î¼ÎÏÎ·: Math, Verbal, Integrated Reasoning, and Writing.
A straight 1-meter long line segment is marked off at its half, thirds, and fourths. Which of the following are the different possible lengths between the marks?
ID: NT - 1
only and
only and Â
onlyÂ , and
only and
only , and
A certain alloy consists of gold, copper, and bonze in proportion of 2 : 5 : 10. How many grams of copper are there in 153 grams of this alloy?
ID: NT - 2
9
18
36
45
90
If the value of a increases from 77 to 78, which of the following expressions will increase as well?
Â Â Â Â Â Â Â Â Â I.Â
Â Â Â Â Â Â Â Â II.
Â Â Â Â Â Â Â III.
ID: NT - 11
I only
I and II only
I and III only
II and III only
None of the above
The x and y are each two-digit positive integers and the digits of y are in reverse order of the digits of x. Which of the following CANNOT be the value of x + y ?
ID: NT - 4
22
44
121
143
161
Jane is now 8 years older than Andrew. If in 6 years Jane will be twice as old as Andrew, how old will Jane be in 4 years from now?
ID: NT - 5
2
4
6
10
14
How many minutes does it take Melanie to package each gift box if she packages n gift boxes in 3 hours?
ID: NT - 7
A positive integer n is divided by 2 and this quotient is then added to 5. If the result of these operations equals n, what is the value of n?
ID: NT - 8
2
5
10
12
15
The ratio of to is equivalent to the ratio of which of the following?
ID: NT - 9
2 to 5
5 to 8
5 to 9
9 to 5
1 to 9
If the digits of a two-digit number are reversed, the resulting number differs from the original one by 36. What is the difference between the two digits?
ID: NT - 12
4
5
6
7
8
If the digits of a three-digit number are reversed, the resulting number differs from the original number by 198. What is the difference between the first and the last digits of the original number?
ID: NT - 13
1
2
3
4
5
IfÂ Â andÂ , then the values of a and b are
ID: NT - 15
3 and 1
-1 and 2
3 and -1
2 and 3
3 and 2
If x is the product of all positive integers from 5 to 10 inclusive and if x = 2^{a} Â· 3^{b} Â· 5^{c} Â· 7^{d}, then what is the value of a + b + c + d?
ID: NT - 16
5
11
17
19
23
For which of the following values of x is the value ofÂ NOT an integer?
ID: NT - 17
0
1
2
3
4
If , , , and , then which of the following is the correct ordering of a, b, c, and d ?
ID: NT - 18
If A, B, and C in the expression 1A1 + 2B5 + 36C2 = 4,008 are one-digit integers then value of A + B + C is:
ID: NT - 21
9
10
11
12
13
What is the smallest integer value of x, when 5^{x} > 10^{3}?
ID: NT - 22
2
3
4
5
6
The sum of all prime numbers greater than 38 and smaller than 55 is
ID: NT - 24
137
184
223
233Â
274
The expressionÂ is equal to which of the following?
ID: NT - 25
0.2
2
4
0.4
0.04
What is the 16^{th} digit to the right of the decimal part of fraction after it is converted into a decimal number?
ID: NT - 28
1
6
7
8
9
A jar contains some number of white, red, and black balls, and each color has a denomination of 2, 5, and 7 points respectively. Some balls are removed from the jar. If the product of the point values of the balls removed from the jar is 490,000, how many white balls are removed?
ID: NT - 30
4
5
6
7
8
If a, b, c, and d are consecutive positive integers and a < b < c < d, then which of the following must be true?
Â Â Â Â Â Â Â Â Â I. d â€“ a = 3
Â Â Â Â Â Â Â Â II. bc is an even integer
Â Â Â Â Â Â Â III. abcd is evenly divisible by 5
ID: STAT - 1
I only
II only
I and II only
II and III only
I, II, and III
Name of the Supplier | Number of Shipments | Contract Amount |
Arden Corp. | 3 | $5,000 |
Braidon Group | 2 | $16,000 |
Chief & Co. | 1 | $7,000 |
Delver Inc. | 4 | $4,000 |
The table above shows the numbers and dollar amounts of shipments the Shummer Corporation received this year for a particular product. What is the average dollar amount of each shipment?Â
ID: STAT - 2
7,000
8,000
8,150
8,170
8,800
During the first month of a certain sporting contest each team played exactly one game with every other team. If there are 25 teams participating, a total of how many games have been played during the month?
ID: STAT - 3
300
325
330
450
600
If a, b, c, and d are consecutive positive integers and a < b < c < d, then which of the following MUST be true?Â
Â Â Â Â Â I. abcd has to be evenly divisible by 12.
Â Â Â Â Â II. bcd has to be evenly divisible by 3.Â
Â Â Â Â III. abc has to be evenly divisible by 2.
ID: STAT - 4
Â Â Â Â Â Â
I only
II only
I and II only
II and III only
I, II, and III
For the past k days a store had a daily average (arithmetic mean) of 30 visitors. What is the value of k if today 75 people visited the store, which increased the average to 35?
ID: STAT - 5
6
7
8
9
10
On Monday Jane spent 2 hours on preparation for her university admission test. On each of the days through Tuesday to Friday she spent 3 hours, while she only spent 1 hour on preparation on Saturday. How many hours should Jane spend on test preparation on Sunday for her weekly average of the study hours to become 3.Â
ID: STAT - 6
2
3
4
5
6
How many integers are there from 101 to 732 inclusive, each of which is leaving a remainder of 2 when divided by both 7 and 5?
ID: STAT - 7
16
17
18
19
20
On the first day of sales a store sold 14 men suits for $150 each. On the second day it sold 20 suits at $120 each, and on the third day it sold 10 suits at $100 each. What was the average price, in dollars, of each suit the store sold over these three days?
ID: STAT - 8
125
126
127
128
129
What is the positive difference between the average (arithmetic mean) and the median of the following numbers?
xÂ Â Â x + 1Â Â Â x + 2Â Â Â x + 5Â Â Â x + 7
ID: STAT - 9
0
1
Departments |
Number of Voters |
Candidate A, % of votes |
Candidate B, % of votes |
Marketing |
120 |
70 |
30 |
Sales |
80 |
40 |
60 |
R&D |
60 |
50 |
50 |
Human Resources |
40 |
20 |
80 |
Engineering |
10 |
50 |
50 |
The table above shows the employees' election results for Director's position by each department of the company. A candidate wins the election if he/she receives the greatest number of votes from all the departments combined. Which department had the greatest number of votes for the winning candidate?
ID: STAT - 10
Marketing
Sales
R&D
Human Resources
Engineering
Group A:Â 10, 11, 17, 18
Group B: 9, 10, 14, 16, x
Which of the following must be the value of x for the medians of Group A and Group B to be equal?
ID: STAT - 11
10
11
12
13
14
If k is the median of the first eight positive multiples of 7, and if n is the average (arithmetic mean) of the first eight positive multiples of 7, then what is the average (arithmetic mean) of k and n?
ID: STAT - 12
63
31.5
15.75
8
7
Set A: 37, 37, 37, 37, 37, 37
Set B: 35, 36, 37, 38, 39, 40
Set C: 30, 31, 37, 37, 40, 41
Which of the following represents an increasing order of standard deviations of the data sets above?
ID: STAT - 13
A, B, C
B, A, C
C, A, B
B, C, A
C, B, A
The average (arithmetic mean) temperature records, in Celsius, on Monday, Tuesday and Wednesday were 18, 22, and 20 respectively. What should the temperature record be on Thursday for the average of all four days be 2 degrees higher than the average of the first three days?
ID: STAT - 14
28
27
26
25
24
The average of 20, 30 and 40 is larger than the average of 15, 25 and which of the following?
ID: STAT - 15
49
59
69
79
89
a, b, c, d, e
An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If the list of letters shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?
Â Â I. Â Â , , , ,
Â Â II.Â Â a + 1, b + 2, c + 3, d + 4, e + 5
Â Â III.Â a â€“ 1, b â€“ 1, c â€“ 1, d â€“ 1, e â€“ 1,
ID: STAT - 16
I only
II only
III only
I and II
I, II, and III
While watching a movie, Annâ€™s eyes blink every 3 seconds, Bobâ€™s eyes blink every 4 seconds and Charleyâ€™s eyes blink every 6 seconds. If at a certain moment Annâ€™s, Bobâ€™s and Charleyâ€™s eyes blink simultaneously, in how many seconds will their eyes blink together again?
ID: PI - 1
12
13
24
36
108
If s is the product of all integers from 20 to 50 inclusive, what is the greatest integer r for which 5^{r} is a factor of s?
ID: PI - 3
6
7
8
9
10
What is the number of integers between 88 and 181, which leave a remainder of 3 when divided by 5?
ID: PI - 4
18
17
16
15
14
If x is an even integer and y is an odd integer, which of the following MUST be even?Â
ID: PI - 5
For all positive integer values of k, the number 3k + 15! must be evenly divisible by which of the following?
ID: PI - 6
2
3
4
5
6
Ben and Linda depart on their cars from the same departure point in Athens and drive at the same speed along the same road. Ben makes a very brief stop every 9 miles, while Linda makes a very brief stop every 12 miles. At about which mile will both Ben and Linda stop?
ID: PI - 7
18
21
24
36
108
When positive integer a is divided by positive integer b the result is 26.16. Which of the following can be the value of b?
ID: PI - 8
108
48
32
26
25
The number of bolts in a kid's metallic construction kit can be divided either into groups of 6 bolts or groups of 15 bolts. What is the minimum number of bolts possible in the construction kit?
ID: PI - 9
6
15
30
60
90
If x is a positive integer, then x(x + 1)(x + 2) is
ID: PI - 10
even, only when x is even
even, only when x is odd
divisible by 2, only when x is even
divisible by 3, only when x is odd
divisible by 5 if x â€“ 3 is divisible by 15
If k = 4m, where m is a prime number greater than 2, how many different positive odd divisors does k have?
ID: PI - 11
Zero
One
Two
Three
Four
If k = 4m + 1, where m is a prime number greater than 2, how many different positive even divisors does k have?
ID: PI - 12
Zero
One
Two
Three
Four
If x is a prime number greater than 3, what is the remainder when x^{2} + 1 is divided by 12?
ID: PI - 13
0
1
2
3
4
A gift shop sells small postcards at $0.3 and large ones at $0.7. If a customer purchases small and large postcards for a total amount of $4.3, which of the following can be the number of small postcards that the customer purchased?
ID: PI - 14
2
3
4
5
It cannot be determined.
IfÂ and a and b are integers, then which of the following must be greater than 1?
ID: PI - 15
a^{2}b
ab^{2}
a^{2}b^{2}
a + b
If x + 5 is positive, then which of the following MUST be positive?
ID: AFAVI 3
x + 4
x â€“ 6
(x + 5)(x + 6)
x^{3} + 5
(x + 5)(x + 1)
If the product of 2x and 5, added to the sum of x and 2, is equal to 123, then what is the value of x?
ID: AFAVI - 4 Â
10
11
12
Which of the following CANNOT be the value of x for the expressionÂ ?
ID: AFAVI - 7
â€“ 2
â€“Â 1
0
1
How many possible values does x have, ifÂ ?
ID: AFAVI - 8
one
two
all numbers greater than 3
all numbers smaller than -2
all numbers between -2 and 3
IfÂ , then which of the following MUST be true?
Â
ID: AFAVI - 2
x + y > 0
x â€“ y < 1
xy > 0
x + y > 1
y â€“ x < 0
The expression is equal to which of the following?
ID: AFAVI - 5
11
1
-1
-11
-13
IfÂ , then which of the of the following CANNOT be the value of k ?
ID - AFAVI 1
â€“1
0
1
2
3
Which of the following is equivalent to the pair of inequalitiesÂ andÂ ?
ID: AFAVI - 9
If and , then if is replaced by everywhere in the expression above, which of the following is the resulting expression?
ID: AFAVI - 10
What are the possible integer values of x if 2x + 3 â‰¥ 15Â andÂ Â ?
ID: AFAVI - 11
6, 7 and 8
6 and 7
7 only
7, 8 and 9
7 and 8
An operation â†’ is defined by equationÂ for all values of x and y. IfÂ and , then z equals which of the following?
ID: AFAVI - 12
0
2
x^{2}
Which of the following inequalities represents the shaded part of the number line above?
ID: AFAVI - 13
If , then which of the following is correct?
ID: AFAVI - 14
x^{3} > x^{2} > x
x >Â x^{2} > x^{3}Â
IfÂ , then what are the possible values for x?
ID: AFAVI - 15
3 and âˆ’4
3 and 4
âˆ’3 and 4
âˆ’3 and 2
3 and âˆ’2
If n is a positive integer andÂ =Â , then what is the value of n in terms of m?
ID: AFAVI - 16
m^{2} + 2
If x is an integer, then, from the given answer choices, the smallest value of |17 â€“ 5x| is when x equals which of the following?
ID: AFAVI - 17
0
1
2
3
4
A consultant whose hourly wage was increased from $100 to $125, decided to reduce the total number of daily work hours so that her daily income remains unchanged. By what percent did she decrease the number of working hours?
ID: WP1 - 1
20%
25%
50%
In a certain town elections, 60% of all eligible voters voted for Party A, while the rest voted for Party B. If 40% of all the voters were males, what percentage of the female voters voted for Party B?
ID: WP1 - 2
16%
24%
36%
60%
76%
A consumer cooperative has 600 members, of which 60% are female. If 120 additional members are going to join the cooperative next month, how many of the additional members need to be female so that the total number of female members becomes 55%?
ID: WP1 - 3
36
42
48
52
72
A certain tank contains 5,000 liters of a solution which is 10% sodium chloride, by volume. If 1,000 liters of water evaporate from that tank, what percent of the new solution is sodium chloride?
ID: WP1 - 4
5%
10%
12.5%
25%
A store used to have a constant price and monthly sales amount of oranges. However, during March the store doubled the price of oranges which resulted in reduction of the sales amounts. Due to this increase in price, and despite of reduction in sales, the total monthly income from sales of oranges remained unchanged. What was the percentage decrease in sales?
ID: WP1 - 5
20%
25%
30%
50%
Working at the same rate, 4 machines can pack a total of 360 boxes of cookies per minute. At this rate, how many boxes of cookies will 6 such machines pack in 3 minutes?
ID: WP1 - 6
720
1120
1620
1720
1800
Jackie deposited $10,000 in her savings account which pays 10% interest compounded semiannually. If 6 months after her initial investment she added $6,000 more on the same account, what will be Jackie's interest earning exactly 1 year after the initial investment?Â
ID: WP1 - 7
$1,300
$1,325
$1,600
$1,655
$1,675
Jane's weekly salary is $1,200. For any amount of weekly sales exceeding $10,000 Jane is paid a bonus of 3% of that exceeding amount. What was Jane's total earning for last week if her sales totaled to $17,500 ?
ID: WP1 - 8
$225
$525
$1,200
$1,425
$1,725
The local butcher shop opened in the morning with a stock of 60 pounds of beef, 20% of which was sold by noon. During the afternoon it sold another 20% of beef and right before closing it sold 10 more pounds. How many pounds of beef have not been sold?
ID: WP1 - 9
26
26.4
28.4
28.8
36
It would take 3 machines an hour, working at the same rate, to harvest a field of corn. In how many hours can 2 of these machines harvest 3 fields like this? Â
ID: WP1 - 10
2 hours
3 hours
3.5 hours
4 hours
4.5 hours
If Store A sold 40% more than what Store B did, and Store B sold twice less than what Store C did, what percent of Store C's sales are the sales of store A?
ID: WP1 - 11
40%
50%
60%
70%
80%
An investment company charged a $2mln commission for its client's investment profit of $100mln. Next year it charged a $3mln commission for that client's profit of $150mln. By how much did the percentage of commission change from the first to the second year? Â
ID: WP1 - 12
0%
10%
20%
33.33%
50%
A consulting company employs 10 economists, 8 biologists, and 6 mathematicians. To complete a project, 3 economists, 2 biologists, and 5 mathematicians are involved. Of all the employees, what is the percentage of economists and mathematicians who are NOT involved in the project?Â
ID: WP1 - 13
20%
25%
50%
If the postcards usually sold for $0.8 each are discounted to $0.5 each, what is the percentage change of total saving that Kelly will have if she buys 3 postcards at the discounted price?
ID: WP1 - 14
30%
37.5%
39%
66.9%
75%
In a certain company 80% of all employees are working full-time, while the rest are working part-time. Of all full-time employees, 60% received bonuses while only 10% of all part-time employees received bonuses. What percentage of all employees at this company received bonuses?
ID: WP1 - 15
50%
60%
70%
72%
80%
A tractor can ploughÂ of the field in 5 hours. How many more hours will be needed for that tractor to plough the rest of the field?
ID: WP1 - 16
3
5
7.5
12.5
13
According to the predefined budget, the project costs will sum up to $36,000 for a 12-month period. However, unexpected additional costs occur and the project has to be extended for another 6 months. What will be the average monthly cost of the project for the entire implementation period if the total cost for the additional 6 months if $9,000 ?
ID: WP1 - 17
$2,500
$2,650
$3,000
$3,750
$5,000
WhenÂ percent of 500 is added toÂ th of 500 and then the result is subtracted from 5% of 5,000, then the final result is:
ID: WP1 - 18
40
49
50
59
149
Sam filled water to the water pond, which was half-full, to 80% of its total capacity. Then, over some days, 5% of the existing water evaporated. If the evaporated amount of water was equal to 5 liters, what is the total capacity of the water pond in liters?
ID: WP1 - 19
100
105
110
120
125
Car A and Car B left Neapoli and drove towards Brindisi along the same route. Car A's speed is 50 mi/h and it left Neapoli at 3:00 p.m. Car B's speed is 60mi/h and it left Neapoli at 3:15 p.m. At what time did Car B catch up with Car A?
ID: WP1 - 20
4:30 p.m.
4:40 p.m.
4:45 p.m.
5:00 p.m.
5:20 p.m.
The daily diet of a cow consists of 12kg of mixture of maize and rye grass. Maize contains 10% of protein while rye grass contains 5% of protein. If the cow's daily diet contains a total of 950 grams of protein, how many kilograms of maize is in the mixture?
ID: WP1 - 21
4
5
6
7
8
All the postcards at a souvenir shop are currently sold at the same price. When the current price increases by 20%, 5 less postcards can be bought for $25. What is the current price of each postcard?
ID: WP1 - 22
5
6
6.5
12.5
A glass was filled with 50 grams of water, 0.4 grams of which was evaporating every day. What percent of the initial amount of water evaporated from the glass by the end of the 10^{th} day?
ID: WP1 - 23
0.04%
0.4%
4%
0.8%
8%
Jane invested $6,000 in an investment fund which pays 6% interest, compounded annually. What will be the approximate total amount of that investment in 13 years, if money invested in that fund at n percent interest, compounded annually, is approximately doubling every years?
ID: WP1 - 24
15,100
14,400
13,200
12,700
8,100
A car dealer sold n cars this month,Â of which were sedans and half of the rest were SUVs. If 20% of SUVs and 30% of sedans were red, what is the proportion of red SUVs and red sedans in all cars the dealer sold this month?
ID: WP2 - 1
Solution A, which is 200 liters, contains 5% of sodium by volume. Solution B, which is 300 liters, contains 10% of sodium by volume. If the two solutions are mixed, what is the percentage of sodium in the mixture?
ID: WP2 - 3
3%
4%
6%
8%
12%
A half-full water tank needs 5 hours to be filled toÂ of its capacity. How many more minutes will it take the tank to be filled at the same rate to its full capacity?
ID: WP2 - 4
20 minutes
40 minutes
60 minutes
200 minutes
400 minutes
In each of the poultry houses there are 5 blocks of cages. Each block has a floors and each floor has b cages in it. How many cages are there in 2 such poultry houses?
ID: WP2 - 5
5ab
10ab
There are 120 fishing boats passing monthly through the channel of Potidea. Each boat carries 7 metallic containers of fish while each container consists of 10 plastic boxes. How many plastic boxes of fish are carried by fishing boats through Potidea channel annually?
ID: WP2 - 6
1,200
8,400
10,800
84,000
100,800
The General Assembly of an agricultural cooperative consists of 120 member-farmers. To approve the purchase of the new machinery at least of member-farmers must vote in favor. At least how many member-farmers should vote against for the decision of buying the machinery NOT to pass?
ID: WP2 - 7
40
41
80
81
82
Ann has x apples which isÂ of the apples that Bill has, while Bill has 5 more apples than Charlie has. What is the number of apples that Charlie has in terms of x ?
ID: WP2 - 8
x â€“ 5
3x â€“ 5
3x
x + 5
3x + 5
Cocktail A contains 20% alcohol and 80% orange juice, by volume. Cocktail B contains 40% alcohol and 60% apple juice, by volume. If the mixture of cocktails A and B contains 30% alcohol, what percent of the volume of the mixture is Cocktail A?
ID: WP2 - 9
20%
50%
75%
Mikael has 3 more apples than oranges. How many apples does he have, if the total number of apples and oranges he has is 27?
ID: WP2 - 2
7
12
15
27
30
In a certain class of 30 students, 10 are in football team and 15 are in basketball team. There is at least 1 student who is in both football and basketball teams. What is the maximum possible number of students in this class who are in neither team?
ID: WP2 - 10
6
7
10
15
24
Of all the 150 Master students in the university, 110 are taking Econometrics course and 90 are taking Forecasting course. If at least 10 students are not taking either Econometrics or Forecasting, then the number of students taking both courses has to be a number betweenÂ
ID: WP2 - 11
0 and 60
60 and 90
20 and 110
90 and 150
20 and 150
The current ratio of boys to girls in a certain class is 5 to 4. If the number of boys is increased by 2 and the number of girls is increased by 3, what is the new ratio of boys to girls?
ID: WP2 - 12
1
It cannot be determined.
Of all the students in a certain class who took the midterm exam, got As, got Bs, got Cs, and the remaining 5 students failed the test. What is the total number of students taking the midterm exam?
ID: WP2 - 13
10
15
18
20
22
The 150 grams of water and alcohol solution contains 5 grams of alcohol. A certain amount of this solution is separated into a glass so that the amount of alcohol in that separated amount is 3 grams. How many grams of the solution is separated into a glass?
ID: WP2 - 14
80
90
100
110
120
At a certain car dealership, the ratio of the number of SUVs to the number of Trucks is 7 to 3, and the ratio of the number of Motorcycles to the number of SUVs is 1 to 4. If the ratio of Sedans to the number of Trucks is 3 to 5, what is the ratio of the number of Motorcycles to the number of Sedans?
ID: WP2 - 15
Â Â
Ann has a marbles, which is as many as John has and 3 times as Karen has. What is the total number of marbles that Ann, John, and Karen have altogether, in terms of a?
ID: WP2 - 16
The Armland has a total population of 3.6 million and its GDP (Gross Domestic Product), measured in dollars, is $1.8Â Â· 10^{10}. What is the per capita GDP, in dollars, in Armland?
ID: WP2 - 17Â
9,000
8,000
7,000
6,000
5,000
In the coordinate system above, which of the following could be the equation of line l ?
ID: CG -1
5y = â€“2x + 15
5y = 2x + 15
5y = 2x â€“ 15
â€“5y = 2x + 15
â€“5y = 2x â€“ 15
Segment AB has length of 5 and is parallel to x axis. The coordinates of the point A have integer values. How many possible options are there for such a segment AB, if it falls in boundaries betweenÂ â€“6 and 10 inclusive along x axis, and between 5 and â€“3 inclusive along y axes. Â
ID: CG - 2
88
99
108
128
153
On the graph above, when x = 0, y = âˆ’1; and when x = âˆ’1, y = 0. The graph is a parabola and represents a specific case of function y = ax^{2} + bx + c. What is the value of y when x = 5?
ID: CG - 3
-20
-32
-36
-38
-42
In the coordinate system above, the coordinates of point A are:
ID: CG - 4
(3 ; 4)
(3 ; âˆ’4)
(â€“4 ; 3)
(â€“3 ; â€“4)
(â€“4 ; â€“3)
In the coordinate system above, if point Q (not shown) lies on the negative y-axis and the area of rhombus MNPQ is 30, then what is the y-coordinate of point Q?
ID: CG - 5
âˆ’1
âˆ’3
âˆ’5
âˆ’6
âˆ’7
Point A, which has coordinates (3; 0) is the midpoint of the base of isosceles triangle XYZ, in which point Y has coordinates (3; 4). What are the coordinates of point K, if X is the midpoint of the line KY?
ID: CG - 6
(0; âˆ’3)
(âˆ’4; 0)
(0; 5)
(âˆ’3; âˆ’4)
(âˆ’3; 4)
Which of the following statements is true about the line passing through points (â€“3; â€“3) and (4; 5)?
ID: CG - 7
Crosses the origin
Passes through quadrants I, II, and III only
Passes through quadrants I and III only
Crosses the x and y axes on their negative sides
Creates a 45^{o} angle with x-axis
In the coordinate system above, the point (a; b) lies in Quadrant I. In which quadrant does the point (–b; a) lie?
ID: CG - 8
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
It cannot be determined.
The slope of the line is NOT the same as the slope of which of the following lines?
ID: CG - 9
In the coordinate system above, EB = DF and point O is in the midpoint of both BD and AC. Which of the following is true?
Â Â I.Â Â Â EF > BD
Â Â II.Â Â angle ODF < 60^{o}
Â Â III.Â AB is parallel to DC
ID: CG - 10
I only
II only
III only
I and III
I, II, and III
What is the slope of the line passing through point (−2; 3) and the origin?
ID: CG - 11
In the coordinate system above, in which quadrant will point (k; –n) lie, if point (k; n) lies in Quadrant II ?
ID: CG - 12
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
It cannot be determined
In the coordinate system above, all the lines are either parallel or vertical with respect to x-axis. What is the area of the shaded region?
ID: CG - 13
63
89
92
102
112
Two rectangular showrooms have equal areas. The first one has a length of 20 feet and a width of 6 feet. What is the width of the second show room if its length is 10 feet ?
ID: G - 1
6
10
12
14
16
A rectangular poster has a width and length in proportion 3:5. If the length is 70 centimeters, what is the width of that poster?
ID: G - 2
42
56
60
70
84
An object is flying up vertically from its starting point O. There are two observers, one at point A and one at point B. What is the distance between the observers at the moment when the object reaches point M, if OM = 4, AM = 5, and OB = 2 respectively?
ID: G - 3
1
2
3
4
5
In the figure above if y = 130^{o}, what is the value of x?
ID: G - 4
130
140
150
160
170
A circle with center O is inscribed in a square ABCD. If the distance from A to O equals m, what is the radius of the circle?
ID: G - 5
2m
m
What is the side measure of the square above if the area of the smaller shaded triangle is 7.5 and cÂ â€“ b = 2 ?
ID: G - 6
2
3
9
15
The side measure of a cube is x. If the measure of each side of that cube is doubled, what is the percentage increase in its volume measure?
ID: G - 7
20%
70%
80%
700%
800%
What is the sum of the angle measures of a, b, c, and d ?
ID: G - 8
180
270
360
420
It cannot be determined
What is the longest possible straight-line distance between any two points of a rectangular solid which has edge measures of 20, 10, andÂ ?
ID: G - 9
25
30
The circle above with center O is inscribed into the square ABCD. If the distance from A to O equals m, what is the area of the shaded region?
ID: G - 10
2m^{2}
Ï€Â·m^{2}
On his hiking trip, starting from the camp at point A, Jim walked 11km to north, then 6km to west and then 5km to south to point B. What is the distance between points A and B?Â
ID: G - 11
8
The square A and the rectangle B have equal areas. If the diagonal of square A isÂ , and the length of rectangle B is 50% larger than the side of square A, what is the width of rectangle B?
ID: G - 12
9
5
4
If a square flower bed has a diagonal length of meters, what is its perimeter?
ID: G - 13
32
64
128
Jim built an aquarium with a capacity of 1m^{3}. Then he built another aquarium with length 20% longer, width 10% wider and the same height as the first aquarium. What is the volume, in cubic meters, of the second aquarium?
ID: G - 14
1.2m^{3}
1.32m^{3}
1.35m^{3}
1.37m^{3}
1.39m^{3}
A point on the edge of a rotating wheel is 20 centimeters far from the center of the wheel. What is the distance travelled, in centimeters, by this point in 3 seconds, if the wheel is rotating at speed of 40 resolutions per minute?
ID: G - 15
80Ï€
800Ï€
1,000Ï€
1,600Ï€
2,000Ï€
The trapezoid above represents a cross section of a storage room. If the distance BD = 5, AB = 3 and CD = 2, what is the area of ABCD?
ID: G - 16
4
6
8
10
20
A rectangular rug is three times as long as it is wide. If its perimeter is 32, then what is its surface area?
ID: G - 17
24
36
48
72
144
In the figure above DE is parallel to AC. IfÂ , DB = 4, and EF = 2, what is the area of triangle ABC ?
ID: G - 18
8
12
16
18
24
The area of the parallelogram ABCD above equals which of the following?
ID: G - 19
15
What is the value of z â€“ x in the parallelogram above?
ID: G - 20
10^{o}
20^{o}
30^{o}
45^{o}
60^{o}
The figure above is not drawn to scale
In the figure above, the lines a, b, c, d, e, f, g, h, and i are all chords of the circle. Which two chords are parallel to each other?
ID: G - 21
a and e
b and f
c and g
c and h
d and h
What is the surface of quadrilateral DEFC above, if DE = 4 and DC = 20?
ID: G - 22
15
16
40
In the figure above, AC and DB are diameters of the circle with center O. What is the measure of angle a if angle BDC is 10^{o}?
ID: G - 23
110^{o}
120^{o}
145^{o}
160^{o}
170^{o}
In the figure above, ABCD is a square and AD is tangent to the circle with center O and radius of 5. What is the area of square ABCD, if AE = 8?Â
ID: G - 24
81
100
121
144
169
In the figure above, if CD = 10, AD = DB = 5, what is the length of BE?
ID: G - 25
5
10
What is the measure of angle x in the figure above, if line l_{1} is parallel to line l_{2}?Â
ID: G - 26
36^{o}
45^{o}
60^{o}
75^{o}
It cannot be determined
In the figure above, lines l_{1}, l_{2}, and l_{3} are parallel to one another. Lines AC and DF intersect the l_{1}, l_{2}, and l_{3}. What is the measure of DF, if AB = 3, BC = 4, and DE = 5?
ID: G - 27
In the figure above, ABCD is a square and BEC is an equilateral triangle. What is the measure of angle z?
ID: G - 28
7.5
15
30
45
60
There are 10 teams participating in a tournament. If each teams plays every other team exactly 2 games and if each game can only be played by two teams, how many games in total have been played during the tournament?
ID: CP - 1
20
50
90
100
200
On his hiking trip from Thira to Kamari, Kevin may choose any of the paths as drawn above. How many different paths may Kevin choose for his trip?
ID: CP - 2
6
9
12
18
24
A certain cafe offers 4 varieties of ice-cream: chocolate, vanilla, cappuccino, and cherry. Charlie can choose 3 different cups for an ice-cream: small, medium, and large. In addition, the cafe offers 2 different toppings for any ice-cream: nuts and cookies. If Charlie chooses and ice-cream in a cup with one of the toppings, how many different combinations can he choose?Â
ID: CP - 3
6
9
12
18
24
In how many ways can a Board of Trustees of 6 people be formed from 4 men and 5 women, so that at least 4 women are on the Board?
ID: CP - 6
17
34
68
136
272
The Verenia Tech University, Perdain University and the Menevan State University each have 6 soccer players. If a team of 12 soccer players needs to be formed with equal number of players from each university, how many different teams can be formed in total?Â
ID: CP - 7
15
30
45
60
15^{3}
A local restaurant offers for lunch 2 types of salads, 4 types of burgers, and 3 types of soda. How many possible lunch combinations can Bill choose? (a lunch must contain a salad, a burger, and a soda).
ID: CP - 8
2! Â· 4! Â· 3!
2! + 4! + 3!
2 Â· 4 Â· 3
6
In how many ways can a group of 2 boys and 4 girls be formed from 5 boys and 6 girls?
ID: CP - 9
150
160
170
180
200
How many different options can a 4-digit banking card PIN code have?
ID: CP - 10
10!
10! Â· 4
9 Â· 10^{3}
10^{4}
By the end of the working day there are only 10 flowers of different types left in a flower shop. This shop sells flowers in bouquets. How many different 4-flower bouquets containing 4 different types of flowers can the shop offer?
ID: CP - 11
10 Â· 9 Â· 8 Â· 7
210
105
If there are 13 teams in the chess tournament and each team plays with the other team exactly one game, what is the total number of games played at that tournament?
ID: CP - 4
12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
13!
12!
13^{2}
A company is hiring to form a three-person management team for a project. The project requires a Project Manager, a Researcher, and an Accountant. If there are 4 candidates for Project Manager's position, 5 for Researcher's position, and 2 for Accountant's position, how many different hiring options are possible?
ID: CP - 5
4 + 5 + 2
4 Â· 5 Â· 2
(4 + 5 + 2)^{3}
(4 + 5 + 2)!
4! + 5! + 2!
Cards numbered consecutively from 101 to 200 inclusive are placed in a box. What is the probability that a card picked randomly from the box will be divisible by both 2 and 3, and will have 5 or 6 in its tenths digit?
ID: P - 1
In a backgammon tournament Ann first plays with Ben and then whoever wins plays with Kevin. There is a 25% chance that Ann will win Ben and aÂ probability that Kevin will lose in a game with Ann. What is the probability what Ann will win both Ben and Kevin?
ID: P - 2
0
The 70% of all students in a certain class are female, half of which are members of the student club. If a student is picked at random from the class, what is the probability that it is a female student and is a member of a student club?
ID: P - 3
0.2
0.25
0.3
0.35
0.4
z is a set of numbers which contains all integers from 20 to 40 inclusive. Each number in set z has a formula n + 2, where n is a prime number greater than 20. What is the probability that a number picked at random from set z is divisible by 3?Â
ID: P - 4
0
In a certain classroom there are g girls and b boys. One of the girls leaves the classroom and 3 boys enter the classroom. If one student is now picked at random from that classroom, what is the probability that it is a girl?
ID: P - 5
Andy and Mike are playing a game of shooting at targets. Each of them shoots 3 times. At each shooting, Andyâ€™s and Mikeâ€™s probabilities to hit the targets areÂ andÂ respectively. What is the probability that Andy will only hit the target at his third shooting, and Mike will not hit his target at all.
ID: P - 6Â Â
X = { 4, 5, 6, 7 }
Y = { 1, 2, 3 }
If two integers are randomly selected from the two sets above, one from set X and one from set Y, what is the probability that the product of these integers is divisible by 4?
ID: P - 7
X = { 4, 5, 6, 7 }
Y = { 1, 2, 3 }
If two integers are randomly selected from the two sets above, one from set X and one from set Y, what is the probability that the sum of these integers is a prime number?
ID: P - 8
John needs to pass Math and Physics exams. The probability that he will pass the Math exam is , and the probability that he will pass the Physics exam isÂ . What is the probability that John will pass both Math and Physics exams.Â
ID: P - 9
The shop assistant has 10 different dresses, each priced differently. If the shop assistant chooses 3 dresses to present on the display, what is the probability that she chooses the 3 most expensive dresses?
ID: P - 10
Two standard six-sided dice are rolled once. What is the probability of getting exactly one 3 on the top of the faces?
ID: P - 11
There are 4 boys and 6 girls in the room. If two of them are asked to go out, what is the probability that at most 1 of them is a boy?
ID: P - 12
There are 4 boys and 6 girls in the room. If 1 of them leaves the room, what is the probability that it is a girl?
ID: P - 13
A coin is tossed five times. What is the probability of having tales appear at least 4 times?
ID: P - 14