Toiya Original ISEE Upper Level Practice Test 3 — Quantitative Reasoning.
37 questions · Free online practice
Open the interactive worksheetQuestion 1
The graph shows Maya’s distance from home as she rides her bike home from practice. At one point during the ride, Maya stopped for several minutes to talk with a friend. How far was Maya from her home when she stopped? A. 6 miles B. 7 miles C. 10 miles D. 12 miles
Question 2
A figure is made by stacking cubes, as shown. Which could represent the top view of the figure? A. B. C. D.
Question 3
The ribbons in a craft box have a mean length of 56 centimeters. Lia trims 9 centimeters from every ribbon. What is the mean length of the ribbons after they are trimmed? A. 38 cm B. 47 cm C. 56 cm D. 65 cm
Question 4
A student answered \(75\%\) of the questions on a quiz correctly. Which could be the exact number of questions answered correctly and answered incorrectly? A. 15 correct, 20 incorrect B. 12 correct, 6 incorrect C. 15 correct, 5 incorrect D. 9 correct, 4 incorrect
Question 5
Triangles \(A\) and \(B\) are similar. What is the length of the side with the question mark? A. 5.5 inches B. 8.5 inches C. 11 inches D. 16.5 inches
Question 6
Rectangle \(ABCD\) is shown. Point \(M\) is the midpoint of side \(DC\). What is the area of \(\triangle BCM\)? A. \(20\text{ cm}^2\) B. \(40\text{ cm}^2\) C. \(60\text{ cm}^2\) D. \(80\text{ cm}^2\)
Question 7
A class of 25 students earned a mean score of \(84\%\) and a median score of \(82\%\) on a test. Only three students scored below \(60\%\). If those three students retook the test and scored \(62\%\), \(70\%\), and \(78\%\), which statement would be true? A. The mean and median would both increase. B. The median would increase, and the mean would remain unchanged. C. The mean would increase, and the median would remain unchanged. D. The mean and median would both stay the same.
Question 8
If the sum of all integers from 1 to 300, inclusive, is \(S\), which expression represents the sum of all integers from 1 to 296, inclusive? A. \(S+1{,}194\) B. \(S-297\) C. \(S-894\) D. \(S-1{,}194\)
Question 9
If \(m\) is a positive integer and \((x+7)^2=x^2+mx+49\), what is the value of \(m\)? A. 7 B. 14 C. 28 D. 49
Question 10
If \(3k+1=k\star\), what is the value of \(4\star\)? A. 4 B. 7 C. 12 D. 13
Question 11
The area of a rectangular garden is 60 square meters. If the length and width are both whole numbers of meters, what is the least possible perimeter of the garden? A. 31 m B. 32 m C. 34 m D. 38 m
Question 12
If \(\tfrac14a+\tfrac14b=-3\), what is the value of \(2a+2b\)? A. \(-24\) B. \(-12\) C. \(-6\) D. \(-3\)
Question 13
The incomplete bar graph shows the quiz scores in a class. The mean and median of the scores are both 72, and the data is symmetric around this score. If the range of the data is 12 and the minimum score is 66, how many students scored 67, 70, 75, or 78? A. 8 B. 10 C. 13 D. 20
Question 14
If \(x\) is a multiple of 6 and \(y\) is a multiple of 10, what is the least possible positive value that could be a multiple of \(xy\)? A. 16 B. 30 C. 60 D. 120
Question 15
A drawer holds 8 red socks, 4 green socks, and 9 blue socks. What is the minimum number of socks that must be taken out, without looking, to guarantee at least one sock of each color? A. 3 B. 9 C. 17 D. 18
Question 16
If the base of a triangle is increased by 30 percent and its height is decreased by 20 percent, by what percent does the area of the triangle increase? A. \(4\%\) B. \(6\%\) C. \(10\%\) D. \(50\%\)
Question 17
The ratio of the radius of Sphere \(P\) to the radius of Sphere \(Q\) is 2 to 5. Which statement could be true? (Surface area of a sphere \(=4\pi r^2\)) A. The surface area of Sphere \(Q\) is 2.5 times the surface area of Sphere \(P\). B. The surface area of Sphere \(Q\) is 5 times the surface area of Sphere \(P\). C. The surface area of Sphere \(Q\) is 6.25 times the surface area of Sphere \(P\). D. The surface area of Sphere \(Q\) is 15.625 times the surface area of Sphere \(P\).
Question 18
What is the sum of the two smallest factors shared by 50 and 75? A. 5 B. 6 C. 10 D. 30
Question 19
Quantity A Quantity B \(3(x^2+2)\) \(3x^2+5\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 20
\(y=3x,\ t=3^x\) Quantity A Quantity B The value of \(y\) when \(x=3\) The value of \(t\) when \(x=3\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 21
A 6-sided die numbered 1–6 is rolled, and a spinner divided into 3 equal sections colored red, blue, and yellow is spun. Quantity A Quantity B The probability of rolling a number greater than 4 The probability that the spinner lands on red A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 22
A bag holds cards numbered 11 through 19, one card for each number. Quantity A Quantity B The probability of choosing a multiple of 3 The probability of choosing a number greater than 16 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 23
A shelf holds only novels and comic books. There are 4 times as many novels as comic books, and there are 45 books in all. Quantity A Quantity B The number of novels 30 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 24
Both \(a\) and \(b\) are positive integers. \(a+b=15\) and \(2a-b=-3\). Quantity A Quantity B \(a\) \(b\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 25
The area of Rectangle G is \(64\text{ ft}^2\). Quantity A Quantity B \(m\) \(n\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 26
A store’s sales in April were \(\$80{,}000\). Sales in May were \(20\%\) lower than in April. Sales in June were \(20\%\) higher than in May. Quantity A Quantity B The sales in June \(\$80{,}000\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 27
The figure is a square with side \(y\). The white band has height \(x\). Quantity A Quantity B Area of the shaded region \(y^2-x^2\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 28
The sum of the interior angles of a polygon with \(n\) sides is \(180(n-2)\). Quantity A Quantity B The measure of an interior angle of a regular pentagon The measure of an interior angle of a regular octagon A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 29
A museum had 2,000 visitors in June. In July, the number of visitors was \(25\%\) higher than in June. In August, the number was \(20\%\) lower than in July. Quantity A Quantity B The number of visitors in August 2,000 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 30
Quantity A Quantity B Area of the shaded region \(\pi(y-x)^2\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 31
Seven people meet, and each person shakes hands once with every other person. Quantity A Quantity B The total number of handshakes 20 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 32
\(x>0\) Quantity A Quantity B \((x-3)^2\) \(x^2+9\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 33
Rosa has \(\$1.87\) in coins. Each coin is a quarter, dime, nickel, or penny. (1 quarter \(=\$0.25\); 1 dime \(=\$0.10\); 1 nickel \(=\$0.05\); 1 penny \(=\$0.01\)) Quantity A Quantity B The smallest number of coins Rosa could have 10 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 34
\(n\) is a positive odd integer. Quantity A Quantity B \(-2^n\) \((-2)^{n+1}\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 35
The surface area of Cube A is \(150\text{ cm}^2\). The volume of Cube B is \(64\text{ cm}^3\). (\(SA=6a^2\) and \(V=a^3\), where \(a\) is the edge length.) Quantity A Quantity B \(x\) \(y\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 36
The two right triangles are not drawn to scale. Quantity A Quantity B \(3y\) \(z\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Question 37
The area of a rectangle is \(36\text{ cm}^2\). Quantity A Quantity B The perimeter of the rectangle 24 cm A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.