Manhattan
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$$10 ^{5} – 560 $$ is divisible by all of the following EXCEPT:
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Manhattan
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Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?
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Manhattan
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How many units long is the straight line segment that connects the points (-1,1) and (2,6) on a rectangular coordinate plane?
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Manhattan
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If the side length of Square B is twice that of Square A, the area of Square B is how many times the area of Square A?
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Which of the following is the second greatest?
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Given the circle to the right, with center O, diameter AOB, a radius of 5, and the inscribed triangle ABC, what is the length of AC?
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John was 27 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now $$\frac{7}{8}$$ of John's. How old is Betty?
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Manhattan
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There are X girls in a class, and their average height is M inches. In the same class, there are Y boys with an average height of N inches. What is the average height of all the students in the class?
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If $$x^{2} – 4x = 5$$, then one possible value of x – 4 =
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Manhattan
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In the figure to the right, what is the value of x?Note: Not drawn to scale.
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Manhattan
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What is the slope of the line represented by the equation x + 2y = 1?
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Manhattan
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Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete$$ \frac{1}{2}$$ of the same production lot in z hours. What is the value of y in terms of x and z?
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Manhattan
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Two circles share a center at point C, as shown to the right. Segment AC is broken up into two shorter segments, AB and BC, with dimensions shown. What is the ratio of the area of the large circle to the area of the small circle ?
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Manhattan
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If a, b, c, and d are integers and$$ ab^{2}c^{3}d^{4} > 0$$, which of the following must be positive? I. $$a^{2}cd $$II. $$bc^{4}d $$III.$$ a^{3}c^{3}d^{2} $$
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Manhattan
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Pablo plays 3 rounds of a game, in which his chances of winning each round are$$\frac{1}{3} ,\frac{1}{6} , and\frac{1}{n}$$ , respectively. If$$ n \neq 0$$, what is the probability that Pablo wins the first two rounds, but loses the third?
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Manhattan
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Two buses and a van were employed to transport a class of students on a field trip. $$\frac{3}{5}$$ of the class boarded the first bus. $$\frac{2}{3}$$ of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down,$$\frac{ 1}{2}$$ of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
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Manhattan
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If a and b are positive integers and$$ x = 4^{ a} and y = 9^{ b}$$, which of the following is a possible units digit of xy?
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Manhattan
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When a is divided by b, the quotient is c and the remainder is d. Which of the following expressions is equal to d?
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Manhattan
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If$$ 9^{2x + 1} = 27^{2}$$, then x =
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Manhattan
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Jack pours water into a bucket until the bucket is filled to 60% of its capacity. Jill then fills the bucket to capacity by pouring an additional $$\frac{2}{3}$$ of a gallon of water into the bucket. What is the capacity of the bucket, in gallons?
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