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In the figure above, what is the value of ?
A. 56B. 128C. 256D. 264E. 322
2. If f (x) =x2 - 4, for what positive value of x does f (x) = 32?
A. 5B. 6C. 7D. 8E. 9
3. A can of mixed nuts contains cashews, almonds, peanuts, and walnuts in the ratio of 2 to 4 to 5 to 7, respectively, by weight. What fraction of the mixture by weight is almonds?
A. B. C. D. E.
4. Twenty students in a chemistry class took a test on which the overall average score was 75. If the average score for 12 of those students was 83, what was the average score for the remaining members of the class?
A. 60B. 61C. 62D. 63E. 64
In the figure above, the vertices of square EFGH are on the diagonals of square ABCD. If and what is the sum of the lengths (heavier lines)?
A. 24B. 28C. 32D. 36E. 38
In the correctly worked addition problem above, each letter represents a different nonzero digit. What is the value of 2R + T?
A. 4B. 5C. 10D. 11E. 13
7. If , what is the value of ?
A. 3B. 7C. 16D. 23E. 30
8. If one serving of cereal is cup, how many servings are in 3 pints of cereal? (1 pint = 2 cups)
A. 3B. 9C. 18D. 27E. 36
If the radius of the circle with center O above is 4, what is the length of arc RST?
A. 2πB. 4πC. 8πD. 12πE. 16π
In the triangle above, what is the value of x?
A. 7B. C. D. E.
11. For , let ?x be defined by the equation . Which of the following is equivalent to
A. ▽2B. ▽3C. ▽6D. ▽8E. ▽9
12. Stephanie can clean a pool in 1 hour, and Mark can clean the same pool in 1.5 hours. If the rate at which they work together is the sum of their rates working separately, how many minutes should they need to clean the pool if they work together? (1 hour = 60 minutes)
A. 24 minutesB. 36 minutesC. 60 minutesD. 72 minutesE. 100 minutes
13. Which of the following has the greatest value?
A. (1003)4B. (1005)(1006)C. (10,000)4D. (1002 × 1002)2E. (1,000,000)3
Line m (not shown) is the reflection of line l over the x-axis. What is the slope of line m?
A. 3/2B. 2/3C. 0D. -2/3E. -3/2
15. If and , what is the value of ?
A. 10B. 12C. 14D. 16E. 18
The figure above shows the dimensions, in feet, of a stone slab. How many of these slabs are required to construct a rectangular patio 24 feet long and 12 feet wide?
A. 18B. 20C. 24D. 36E. 48
17. $12,000 in winnings for a golf tournament were distributed in the ratio of 7:2:1 to the first-, second-, and third-place finishers, respectively. How much money did the first-place finisher receive?
A. $1,200B. $1,700C. $2,400D. $8,400E. $10,000
18. If and, what is the value of ?
A. 5B. 8C. 15D. 17E. 19
19. If r and s are positive integers and , which of the following must be true?
I. s is odd
II. r is even
is an integer
A. I onlyB. III onlyC. I and II onlyD. I and III onlyE. I, II, and III
20. A bag contains six chips, numbered 1 through 6. If two chips are chosen at random without replacement and the values on those two chips are multiplied, what is the probability that this product will be greater than 20?
In the sequence above, each term after the second is equal to the product of the two preceding terms. For example, the third term, -8, is the product of 2 and -4. How many of the first 100 terms of this sequence are negative?
A. 33B. 34C. 50D. 66E. 67
In the figure above, points C and D are midpoints of edges of a cube. A triangle is to be drawn with R and S as two of the vertices. Which of the following points should be the third vertex of the triangle if it is to have the largest possible perimeter?
A. AB. BC. CD. DE. E
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