The median of the five numbers 2, 6, 7, 9, and x is 6.Quantity AxQuantity B3
Answer(s): D
To keep the median (third number when ordered) equal to 6, the five numbers in ascending order must have 6 in the middle position.Possible cases for x:Case 1: x 2Ordered list: x, 2, 6, 7, 9 median = 6.Case 2: x = 6Ordered list: 2, 6, 6, 7, 9 median = 6.Any other value of x would move the middle value away from 6.Thus, x can be 2 (less than 3) or equal to 6 (greater than 3).Because x could be either less than 3 or greater than 3, the two quantities cannot be definitively compared.
The surface area and the volume of a spherical marble are s square centimeters and v cubic centimeters, where s = v.What is the radius, in centimeters, of the marble? (Note: The surface area of a sphere with radius r is 4r2, andthe volume of a sphere with radius r is .)
Answer(s): C
For a sphere of radius r:Given s = v, we set the two formulas equal:Divide both sides by 4r2 (r > 0):
FILL BLANKIf u postage stamps were divided evenly among 4 people, each person would receive v postage stamps. If the u postage stamps were divided evenly among 8 people, each person would receive x postage stamps. If v x = 26, what is the value of u?
Answer(s): A
Dividing the u stamps evenly givesGiven v - x = 26:
The operation is defined by ab = a2 + 2ab for all numbers a and b.Which of the following is equal to (2x)(3x2)?
Answer(s): E
Using the definition ab=a2+2ab,(2x)(3x2) = (2x)2 + 2(2x)(3x2) = 4x2 + 12x3
What is the remainder when 327 is divided by 5?
Powers of 3 modulo 5 repeat in a cycle of length 4:31 = 3 (mod 5)32 = 9 = 4 (mod 5)33 = 4 × 3 = 12 = 2 (mod 5)34 = 2 × 3 = 6 = 1 (mod 5).Because the pattern 3, 4, 2, 1 repeats every 4 powers, reduce the exponent 27 modulo 4:27 mod 4 = 3.Hence327 33 2 (mod5).The remainder when 327 is divided by 5 is 2.
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