In the xy-plane, line l has x-intercept 3 and y-intercept 4, and line m has x-intercept 4 and y-intercept 3.Quantity AThe slope of line lQuantity BThe slope of line m
Answer(s): B
Line l passes through (3, 0) and (0, 4), so its slope isLine m passes through (4, 0) and (0, 3), so its slope is
When the positive integer n is divided by 7, the remainder is 2.Quantity AThe remainder when 2n + 1 is divided by 7Quantity B5
Answer(s): C
n 2 (mod 7).Then 2n + 1 2 × 2 + 1 = 5 (mod 7).
Quantity AThe greatest prime factor of the product (88)(693)Quantity B11
Factor 88: 88 = 8 × 11 = 23 × 11.Factor 693: 693 = 7 × 99 = 7 × 9 × 11 = 32 × 7 × 11.Product (88)(693) has prime factors 2, 3, 7, 11.The greatest prime factor is 11.
For the frequency distribution of the variable x shown in the table above, what is the median value of x?
Total number of data values = 4 + 15 + 10 + 8 + 6 + 2 + 2 = 47.The median is the 24th value.Cumulative frequencies:Up to 15: 4Up to 16: 4 + 15 = 19Up to 17: 19 + 10 = 29The 24th value falls in the 17 group, so the median is 17.
Which of the following is NOT equivalent to x(y + z) - y(x + z)?
Answer(s): D
x(y + z) - y(x + z) = xy + xz - yx - yz = xz - yz = z(x - y).So any equivalent form must simplify to z(x - y).z(x + y) is not equal to z(x - y) in general.
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