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Math

By Sarah Watson,2014-12-12 17:25
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SAT math

Mathematics >

    1. There are n students in a biology class, and only 6 of them are seniors. If 7 juniors are added to the class, how many students in the class will not be seniors? Answer Choices

    ; (A) n-3

    (B) n-2 ;

    ; (C) n-1

    (D) n+1 ;

    ; (E) n+2

    Explanation

    Choice (D) is correct. At first, there are n students in the class, and 6 of them are seniors. It follows that initially n-6 students are not seniors. If 7 juniors are added to the class, there will be n-6+7, or n+1, students in the class who are not seniors. 2. For how many positive two-digit integers is the ones digit greater than twice the tens digit?

    Answer Choices

    ; (A) 16

    ; (B) 20

    ; (C) 28

    ; (D) 32

    ; (E) 36

    Explanation

    Choice (A) is correct. If the tens digit is 1, there are 7 positive two-digit integers with the ones digit greater than twice the tens digit13, 14, 15, 16, 17, 18 and 19. If the tens

    digit is 2, there are 5 positive two-digit integers with the ones digit greater than twice

    the tens digit 25,26,27,28 and 29. If the tens digit is 3, there are 3 positive two-digit integers with the ones digit greater than twice the tens digit: 37, 38 and 39. If the tens digit is 4, there is 1 positive two-digit integer with the ones digit greater than twice the tens digit: 49. If the tens digit is equal to or greater than 5, then the ones digits, which cannot be greater than 9, is not greater than twice the tens digit. Therefore, there is a total of 7+5+3+1=16 positive two-digit integers for which the ones digit is greater than twice the tens digit.

    3. If the graph of the function f is a line with slope 2, which of the following could be the equation of f?

    Answer Choices

    ; (A) f(x)=4x-2

    ; (B)f(x)=2x+4

    ; (C)f(x)= -2x-2

    ; (D)f(x)=1x/2+2

    ; (E)f(x)= -1x/2+1/2

    Explanation

    Choice (B) is correct. The graphs of all the given functions are lines, and the equations are all in the form y=mx+b. When a linear equation is in the form y=mx+b, the slope of the graph of the equation is m, the coefficient of x. The graph of the function f is a line with slope 2, so the only choice that could be the equation of f is f(x)=2x+4.

    4. A line segment containing the points (0,0) and (12,8) will also contain the point Answer Choices

    ; (A) (2,3)

    ; (B) (2,4)

    ; (C) (3,2)

    ; (D) (3,4)

    ; (E) (4,2)

    Explanation

    Choice (C) is correct. The slope of the line containing the points (0, 0) and (12, 8) is 8/12, or 2/3. If (x, y) is another point on this line segment, then x and y must satisfy y/x=2/3, or y=2x/3. Of the five choices, (3, 2) is the only point for which y=2x/3. 5. In a community of 416 people, each person owns a dog or a cat or both. If there are 316 dog owners and 280 cat owners, how many of the dog owners own no cat? Answer Choices

    ; (A) 36

    ; (B) 100

    ; (C) 136

    ; (D) 180

    ; (E) 316

    Explanation

    Choice (C) is correct. To solve this problem, you must realize that some of the 316 dog owners also own cats and some of the 280 cat owners also own dogs. This has to be true because 316+280 is more than 416! The question asks how many of the dog owners do not own cats. To solve the problem, first find the number of people who own both a dog and a cat. To do this, let b equal the number who owns both a dog

    and a cat. Then 416=316+280-b. (Note: Adding 316 and 280 counts b twice, so b must be subtracted from the sum to get 416.) Next, the equation 416=596-b can be solved for b, yielding b=180. Finally, the number of dog owners who own no cat is 316-180=136.

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