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SAT Sample Questions » Quantitative Section : Quantitative Ability

SAT Sample Questions

Quantitative Section : Quantitative Ability

Below are the few questions on Multiple Choices. Choose the correct answer from the following questions

  1. In the above figure sin angle BAC =

    1. 5/13
    2. 8/45
    3. 14/15
    4. 34/12
    5. 12/18

    Answer (a)

    Explanation: In a right angle triangle the sine of an angle equals the length of the opposite side over the length of the hypotenuse. You can easily find the length of the opposite side over the length of hypotenuse. You can easily find the length of sides AB and BC. The hypotenuse length can be found with the Pythagorous theorem. To find the sine of angle BAC, then you just need to find the value of BC/AC which equals to 5/13.

  2. 15!/13!2! =

    1. 54
    2. 78
    3. 91
    4. 105
    5. 312

    Answer (d)

    Explanation: You need to expand the factorials in the fraction 15!/13!2!, then you get

    15*14*13*11*12*9*10*7*6*5*3*4*2*1

    --------------------------------------------

    (13*12*11*9*10*8*7*6*5*4*2*3*1)(1*2)

     

    You will observe that every factor from 1 to 13 in the numerator is also in the denominator, it is only left with 15*14/2*1 or 210/2 which comes to 105.

     

  3. If f(x) = |x| + 10 for which of the following values of x does f(x) = f(-x)?

    1. 15 f
    2. 18x
    3. All real x
    4. 10 except x
    5. 10x

    Answer (c)

     

    Explanation: To start with the equation the statement f(x) = f(-x) when x = -10 and 10. A simple number like zero works best. f(0) = Ι0Ι + 10 = 10. You can see that f(0) = f(-0) so zero must be the part of correct answer, therefore (c) is the correct option.

  4. If f(x) = 3√x and g(x) = ½ √x + 1, then f (g(2.3)) =

    1. 5.4
    2. 1.2
    3. 8.6
    4. 4.3
    5. 2.8

    Answer (b)

    This is a compound question, in which you are required to apply two functions in combination. You require to place the numbers 2 and 3 in place of x is the definition of g(x) g(2,3) = ½ √2.3 is equal to f (1.76), which can easily be solved by f(1.76) = 2√1.76 = 1.21. The correct option is (b).

  5. If x mod y is the remainder when x is divided by y, then (61 mod 7) - (5 mod 5) =

    1. 9
    2. 10
    3. 6
    4. 5
    5. 63

    Answer (d)

    Explanation: To find the value of y and x just take the number as the x position and divide it by the number in y position. The remainder is the value of x and y of those numbers. The value of 61 and 7 is 5. The expression (61 mod 7) - (5 mod 5) can be rewritten as 5 - 0 which equals 5. Therefore the correct answer is (d).

  6. Which of the following must be true?
    1. Sin(- ?) = -Sin ?
    2. Cos (- ?) = -cos ?
    3. Tan (- ?) = - tan ? (Where tan ? is defined
     

    1. 1 and 2 only
    2. 1 only
    3. 3 and 2 only
    4. 1 and 3 only
    5. 2 only

    Answer (d)

    Explanation: You need to solve this question by using the trignometry theory. Place the few numbers for example angles between 0° and 90°, you will soon find out that statement 1 and 3 always will be true, but it's easy to find an exception to statement 2, therefore the right answer is (d)

     

  7. If the ratio of sec x to csc x is 1:4, then the ratio of tan x to cot x is

    1. 1:16
    2. 2:7
    3. 5:6
    4. 8:14
    5. 3:8

    Answer (a)

    Explanation: The ratio which is given can be written in fractional form like sec x/csc x = ¼. The secant and cosecant can also be expressed in terms of sine and cosine. 1/cos x/1/sin x = ¼. The cotangent is the reciprocal of the tangent so cot x = 4. Therefore the correct answer would be (a)

  8. If a/b = 0.595, then b/a is equal to which of the following?

    1. 6.45
    2. 2.67
    3. 8.41
    4. 9.13
    5. 5.15

    Answer (b)

    Explanation: Make the base on both sides of the equation the same. 243 is similar as 35. So 35x  = 35, which means that x = 1

  9. The distance between the points (-3, 6) and (-3, -14) is

    1. √15
    2. 56
    3. 4
    4. 17
    5. √25

    Answer (d)

    Explanation: Notice that the x coordinate in both points is the same. So you just have to find the difference in the y coordinates. The difference is 6 - (-14) = 17

  10. If x - 5 = 5 (1 - x), then what is the value of x?

    1. 0.33
    2. 2.78
    3. 9.45
    4. 8.45
    5. 6.45

    Answer (a)

    Explanation: The fraction b/a is a equal to a/b. To find the numerical value of b/a just turn the numerical value of a/b; this  comes to 0.625. Your calculation will tell you that 1/0.625 = 1.6.

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