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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. A fair cube is one that is labeled with the numbers 1, 2, 3, 4, 5, and 6 such that there is an equal probability of rolling each of those numbers. If jade rolls two fair cubes at the same time then what is the probability that the product of the two numbers she rolls will be greater than 18?

    1. 0.222
    2. 0.568
    3. 0.7
    4. 0.3
    5. 0.658

    Answer (a)

    Explanation: If you want to find the probability first find out the total number of possibilities and then figure out how many meet the condition you want. Since there are 6 possible rolls on a fair cube, the total number of possibilities for two rolls is 6 * 6 = 36. Now you are required to figure out all the ways to get product greater than 18. The rolls that will work are 4 * 5, 4 * 6, 5 *5, 5 * 4, 6 * 5, 6 * 6, 6 *4, 5 * 6. That's 8 rolls out of 36 which is a probability of 8/36 = 0.222

  2. If f(x) = 4x2+4x+4, which of the following is equal to f(-3.5)?

    1. f9
    2. f89
    3. f(2.5)
    4. f78
    5. f(5.7)

    Answer (c)

    Explanation: You require a graphing calculator, you need to press the Y key and enter the function. You will check the value of the Table you can find that f(-3.5) and f(2.5) both are equal to 39. But if you do not possess graphing calculator, you can make the use of PITA.

  3. Which of the following has the greatest value?

    1. 4400
    2. 290600
    3. 1.798
    4. 36
    5. 78

    Answer (a)

    Explanation: The important fact about this interesting question is that it not essential to find the accurate value of the expression. You need to rearrange as many answer choices as possible so that they possess the exponents of 100. Take a close look on each an expression 290600, 36, 78, 1.798, 4400. It will make clear that (a) is bigger than (c), therefore the answer is (a)

  4. Which of the following represent the solution set of Ιx3 - 8Ι ≤ 5?

    1. 2.5 ≤x ≤ 1.98
    2. 8.6  ≤x ≤ 1.23
    3. 8.5 ≤x ≤ 1.21
    4. 1.44 ≤ x ≤ 2.35
    5. 0.5 ≤x ≤ 1.81

    Answer (d)

    Explanation: In this problem choose a simple number that is in some, but not all of the ranges in the answer choices. Assume x = 1 this gives you [(1)3- 8] ≤ 5, which means 7 ≤ 5, but this is not correct. Remove any answer choice that includes one. Now use x = 2, this comes to [(2)2 - 8]≤ 5, which simplifies to 0 ≤ 5, therefore the answer is (d)

  5. The researcher finds that an ant colony's population increases by exactly 8% each month. If the colony has an initial population of 1,250 insects, which of the following is the nearest approximation of the population of the colony two years later?

    1. 7,926
    2. 5,879
    3. 4,213
    4. 7,984
    5. 2,125

    Answer (a)

    Explanation: You are require to use the formula Final = Original * (1 + rate)# of changes This colony has a original size of 1,250 and increases by 8% each month. In 2 years it will make 24 of these increases. If you will pay attention you will find that final = 7,926.456 which is very close to the option (a).

  6. What is the distance between the x intercept and the y intercept of the line given by the equation

    2y = 6 - x?

    1. 8.56
    2. 2.45
    3. 6.71
    4. 5.64
    5. 1.89

    Answer (c)

    Explanation: To find the y - intercept just make x = 0 and solve for y. Y= 3. Now to find the x intercept, make y = 0 and solve for x. You will see that they form a right angle triangle with length of 3 and 6, in which the hypotenuse represents the distance in between the  two distinct points. You are required to used Pythagoras theorem to find the length of the hypotenuse, which will be equal to 6.7156 approximately; therefore the answer is (c).

  7. If 0 < q < 1 then all of the following must be true except:

    1. Q3 < n
    2. q < cube root of q
    3. q < q
    4. -q < q
    5. q < 1/q

    Answer (c)

    Explanation: Apply 0.5 in place of q and try to solve the equation. Now q2 = 0.25, square root of q = 0.707, q = 0.5, - q = - 0.5, -q = -0.5, and 1/q = 2. This makes A B D and E true, therefore (c) is false.

  8. If x - 3 = 3 (2- x), then what is the value of x?

    1. 0.33
    2. 0.87
    3. 8.80
    4. 1.87
    5. 2.55

    Answer (a)

    Explanation: The fraction b/a is a reciprocal of a/b. To find the numerical value of b/a, just change the numerical value of a/b, which comes to 0.625. Your calculation will tell you that 1/0.625 = 1.6.

  9. If the cube root of the square root of a number is 3, what is the number?

    1. 19
    2. 54
    3. 148
    4. 286
    5. 1,094

    Answer (b)

    Explanation: Translate the whole into math's 3√x = 3. Now take away. First cube both sides. √x = 8. Now square both sides; x = 54

  10. What is the slope of the line given by the equation

    Y = 3 = 5/4(x - 7)?

    1. 7/4
    2. 8/1
    3. -3/4
    4. 2/4
    5. 5/4

    Explanation: You might observe that this is the point slope form and that the slope is 5/4, if you are still not clear you can rewrite the equation into the slope intercept form.

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