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SAT Sample Questions » Quantitative Section : Quantitative Ability

Quantitative Section : Quantitative Ability

Given below are a few important questions on Multiple Choices with answers and explanation. Select the right answer from the following questions.

1. Seven pink marbles and six yellow marbles are held in a single container. Marbles are randomly selected one at a time and not returned to the container. If the first two marbles selected are pink. What is the probability that at least two marbles will be chosen in the next three selections?

1. 712
2. 78/56
3. 87.78
4. 19/33
5. 8/6

Explanation: You are given a container that holds five pink marbles and six yellow marbles. Here is the probability 6/11 * 5/10 * 5/9 * = 150/990 = 5/33

There are six yellow marbles out of the total of eleven on the first drawing and 5 red marbles out of ten and five pink marbles out of nine. Therefore the total probability of drawing

6/11 * 5/10 * 5/9 = 150/990 = 5/33

Therefore the correct answer would be (d)

2. If (s - 3) = 4s - 7, then which of the following could be the value of s?

1. 12
2. 843
3. 78
4. 2
5. 29

Explanation: The first equation is s - 3 = 4s - 7, which simplifies to s = 4/3 but this is not the answer. Let us look at the second equation -(s - 3) = 4s - 7. This simplifies to 3 - s = 4s - 7 that means 5s = 10 and s = 2.

3. If (k - 3) = 4k - 7, then which of the following could be the value of k?

1. 324
2. 124
3. 13
4. 2
5. 43

Explanation: The first equation is k - 3 = 4k - 7, which simplifies to k = 4/3 but this is not the answer. Let's look at the second equation - (k - 3) = 4k - 7. This simplifies to 3 - k = 4k - 7 that means 5k = 10 and k = 2.

4. If d = 2/3 and e = 6 then e/d + 4/d2 =

1. 323
2. 76
3. 10
4. 12
5. 2346

Explanation: Insert the values given for d and e into the equation

e/d + 4/d2 =

6/2 + 4/(2/3)2 =6/2/3 + 4/4/9 =

(6*3/2) + (4 * 9/4) =

18/2 + 36/4 = 9 + 9 = 18 therefore the correct answer is (d).

5. If sin θ = 1/2 and - Π/4 ≤ θ ≤ Π/4, then cos (3θ) =

1.   6/3
2.   89
3.   25.78
4.   7/9
5.   87/12

Explanation: An angle of Π/4 radians is equivalent to an angle of 35°. Now you should look for an angle between 35° and -35° and sin = 1/2. The simplest way to find this number is to place the quantity 1/2 and you are required to reverse the sine.

6. If m - h > m + h, then which of the following must be true?

1. 89/m
2. h < 8
3. h/m
4. mh
5. 12/3

Explanation: Algebra manipulation is the easiest way to solve this problem. You need to add h to each side which will give inequality m > m + 2h. Now you are required to subtract from each side to get 0 > 2h and you will find your answer is (b)

7. Points T, N, Y and M are arranged in a line in the similar order. If TY = 18, NM = 15 and TM = 31 then NY =

1. 7/8
2. 21.45
3. 8
4. 92
5. 6.45

Explanation: To answer this question algebraically separate g one step at a time. First you need to multiply by 4 on the right, g - 5 = 5 - 4g. Next add 3g to each side and then add 5 to each side to get 5g = 6. Divide each side by 5 to get g = 8

8. If for all the real numbers d, a function p(b) is defined by p(d) = {2, b ≠ 15 4, b = 15}

Then s(16) - s(15) =

1. 23
2. 0
3. 74
4. 5/6
5. 7/9

Explanation: The equation p(d) = {2, b ≠ 15 4, b = 15} no values are given which is equal to 15, the functions will always come out to 2. p(16) - p(15) = 2 - 2 = 0, therefore the right answer is (b)

9. If p < t < 1 then all of the following must be true except:

1. p3 < t
2. t < 8
3. t < t
4. -56
5. 6/5t

Explanation: Apply 0.5 in place of t and try to solve the equation. Now t2 = 0.25, square root of t = 0.707, t = 0.6, - t = - 0.6, -t = -0.6, and 1/t = 2. This makes A B D and E true and (c) is false.

10. If j - 7 = 7 (2- j), then what is the value of j?

1. 0.33
2. 87.12
3. 12.56
4. 3.78
5. 785

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

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