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SAT Sample Questions » Quantitative Section : Quantitative Ability

# Quantitative Section : Quantitative Ability

Let us discuss few important questions on Multiple Choice with answers and explanation.

1. In the above diagram, the rectangle j contains all points that is x, y. What is the area of a rectangle that contains all points (2x, y - 1)?

1. 52
2. 87
3. 65
4. 36
5. 12

Explanation: If you look at the diagram carefully the x coordinates of the points in region j contain everything from x = 0 to x = 6. A rectangular region containing all points (2x, y - 1) would therefore stretch from X = 0 TO X = 12. Therefore the diagram will look like this.

It would have length around 12 and breadth of 3 and an area of 36. Therefore the correct answer is (d)

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

1.   9/7
2.   15/7
3.   -23/7
4.   7/9
5.   5

Explanation: An angle of Π/4 radians is equivalent to an angle of 45°. Now you should look for an angle between 45° and -45° and sin = 1/3. The simplest way to find this number is to place the quantity 1/3 and you are required to reverse the sine.

3. If u - t > u + t, then which of the following must be true?

1. 5/u
2. t < 8
3. u > 9
4. t > 0
5. 4 / t

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

4. Points J, K L and M are arranged in a line in the similar order. If JL = 13, KM = 14 and JM = 21 then KL =

1. 45
2. 7
3. 8
4. 23
5. 32

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

5. If r - o > r + o, then which of the following must be true?

1. 0/r
2. q < 0
3. 9 > 0
4. 7 > 0
5. o / 10

Explanation: Algebraic manipulation is the best way to answer this problem. You have to add o to each side which will give dissimilarity r > r+ 2o. Now you have to subtract from each side to get 0 > 2o and therefore the answer is (b)

6. If for all the real numbers y, a function i(h) is defined by i(y) = {2, h ≠ 13 4, h = 13}

Then g(16) - g(15) =

1. 31
2. 0
3. 91
4. 1
5. 43

Explanation: The equation i(y) = {2, h ≠ 13 4, h = 13} no values are given which is equal to 13, the functions will always come out to 2. i(16) - i(15) = 2 - 2 = 0, therefore the right answer is (b)

7. If t(x) = 5m2+5m+5, which of the following is equal to t(-3.5)?

1. F9
2. F89
3. F(2.5)
4. F78
5. F(5.7)

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

8. If 0 < b < 1 then all of the following must be true except:

1. b3 < n
2. b < square root of b
3. b < b
4. -q < q
5. q < 6/q

Explanation: Apply 0.5 in place of b and try to solve the equation. Now b2 = 0.25, square root of b = 0.707, b = 0.5, - b = - 0.5, -b = -0.5, and 1/b = 2. This makes A B D and E true and (c) is false.

9. If the cube root of the square root of a number is 8, what is the number?

1. 23
2. 512
3. 451
4. 784
5. 102

Explanation: Translate the whole into math's 3√x = 8. Now take away. First cube both sides. √x = 8. Now square both sides; x = 512

10. If d - 5 = 5 (2- d), then what is the value of d?

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

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

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