Question 1 :
The perimeter of a square is four times the circumference of a circle with radius of 1 m. What is the area of the square ?
(A) 4π (B) 8π (C) 4π2 (D) 8π2 (E) 16π2
Solution :
Perimeter of square = 4 Circumference of circle
Radius of circle = 1 m
4a = 4(2π r)
4a = 8π(1)
a = 8π/4 ==> 2π
Area of square = a2
= (2π)2
= 4π2
Question 2 :
(A) 24 (B) 66 (C) 67 (D) 68 (E) 1120
Solution :
Since the given shapes are similar, we may equate the corresponding angles.
<a = 4, <b = 5, <c = 7 and <d = 8
bc + ad = 5(7) + 4(8)
= 35 + 32
= 67
Question 3 :
Convert 3/40 to a decimal.
(A) 0.0075 (B) 0.075 (C) 0.06 (D) 0.75 (E) 7.5
Solution :
To present the given fraction in decimal form, we have to convert the denominator as 10, 100 or 1000 etc.
When we multiply 40 by 25, we get 1000.
= (3/40) ⋅ (25/25)
= 75/1000
= 0.075
Question 4 :
For what value of q is 6(q + 3) = 2(q + 4) ?
(A) -1/2 (B) -4/9 (C) -5/2 (D) -3 (E) -2/5
Solution :
6(q + 3) = 2(q + 4)
6q + 18 = 2q + 8
6q - 2q = 8 - 18
4q = -10
q = -10/4
q = -5/2
Question 5 :
What is angle x of the circle O?
(A) 45 degree (B) 60 degree (C) 75 degree
(D) 150 degree (E) 90 degree
Solution :
OA = OB = r
OA = OB (Equal sides makes an equal angle)
The sum of the angles in a triangle.
x + x + 30 = 180
2x + 30 = 180
2x = 180 - 30
2x = 150
x = 150/2 = 75
Question 6 :
For how many values of x is -3x2/4 > 0
(A) 0 (B) 1 (C) 3 (D) 5 (E) 6
Solution :
For all positive and negative values of x, x2 will be positive, but in front 3x2/4 we have negative sign. For no values of x, we will have negative.
Hence the answer is 0.
Question 7 :
x is 40% of y and y is the square of x, which is x ?
(A) √x (B) 0.4√x (C) 0.4x2 (D) x2 (E) 0.4 x
Solution :
x = 40% of y ----(1)
y = x2 -----(2)
Applying the value of y in (1), we get
x = 40% of x2
x = 0.4 x2
Hence the answer is 0.4 x2.
Question 8 :
If x = 7 and 4x (3y - 2x) = 112, what is the value of y ?
(A) 4 (B) 6 (C) 7 (D) 28 (E) 84
Solution :
By applying x = 7, we get
4x (3y - 2x) = 112
4(7) [3y - 2(7)] = 112
28 (3y - 14) = 112
3y - 14 = 112/28
3y - 14 = 4
3y = 4 + 14
3y = 18
y = 18/3 = 6
Hence the value of y is 6.
Question 9 :
If x ⟩ y = (x + y)/(x - y), what is a ⟩ (a - b) ?
(A) 2a/b (B) (2a - b)/2a (C) (2a - b)/b
(D) (2a - b)/2b (E) (a + b)/(a - 2b)
Solution :
Given that :
x ⟩ y = (x + y)/(x - y)
We need to find, a ⟩ (a - b).
Here, x = a and y = a - b
a ⟩ (a-b) = (a + a - b)/(a - (a - b))
= (2a - b)/(a - a + b)
= (2a - b)/b
Question 10 :
What is the value of √25 + √64?
(A) 10 (B) 13 (C) 14 (D) 89 (E) 100
Solution :
√25 + √64 = √(5 ⋅ 5) + √(8 ⋅ 8)
= 5 + 8
= 13
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