Question 1 :
The average of 7 consecutive even integers is 20. What is the median ?
(A) 18 (B) 20 (C) 20.5 (D) 22 (E) 24
Solution :
Let "x" be the even integer
1st even integer = x
2nd even integer = x + 2
3rd even integer = x + 4
4th, 5th, 6th, 7th numbers are x + 6, x + 8, x + 10 and x + 12 respectively.
Average of 7 consecutive even integer
= (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12)/7
20 = (7x + 42)/7
140 = 7x + 42
7x = 140 - 42
7x = 98
x = 14
Median = x + 6
= 14 + 6
= 20
Question 2 :
What is 0.003815 in scientific notation ?
(A) 3815 x 10-2 (B) 3.815 x 10-3 (C) 3.85 x 10
(D) 0.003815 x 102 (E) 3.815 x 103
Solution :
In order to convert the given number in scientific notation, we have to move the decimal point to the right side
0.003815 = 3.815 x 10-3
Question 3 :
In the figure above, what is the length of AC ?
(A) 8 (B) 12 (C) 2√66 (D) 2√289 (E) √314
Solution :
Since the given triangle is right triangle, we may use the Pythagorean theorem.
BC2 = AB2 + AC2
172 = 52 + AC2
AC2 = 289 - 25
AC2 = 264
AC = √264
AC = √(2 ⋅ 2 ⋅ 66)
AC = 2√66
Question 4 :
What time will it be 53 hours after 3 : 30 P.M on Thursday ?
(A) 10 π/25 (B) 5/2 (C) 2/5 (D) 25 π/10 (E) 5π/25
Solution :
First let us divide 53 by 24.
3 : 30 PM - 3 : 30 PM (Thursday - Friday)
3 : 30 PM - 3 : 30 PM (Friday - Saturday)
53 = 2 (24) + 5
5 hours after 3 : 30 P.M on Saturday
8 : 30 PM on Saturday
Question 5 :
If x represents the circumference of the above figure and y represents the area, what is x/y ?
(A) 9.8 x 105 kg (B) 9.8 x 103 kg (C) 9.8 kg
(D) 9.8 x 10-3 kg (E) 9.8 x 10-5 kg
Solution :
Radius of the circle = 5
Circumference of circle (x) = 2πr = 2 π (5) = 10 π
Area of circle (y) = πr2
x/y = 10 π/πr2
= 10/r2
= 10/52
= 10/25 = 2/5
Question 6 :
A certain substance has a mass of 98 milligrams. What is the mass of this substance in kilograms ?
Solution :
1 milligram = (1/106) kilograms
98 = 98/106 kilogram
= 9.8 x 101 x 10-6
= 9.8 x 10-5 kilogram
Question 7 :
Samuel scored 72, 92 and 80 on his first three exams. What is the minimum score he needs to get an average of 85 ?
(A) 85 (B) 90 (C) 93 (D) 96 (E) 100
Solution :
Let "x" be the required score.
(72 + 92 + 80 + x)/4 = 85
(244 + x) = 340
x = 340 - 244
x = 96
Question 8 :
Five out of 10 marbles in a bag are red. What percentage of the marbles is not red ?
(A) 50% (B) 55% (C) 60% (D) 75% (E) 80%
Solution :
Total number of marbles = 10
Number of red marble = 5
Percentage of red marble = (5/10) x 100 %
= 50%
What percentage of the marbles it is not red = 50%
Question 9 :
In the figure above, the rectangle ABCD is inscribed in the circle.Where E is the center and the radius is 5. If the length of BD is 6, what is the area of rectangle ABCD ?
(A) 30 (B) 48 (C) 60 (D) 25 (E) 180
Solution :
In order to find the area of rectangle, we must know the dimension of rectangle.
width of rectangle = 6
radius of circle = 5 (EB)
EB = EC = 5
CB = 10
In right triangle CDB,
CB2 = CD2 + DB2
102 = CD2 + 62
100 - 36 = CD2
CD2 = 64
CD = 8 (length of rectangle)
Area of rectangle = length (width)
= 8 (6) = 48
Question 10 :
√81 √25 + √16 =
(A) 5 (B) 40 (C) 49 (D) 56 (E) 64
Solution :
= √81 √25 + √16
= √(9 ⋅ 9) √(5 ⋅ 5) + √(4 ⋅ 4)
= (9 ⋅ 5) + 4
= 45 + 4
= 49
Hence the answer is 49.
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