Question 11 :
Express 6.925 x 105 in standard form.
= 6.925 x 105
= 6.925 x 100000
Question 12 :
On the number line above, X is located at -10, Y is at -2, and Z is at 8. M (not shown) is the midpoint of XY, and N (not shown) is the midpoint of YZ. What is the midpoint of MN?
Y is located at -2 and X is located at -10.
Numbers between X and Y are
-2, -3, -4, -5, -6, -7, -8, -9, -10
The midpoint of these two numbers is -6.
So, M is located at -6.
Numbers between Y and Z are
-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8
So, N is located at 3.
Now, let us write the numbers between -6 and 3.
-6, -5, -4, -3, -2, -1, 0, 1, 2, 3
-1.5 is the midpoint of MN.
Question 13 :
If 0 < y < 1, which of the following statements must be true?
(A) y2 > y3 (B) y > 0.5y (C) y > y3
(D) All of the above (E) None of the above
Let x = 0.5
By applying the value of y in option A, we get
0.25 > 0.125 True
By applying the value of y in option B, we get
0.5 > 0.5 (0.5)
0.5 > 0.25 True
By applying the value of y in option C, we get
0.5 > (0.5)3
0.5 > 0.125 True
Hence all of the above is true.
Question 14 :
The area of the square ABCD is 4 times larger than the area of square WXYZ. If the area of square WXYZ is 9, what is the difference between the length of a side of square ABCD and the length of a side of square WXYZ?
Area of the square ABCD = 4 Area of the square WXYZ
Area of the square WXYZ = 9
a2 = 9
a = 3
Side length of square WXYZ = 3
Area of the square ABCD = 4(9) = 36
s2 = 36
s = 6
Difference between side length of ABCD and WXYZ
= 6 - 3
Question 15 :
Triangle GHI is similar to Triangle JKL.
What is the length of side JK?
Since the above triangles are similar, the length of the sides are in the same ratio.
GI/JL = GH/JK = IH/ LK
(3x/4)/x = 12/JK = IH/LK
3/4 = 12/JK
JK = 12(4)/3
JK = 16
Question 16 :
Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hours shifts. Each person will drive for one shift, and take two shifts off to rest. If Wesley’s first shift starts at 6:00 a.m., at what time will Wesley complete his third shift?
6 AM - 1 PM
1 PM - 8 PM
8 PM - 3 AM
3 AM - 10 AM
10 AM - 5 PM
5 PM - 12 AM
12 AM - 7 AM
Hence the required answer is 7 : 00 AM.
Question 17 :
What is the difference between the largest and lowest integer in the sequence of consecutive odd integers whose sum is 15 ?
Let us select three numbers 3, 5 and 7.
3 + 5 + 7 = 15
Difference between largest and lowest integer
= 7 - 3
Hence the answer is 4.
Question 18 :
The half life of a substance is the time it takes for a substance to decrease to half its initial amount. John has a pile of goo that decreases in amount at a constant rate. If John initially had 100 pounds of goo, and ten days later, he only had 25 pounds of goo, what is the half of the goo ?
In 10 days, the goo decreased by 2 half lives. So each life is 5 days.
Question 19 :
What is the value of (94 - 84)/(92 + 82) ?
(94 - 84)/(92 + 82) = [(92)2 - (82)2] / (92 + 82)
= [(92 + 82) (92 - 82)] / (92 + 82)
= 92 - 82
= 81 - 64
Hence the answer is 17.
Question 20 :
Jackie fills a jug with water continuously. It takes her 2 minutes to fill up 50% of the empty space in the jug with water. After every 2 minutes, she puts a penny into a jar to celebrate. How many pennies will she have in the jar at the instant the jug has less than 30% empty space left ?
Now Jackie starts to fill the jug. At the first round, he fills 50% of empty space in the jug in 2 minutes and drop a penny.
Now the jug contains 50% of empty space. If he fills half of the 50% of empty space at that instant, the quantity of water will become 75%. Hence the condition will not satisfy, by filling water in the second round.
So, there is only 1 penny in the jar at the instant the jug has lesser than 30% of empty space.
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