1.Correct Answer: C
Explanation:
2 x 104 = 30,000; 2 x 102 = 200; 4 x 10 = 40
The total is 30,240
2.Correct Answer: B
Explanation:
To find how many problems in the series we need to take the difference and add one.
125 - 74 = 51; 51 + 1 =52
3.Correct Answer: C
Explanation:
Substitute the given values for y and check whether you get an integer value for x.
For example, using 0 we get 3x = 13; x = 13/3 which is not a whole number.
The right answer is 2, since 3x + 2(2) = 13; 3x = 13 - 4 = 9; x = 9/3 = 3.
4.Correct Answer: A
Explanation:
The big triangle ABC is similar to the small triangle ADE because their bases are parallel. If corresponding side of two similar triangles are known the ratio of the areas is also known. In this case, let AD be one unit, then AB is 2 units (given that AB = AD + DB). The ratios of the sides is 1 : 2. The ratio of the areas will be (1)2 : (2)2 ; 1 : 4
Since the big triangle has area 40, using the ratio, the small has area 10.
5.Correct Answer: E
Explanation:
Given that n is positive, it could be a positive fraction, 1, or a fraction of whole number greater than 1.
If n = 1, then case I is not true since n2 = 1
Likewise in II if n = 1, n - n2 = 0, and the statement is not true.
In III, if n = , then 2n - 1 = 0, and again the statement is incorrect.
6.Correct Answer: E
Explanation:
The equation for a straight line is y = mx + c, where m = slope and c = y-intercept.
Putting the given values in this equation we have y = x/2 + 3
The x-intercept occurs where y = 0. Thus, 0 = x/2 + 3 ; -3 = x/2 ; -6 =x
7.Correct Answer: D
Explanation:
Imagine the first person of the six. He or she will have to shake hands with each of the other 5. Now turn to the second person. He or she will have to shake with the other five, but he she has already shaken with the first person. This means 4 new handshakes. The third person will have to shake with 5 - 2 = 3 people, and so on. Total handshakes = 5 + 4 + 3 + 2 + 1 = 15
8.Correct Answer: E
Explanation:
x2 - y2 can be expressed as (x + y)(x - y); since x - y =11 we can write
(x + y)11 = 55; therefore x + y = 5
Adding the two equations x + y = 5 and x - y = 11 we get
2x = 16; x = 8
Therefore 8 - y = 11; y = -3
9.Correct Answer: B
Explanation:
Since 2 do not play either, there are 28 members who play one sport or the other. Let the number who play both be n.
Total (28) will be made up of only badminton players (17 - n), plus only tennis (19 - n) and those who play both (n).
28 = (17 - n) + (19 - n) + n
28 = 36 - n ; n = 8
10.Correct Answer: C
Explanation:
The total perimeter of the un-shaded part is made up of three sides of the rectangle and the perimeter of the half-circle.
The area of a half circle = π r2
8 π = π r2; therefore r = 4
The perimeter of the half circle is 8 π = 4 π
The diameter of the circle (8) = the length of the rectangle.
Total perimeter of the rectangle = 26
Three sides measure 26 - 8 = 18 Ans. 18 + 4π
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