a is an external angle
b is an internal angle
The sum of the exterior angles of the figure | The sum of the interior angles of the figure |
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Solution
The exterior angles of the figure add up to 360 (because starting from any angle and moving around the figure, you turn one complete circle).
The interior angles will add up to 4 x 180 (because you can divide the figure into four triangles by joining opposite vertices).
Also the figure does not say �not to scale� and therefore we can believe what we see. From the figure it is obvious that the external angles are larger than the internal angles, and there are obviously 6 of each.
n > 0
n50 | n550 |
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Solution
Since n is greater than 0 it could be a fraction, 1 or a larger number.
If n = 1, then both columns are equal (1 raised to any power is still 1).
If n > 1 the right column will be greater.
These two different possibilities mean that this is a D answer.
Figure not to scale
The figure above is composed of squares. The larger squares are each of area 49. The area of each small square is 4
x | 3 |
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Solution
Note that the question specifies squares. The side of the larger square = 7
The side of the smaller square = 2
The length of the line formed by the 5 small squares in a row = 5 x 2 =10
The length of x is therefore 10 - the side of the big square. 10 - 7 = 3
Refer to the data from the previous question
p and q are non-negative integers
(p + q)¤ | p + q¤ |
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Solution
Using the same operation as in the previous question, we have
On the left (p + q) + 1
On the right p + (q + 1)
Taking out the brackets shows that both are equal
This question and the next refer to the following definition
For all non-negative numbers
x ¤ = x + 1
(9 ÷ 3)¤ | 9¤ ÷ 3¤ |
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Solution
The strange symbol defines the operation to be carried out on the number.
(In this case, take the number and add 1)
On the left we have (9/3 = 3) on which we perform the operation 3 + 1 = 4
On the right we have 9 + 1 divided by 3 + 1. This equals 10/4 = 2.5
Farm X is 8 miles due west of farm Y, and farm Z is 7 miles due north of farm Y
Distance between X and Z | 10 miles |
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Solution
Draw a sketch. XYZ is a right triangle with the distance between X and Z forming the hypotenuse. Use Pythagoras to find the hypotenuse (8² + 7² = hyp²)
64 + 49 = 113. Root of 113 is obviously greater than 10.
A rectangle has area 30
Perimeter of this rectangle | 25 |
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Solution
The rectangle could be drawn long and thin or made into a square. The maximum perimeter will come when the rectangle is long and thin. We can make the base nearly 30 units long and the perimeter will obviously be more than 25. The minimum perimeter will come when the rectangle is a square. In which case the perimeter will be less than 25. (No need to work it out but we could by taking root 30 for the side and multiplying by 4 for the perimeter)
3 x 10³ + 2 x 10² + 10 | 321 x 10 |
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Solution
The box on the left is equal to 3,000 + 200 + 10 = 3210
The right box is also equal to 3210
k² = 4
km = 6
k | m |
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Solution
If k² = 4, k could be +2 or -2
If km = 6, m could be 3 if k is 2 (In which case the right column is greater)
But m could be -3 if k is -2 (In which case the left column is greater)
Hence this is a D answer.
9 less than 4x = 39
x | 10 |
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Solution
We can write 9 less than 4x as 4x -9
4x - 9 = 39; 4x = 48; x = 12, which is bigger than 10.