Note: figure not to scale
Lines l and m are parallel
AB / AD | DC / CB |
-
Solution
Imagine line segment BC free to move so that B remains stationary, and C moves towards or away from D. We will not affect the ratio AB/AD but will get different rations for DC/CB. Hence this is a D choice.
The sum of all integers from -6 to 30 inclusive | The sum of all integers from 7 to 30 inclusive |
-
Solution
The extra numbers in the series on in the left column are -6 to 6. When we add these up the total is zero (-6 + 6, -5 + 5, -4 + 4 etc.). And so both sums will be the same.
4 < x < 8 , and 3 < y < 7 [/panel-header] [panel-content]
x – y | 5 |
-
Solution
The maximum difference between the numbers will come if we make x as large as possible (just a little less than 8), and make y as small as possible (a little greater than 3).
The maximum difference will, therefore, have to be a little less than 5.
The x coordinate of point P | The y coordinate of point P |
-
Solution
The x-coordinate of P is negative.
The Y-coordinate of P is positive (and is therefore greater)
The average (arithmetic mean) of four numbers is 20. The sum of three numbers is 60
The fourth number | 20 |
-
Solution
If the mean of four numbers is 20, then their sum must be 20 x 4 =80
If the sum of three of them is 60, them the fourth number = 80 - 60 = 20
The area of one face of a rectangular block is 16 and the area of an adjacent face is 20.
Volume of the block | 100 |
-
Solution
We can find the volume of a rectangular block by multiplying the area of the base by the height. But in this case the height is not known. Do not assume that the sides of the faces must be squares. If they are square, the volume = 16 x 5 = 80. But let us assume that one face is 16 x 1 and the other face is 20 x 1. Then the volume becomes 16 x 20 x 1 = 320.
Rob has more money than Paul. Paul has more money than Vinny and Sam has more money than Toni. Toni has less money than Rob but more money than Paul.
Total amount that Vinny and Sam have together | Total amount that Rob and Toni have together |
-
Solution
R > P > V, and S > T
Also R>T>P. Integrating this picture we have R>T>P>V with S occurring in the list somewhere before T. This is the problem - we do not know exactly where to put S. So we cannot decide whether S and V will have more money than R and T.
5 less than 4x = 27
x | 9 |
-
Solution
5 less than 4x can be written 4x - 5
4x - 5 = 27; 4x = 32; x = 8
Each of six sectors of a circle is assigned a number such that the numbers in any two adjacent sectors add up to 15
x | 8 |
-
Solution
The sectors next to the 7 must be assigned 8.
Next to these 8s there must be 7s.
Between the 7.s there must be an 8 = x
Angle ABC =59, angle ACB = 61
The length of side AB | The length of side BC |
-
Solution
Since two angles are given we can find the third. 180 - 59 - 61 = 60
Now we need to realize that the largest angle is opposite the longest side.
AB is opposite angle ACB, which is the largest.