SAT Math : How to find value with a number line
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Example Questions
Example Question #1 : How To Find Value With A Number Line
If the tick marks are equally spaced on the number line above, what is the average (arithmetic mean) of x, y, and z?
4
6
8
7
5
6
First, we must find out by how much they are spaced by. It cannot be 1, since 4(4) = 16, which is too great of a step in the positive direction and exceeds the equal-spacing limit. 2 works perfectly, however, as 4(2) equals 8 and fits in line with the equal spacing.
Next, we can find the values of x and y since we are given a value of 6 for the third tick mark. As such, x (6 – 4) and y (6 – 2) are 2 and 4, respectively.
Finally, z is 4 steps away from y, and since each step has a value of 2, 2(4) = 8, plus the value that y is already at, 8 + 4 = 12 (or can simply count).
Finding the average of all 3 values, we get (2 + 4 + 12)/3 = 18/3 = 6.
Example Question #2 : How To Find Value With A Number Line
How many numbers 1 to 250 inclusive are cubes of integers?
The cubes of integers from 1 to 250 are 1, 8, 27,64,125,216.
Example Question #1 : Other Number Line
On the number line above, the tick marks are equally spaced. Which of the following expresses in terms of ?
If is between and on the number line, then and .
So must be correct because
.
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