jain2016 wrote:The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?
A) 5^ 11
B) 5^ 10
C) -5^ 12
D) (-7)5^ 12
E) (-12)5^ 13
OAD
I believe the question should have had C = 5^12 and D = 5^13.
Let's call the distance of each segment: x. So the distance between A and B is x, and the distance between B and C is x, etc. So the gap between A and C is 2x, meaning that A = 5^12 -2x.
Now we need to solve for x. If the distance between D and C is x, then we set x = 5^13 - 5^12.
Factor out 5^12, so that 5^13 - 5^12 = 5^12(5 - 1) = 5^12 * 4.
If x = (5^12) * 4, and A = 5^12 - 2x, then A = 5^12 - 2[(5^12) * 4] = 5^12 - (5^12)*8 = (5^12)(1 - 8) = (5^12)*(-7)
Answer is
D
