A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 512 and 513, respectively, what is the value of A?
-24(512)
-23(512)
-24(56)
23(512)
24(512)


The distance from G to H is 513 - 512.

The distance between and two consecutive points is constant, so the distance from A to G will be 6 times the distance from G to H or 6(513 – 512).

The value of A, therefore, will be equal to the value of G minus the distance from A to G:

512 – 6(513 – 512) 512 – 6[512(5 – 1)] 512 – 6(512)(4)

512(1 – 24) (-23)512.

The correct answer is B.

I don't see how the second step was achieved. Please explain. Thanks

? Arent the answer choice incorrect ? IF distance between any two consequitive integers is contant , lets say C. So between B and A, D and C etc , the distance is C. And we know the distance between one, so it is 513-512 , which is 1=C

Just subtract one for each and we gt A = 506 ?

I think the question is wrong ? Or the question and answer choices dont match up. Something is missing for sure

if you had 30 seconds to guess on this problem, here's what you'd do. (if you don't understand what i'm talking about, actually get out a sheet of paper and draw it)

* draw the number line with the eight points on it.

* realize that 5^13 is five times as big as 5^12.

* realize that, therefore, zero is going to be between F and G (and is going to be a lot closer to G) on your number line.

* realize that (c) is a tiny tiny fraction of the size of the other numbers in the list, and is nowhere near far enough to the left to be the correct answer. (since your number line shows numbers of the order of magnitude of 5^13, any number like 24*5^6 is so small that it would be indistinguishable from zero if you tried to plot it).

* therefore, you've narrowed the problem down to choices a and b.

--

here's the real way to solve the problem:

* this is a problem about an arithmetic sequence. just as you should start by finding the radius in any problem involving circles, you should find the common difference in any problem involving arithmetic sequences. in this case, the common difference is 5^13 - 5^12 (an expression that can't be reduced; you can factor out 5^12, but that won't help things).

* the number you seek is six more common differences below G (look at your number line and count). therefore, the number you seek is
G - 6(common difference)
= (5^12) - 6(5^13 - 5^12)
= 5^12 - 6*5*5^12 + 6*5^12
= (5^12) - 30(5^12) + 6(5^12)
= -23(5^12)

answer = b

sweetness