[GMAT math practice question]



In the number line above, the ticks are evenly spaced. Which point represents \(2^{10}\)?

A. A
B. B
C. C
D. D
E. E
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Find interval distance between known values

\(2^8 = 256\) * \(2\) =
\(2^9 = 512\)

The distance between the points is \(512 - 256 = 256\)

\(\frac{Difference}{IntervalLength}=\) number of intervals

\(2^{10} = 1,024\)

1) To get there from \(2^9 = 512\):
\((1,024 - 512) = 512\)

\(512\) is difference. Divide by length of interval.

\(\frac{512}{256} = 2\) intervals

Between \(2^9\) and \(2^{10}\) there are two intervals of 256. Count up.

2) To get there from \(2^8 = 256\):
\((1,024 - 256) = 768\)

\(\frac{768}{256} = 3\) intervals of 256. Count up.

\(2^{10}\) is at point B.

Answer B

_|_256_|_256_|_256_|_256_|_256|_
_\(2^8\)____\(2^9\)_____|_____\(2^{10}\)____|_____|_
_\(2^8\)____\(2^9\)_____A_____B______C_____D_
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We first must determine the distance between the evenly-spaced tick marks. We see that the distance between 2^8 and 2^9 is:

2^9 - 2^8 = 2^8(2^1 - 1) = 2^8

Let’s now determine how many tick marks we need, in order to get from 2^9 to 2^10. We can set up the following equation to determine k, the number of tick marks 2^10 is from 2^9:

2^9 + 2^8 x k = 2^10

Dividing both sides of the equation by 2^8, we have:

2 + k = 2^2

2 + k = 4

k = 2

Thus, 2 tick marks from 2^9 will be 2^10, which is point B.

Answer: B
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\(2^1\) ___\(2^2\) ___\(2^3\) ___\(2^4\) ___\(2^5\)

2 ____ 4 ____ 8____ 16 ___ 32

So the sequence is doubling, which means that on the number line above the distance between \(2^9\) and \(2^{10}\) will be double the distance between \(2^8\) and \(2^9\)

B is the answer
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