MathRevolution wrote:

[GMAT math practice question]

Attachment:

A.png

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

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_

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"