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In the number line above, the ticks are evenly spaced. Which point rep

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In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 27 Nov 2017, 01:09
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[GMAT math practice question]

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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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In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 27 Nov 2017, 01:53
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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


Distance between first two points \(= 2^9-2^8=2^8(2-1)=2^8\)

As numbers are evenly spaced so it is an AP series with first term \(a=2^8\), common difference \(d=2^8\) and \(t_n=2^{10}\). We need to find \("n"\) i.e number of terms to reach to \(2^{10}\)

\(t_n=a+(n-1)d => 2^{10}=2^8+(n-1)*2^8\)

or, \(n = \frac{2^{10}}{2^8} = 4\). so fourth term will be \(2^{10}\) i.e point B

Option B

you can also arrive at point B once you know the distance between each point by simple counting.
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In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 27 Nov 2017, 07:26
1
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_
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Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 29 Nov 2017, 00:27
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=>

The distance between each pair of consecutive ticks is \(2^9 – 2^8 = 2^8(2-1) = 2^8\).
Find the values of each point:
\(A = 2^9 + 2^8.\)
\(B = A + 2^8 = 2^9 + 2^8 + 2^8 = 2^9 + 2*2^8 = 2^9 + 2^9 = 2*2^9 = 2^{10}.\)

Therefore, the answer is B.

Answer : B
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Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 29 Nov 2017, 10:53
1
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


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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Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 29 Nov 2017, 19:18
2^8=256
2^9=512
2^10=1024

Points are evenly spaced. From first 2 points we can determine that spacing between 2 points is 256.

So from 2^9 to 2^10 is 512 which is 2 points from 2^9.

Answer is B
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Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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New post 29 Jan 2018, 07:14
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



\(2^1\) ___\(2^2\) ___\(2^3\) ___\(2^4\) ___\(2^5\)

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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Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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