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Math Revolution GMAT Instructor V
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In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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[GMAT math practice question]

Attachment: A.png [ 3.44 KiB | Viewed 1757 times ]

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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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.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3557
In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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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

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.

_|_256_|_256_|_256_|_256_|_256|_
_$$2^8$$____$$2^9$$_____|_____$$2^{10}$$____|_____|_
_$$2^8$$____$$2^9$$_____A_____B______C_____D_
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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1
=>

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.

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

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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

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.

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

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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.

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

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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

$$2^1$$ ___$$2^2$$ ___$$2^3$$ ___$$2^4$$ ___$$2^5$$

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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_________________ Re: In the number line above, the ticks are evenly spaced. Which point rep   [#permalink] 25 Mar 2019, 18:33
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