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

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

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27 Nov 2017, 01:09
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Difficulty:

45% (medium)

Question Stats:

62% (01:31) correct 38% (00:53) wrong based on 101 sessions

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[GMAT math practice question]

Attachment:

A.png [ 3.44 KiB | Viewed 1374 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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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 25 Feb 2013 Posts: 1215 Location: India GPA: 3.82 In the number line above, the ticks are evenly spaced. Which point rep [#permalink] ### Show Tags 27 Nov 2017, 01:53 2 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 Joined: 22 May 2016 Posts: 2642 In the number line above, the ticks are evenly spaced. Which point rep [#permalink] ### Show Tags 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_ _________________ Listen, are you breathing just a little, and calling it a life? -- Mary Oliver For practice SC questions with official explanations that were posted and moderated by the SC Team, go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7230 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the number line above, the ticks are evenly spaced. Which point rep [#permalink] ### Show Tags 29 Nov 2017, 00:27 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. Answer : B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: In the number line above, the ticks are evenly spaced. Which point rep  [#permalink]

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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.

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

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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.

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

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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 $$2^9$$

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

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25 Mar 2019, 18:33
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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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