GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 Apr 2018, 03:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the distances between consecutive ticks in the above number line ar

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5255
GMAT 1: 800 Q59 V59
GPA: 3.82
If the distances between consecutive ticks in the above number line ar [#permalink]

### Show Tags

11 Dec 2017, 01:54
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:06) correct 45% (00:46) wrong based on 47 sessions

### HideShow timer Statistics

[GMAT math practice question]

Attachment:

pic.png [ 1.95 KiB | Viewed 494 times ]

If the distances between consecutive ticks in the above number line are the same, which of the following points represents $$2^{11}$$?

A. A
B. B
C. C
D. D
E. E
[Reveal] Spoiler: OA

_________________

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 $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1055 Location: India GPA: 3.82 If the distances between consecutive ticks in the above number line ar [#permalink] ### Show Tags 11 Dec 2017, 04:38 MathRevolution wrote: [GMAT math practice question] Attachment: pic.png If the distances between consecutive ticks in the above number line are the same, which of the following points represents $$2^{11}$$? A. A B. B C. C D. D E. E as the tick marks are equally spaced so it is an AP series. let $$2^9=a$$ and distance between ticks be $$d$$ so $$2^{10}=a+2d =>2^{10}=2^9+2d$$ $$d=2^8$$ let $$T_n=2^{11}$$ $$T_n=a+(n-1)d =>2^{11}=2^9+(n-1)2^8$$. divide both sides by $$2^8$$ $$2^3=2+n-1=> n=7$$ so the $$7th$$ tick mark will be $$2^{11}$$ which is $$D$$ Option D SC Moderator Joined: 22 May 2016 Posts: 1547 If the distances between consecutive ticks in the above number line ar [#permalink] ### Show Tags 11 Dec 2017, 12:49 MathRevolution wrote: [GMAT math practice question] Attachment: pic.png If the distances between consecutive ticks in the above number line are the same, which of the following points represents $$2^{11}$$? A. A B. B C. C D. D E. E Find the distance between two known values. Divide by number of intervals between them. That = interval length. Thus: $$\frac{Upper-Lower}{No.OfIntervals}=$$ Interval length $$\frac{2^{10}-2^9}{2intervals}=\frac{2^9(2^1-1)}{2}=\frac{2^9}{2}=$$ interval length How many intervals between $$2^{11}$$ and $$2^9$$? Total distance between them, divided by interval length = number of intervals: $$\frac{Upper-Lower}{IntervalLength}=$$ Number of intervals (Upper-Lower) = Distance between $$2^{11}$$ and $$2^9$$ $$(2^{11} - 2^9) = 2^9(2^2 - 1) =$$ $$2^9(3)$$ Divide that distance by interval length to get number of intervals, x $$\frac{2^9(3)}{\frac{2^9}{2}}=x$$ $$2^9(3)*\frac{2}{2^9}=x$$ $$3 * 2 = x$$ $$x = 6$$ $$2^{11}$$ is 6 intervals away from $$2^9$$ That is D on the line. Answer D *Faster but dense: Between $$2^{10}$$ and $$2^9$$ there are TWO intervals. TWO intervals = what length? $$(2^{10} - 2^9) = 2^9(2^1 - 1)= 2^9(1)$$ = $$2^9$$ Distance between $$2^{11}$$ and $$2^9$$:$$(2^{11}-2^9) = 2^9(2^2-1)=2^9(3)$$ There are 3 lengths of $$2^9$$ between $$2^9$$ and $$2^{11}$$ --Length $$2^9 =$$ 2 intervals --(Number of lengths) * (number of intervals for that length) = (Total # of intervals) --3 * 2 = 6 intervals = point D _________________ At the still point, there the dance is. -- T.S. Eliot Formerly genxer123 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5255 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If the distances between consecutive ticks in the above number line ar [#permalink] ### Show Tags 13 Dec 2017, 00:37 => Let $$d$$ be the distance between consecutive ticks. Then $$2d = 2^{10} – 2^9 = 2*2^9 – 2^9 = 2^9$$ $$d=2^8.$$ Since $$2^{11} – 2^{10} = 2^32^8 – 2^22^8 = 8(2^8)– 4(2^8)= 4(2^8)= 4d,$$ $$2^{11}$$ is the fourth point from $$2^{10}$$, which is D. Therefore, the answer is D. Answer : D _________________ 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$79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If the distances between consecutive ticks in the above number line ar   [#permalink] 13 Dec 2017, 00:37
Display posts from previous: Sort by