GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Nov 2018, 20:13

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# 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: 6531
GMAT 1: 760 Q51 V42
GPA: 3.82
If the distances between consecutive ticks in the above number line ar  [#permalink]

### Show Tags

11 Dec 2017, 00:54
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:03) correct 42% (01:05) wrong based on 58 sessions

### HideShow timer Statistics

[GMAT math practice question]

Attachment:

pic.png [ 1.95 KiB | Viewed 704 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

_________________

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 $99 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: 1217 Location: India GPA: 3.82 If the distances between consecutive ticks in the above number line ar [#permalink] ### Show Tags 11 Dec 2017, 03:38 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 Senior SC Moderator Joined: 22 May 2016 Posts: 2117 If the distances between consecutive ticks in the above number line ar [#permalink] ### Show Tags 11 Dec 2017, 11:49 1 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6531 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the distances between consecutive ticks in the above number line ar [#permalink] ### Show Tags 12 Dec 2017, 23:37 => 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$99 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 &nbs [#permalink] 12 Dec 2017, 23:37
Display posts from previous: Sort by