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

Question

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

niks18 · Accepted Answer

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.

generis · Answer

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_

MathRevolution · Answer

=>

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

ScottTargetTestPrep · Answer

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

akadiyan · Answer

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

NDND · Answer

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

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards