The tick marks on the number line shown are equally spaced. What is

Question

https://gmatclub.com/forum/download/file.php?id=74804 The tick marks on the number line shown are equally spaced. What is the value of n? A. 4^{11} B. 4^{13} C. 30(4^7) D. 31(4^7) E. 46(4^7) Untitled.png Screenshot 2024-02-02 151034.png

MartyMurray · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=74804

The tick marks on the number line shown are equally spaced. What is the value of n?

We see that there is one unit between  4^7  and  4^9  and two units between  4^9  and  n .

So, since we are given that "The tick marks on the number line shown are equally spaced," the difference between  4^9  and  n  will be twice the difference between  4^7  and  4^9 .

Accordingly, the value of  n  will be  4^7 +  three times the difference between  4^7  and  4^9 .

The difference between  4^7  and  4^9  is the following:

4^9 - 4^7 = (4^2)(4^7) - 4^7 = 16(4^7) - 4^7 = 15(4^7)

So, each unit between two tick marks is  15(4^7) .

Thus,   n = 4^7 + 3(15(4^7)) = 4^7 + 45(4^7) = 46(4^7) .

A.  4^{11} 
B.  4^{13} 
C.  30(4^7) 
D.  31(4^7) 
E.  46(4^7)

Now, to get the question correct, we must be sure to answer the question asked.

(C) is a trap choice that is the difference between  4^9  and  n .

(D) is a trap choice that is  4^7 +  the difference between  4^9  and  n .

Correct answer:  E

Bunuel · Answer

Since the tick marks are equally spaced, the distance between each two consecutive tick marks is 4^9 - 4^7. The point n on the number line is two units from 4^9, thus its value is:

4^9 + 2(4^9 - 4^7) =

= 4^9 + 2*4^9 - 2*4^7 =

= 3*4^9 - 2*4^7 =

= 4^7(3*4^2 - 2) =

= 46*4^7

Answer: E.

Bunuel · Answer

unraveled · Answer

The tick marks on the number line shown are equally spaced. What is the value of n?

A.  4^{11} 
B.  4^{13} 
C.  30(4^7) 
D.  31(4^7) 
E.  46(4^7)

Good question to test your brain's void/s. 
Equally spaced means that difference between first and second or second and third and so on.
 4^{9}  -  4^{7}  =  4^{7}(4^2 - 1)  =  15 * 4^{7} 
So, the difference between next number wrt  4^{9}  on the number line would be 
 15 * 4^{7}  +  15 * 4^{7}  =  30 * 4^{7} 
And total difference between  4^{7}  and n would be
 30 * 4^{7}  +  15 * 4^{7}  =  15 * 4^{7}(2 + 1)  =  45 * 4^{7}

The number n would be then  4^{7} + 45 * 4^{7}  =  4^{7}(1 + 45)  =  46 * 4^{7}

Answer E.

Kinshook · Answer

https://gmatclub.com/forum/download/file.php?id=74804

Given: The tick marks on the number line shown are equally spaced. 
Asked: What is the value of n?

n - 4^9 = 2(4^9 - 4^7) = 2*4^7(4^2 - 1) = 2*15*4^7 = 30(4^7) 
 n = 4^9 + 30(4^7) = 4^7(4^2 + 30) = 46(4^7)

IMO E

KarishmaB · Answer

A question based on observation. 4^9 = 16 * 4^7 Hence distance between 2 ticks is simply 15*4^7 or we call it '15a'. Now n is another 30a away and hence will be 46a = 46*4^7. Screenshot 2024-04-08 at 7.23.19 PM.png Answer (E) Here is a discussion on exponents on the number line: https://youtu.be/0rpppnnJNRs

mollyweasley · Answer

Bunuel   KarishmaB   MartyMurray  Hi, slightly silly question but just wanted to make sure I got my concept right. Why would it be wrong to assume the sequence is a GP and the difference between two ticks was simply 4^2? This way, n would be 4^13, which I can see is an option here (trap). Thanks!

KarishmaB · Answer

Because the tick marks on the number line for an AP, not a GP. Place a GP on the number line and see what you get: 1, 4, 16, 64... Now place an AP on the number line: 4, 8, 12, 16, 20... Where do you get ticks placed at equal intervals? In an AP because that is how we define an AP - each term is at a fixed distance from the previous term. Here are some blog posts on Sequences: https://anaprep.com/algebra-introducing-sequences/ https://anaprep.com/algebra-a-difficult ... sequences/ https://anaprep.com/algebra-benefits-of ... -concepts/

Gemmie · Answer

n - 4^9 = 2 * (4^9 - 4^7) 
 n - 4^9 = 2 * 4^7 * (16 - 1) 
 n - 4^9 = 4^7 * 30 
 n = 4^7 * (4^2 + 3) 
 n = 4^7 * 46  
Answer E

karu26 · Answer

n-4^9 = 2 * (4^9-4^7)
n - 4^9 = 2*4^7*(16-1)
n = 4^7*46
IMO answer is E

mcelroytutoring · Answer

Attached is an image that should help.

The key 2 steps here are  factoring out 4^7  at the beginning and the end—and of course understanding the concept that the tick marks are evenly spaced.

In other words: each successive tick mark to the right is (4^9 - 4^7) greater than the one immediately to its left.

e3thekid · Answer

Difference between one space mark (k) = 
4^9 - 4^7 = 4^7 (4^2 - 1) -> 4^7(15)

n = 4^9 + 2k 
n = 4^9 + 2(4^7 * 15) 
n = 4^7 (4^2 + 30) 
n = (46)4^7

Option E

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83064 Harsha GMAT-Club-Forum-0dzfrbab.png

MBAToronto2024 · Answer

KarishmaB  
Hmmm...I got into the trap. 
d = 4^9-4^7 = 4^7*15

4^9 = a_1 v+ 2*4^7*15 -> a_1 = -14*4^7

n = -14*4^7 + 4*4^7*15

and that's why I clicked D. What's wrong here?

DanTheGMATMan · Answer

https://www.youtube.com/watch?v=gms9rKMsUx4

ManifestDreamMBA · Answer

If spacing b/w 2 marks is d
n = 4^7 +3d

d= 4^9 - 4^7 = 16 * 4^7 - 4^7 = 15 * 4^7

n = 4^7 + 3 * 15 * 4^7 = 4^7(1+45) = 46 * 4^7

The tick marks on the number line shown are equally spaced. What is

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