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Expert replies
by vipulgoyal » Wed Jul 10, 2013 10:51 pm
In the number line, point A, B, C, D, and E are spaced equally. If point A represents 3^11 and point B represents 3^12, point E represents which of the following values?
(A) 3^11+3^12
(B) 3^13
(C) 3^12+3^13
(D) 3^14
(E) 3^15
B
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Source: — Problem Solving |

by GMATGuruNY » Thu Jul 11, 2013 2:41 am
vipulgoyal wrote:In the number line, point A, B, C, D, and E are spaced equally. If point A represents 3^11 and point B represents 3^12, point E represents which of the following values?
(A) 3^11+3^12
(B) 3^13
(C) 3^12+3^13
(D) 3^14
(E) 3^15
B
Since the points are EQUALLY SPACED, the number line looks like this:
A=3¹¹......B=3¹².....C......D......E

Distance between B and A = 3¹² - 3¹¹ = 3¹¹I3-1) = 3¹¹(2).

To travel from B to E, this distance must be added to B a total of 3 times.
Thus:
E = 3¹² + 3(3¹¹)(2) = 3¹² + (3¹²)(2) = 3(3¹²) = 3¹³.

The correct answer is B.
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by Brent@GMATPrepNow » Thu Jul 11, 2013 6:42 am
vipulgoyal wrote:In the number line, point A, B, C, D, and E are spaced equally. If point A represents 3^11 and point B represents 3^12, point E represents which of the following values?
(A) 3^11+3^12
(B) 3^13
(C) 3^12+3^13
(D) 3^14
(E) 3^15
B
Here's another approach:

First, let's examine some OTHER examples of equally-spaced values:
5, 15, 25, 35, 45
We can rewrite these 5 values as 1(5), 3(5), 5(5), 7(5), 9(5)
Notice that each value is rewritten as a product of 5.
Also notice that the coefficients (1, 3, 5 etc.) increase by 2 each time.

Here some more examples of equally spaced values:
4(2),7(2),10(2),13(2),17(2)
In this example, the coefficients (4, 7, 10 etc.) increase by 3 each time.

-3(11), 5(11), 13(11), 21(11), 29(11),
In this example, the coefficients (-3, 5, 13 etc.) increase by 8 each time.

So, if we can take equally-spaced values and rewrite them as products with like terms, the coefficients will increase (or decrease) the same amount.

Okay, now onto the question.
A = 3^11 = (1)(3^11)
B = 3^12 = (3^1)(3^11) = (3)(3^11)
So, the coefficients must increase by 2 each time, which means . . .
C = (5)(3^11)
D = (7)(3^11)
E = (9)(3^11) = (3^2)(3^11) = [spoiler]3^13 = B[/spoiler]

Cheers,
Brent
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by subhakam » Thu Sep 12, 2013 6:43 pm
Brent@GMATPrepNow wrote:
vipulgoyal wrote:In the number line, point A, B, C, D, and E are spaced equally. If point A represents 3^11 and point B represents 3^12, point E represents which of the following values?
(A) 3^11+3^12
(B) 3^13
(C) 3^12+3^13
(D) 3^14
(E) 3^15
B
Here's another approach:

First, let's examine some OTHER examples of equally-spaced values:
5, 15, 25, 35, 45
We can rewrite these 5 values as 1(5), 3(5), 5(5), 7(5), 9(5)
Notice that each value is rewritten as a product of 5.
Also notice that the coefficients (1, 3, 5 etc.) increase by 2 each time.

Here some more examples of equally spaced values:
4(2),7(2),10(2),13(2),17(2)
In this example, the coefficients (4, 7, 10 etc.) increase by 3 each time.

-3(11), 5(11), 13(11), 21(11), 29(11),
In this example, the coefficients (-3, 5, 13 etc.) increase by 8 each time.

So, if we can take equally-spaced values and rewrite them as products with like terms, the coefficients will increase (or decrease) the same amount.

Okay, now onto the question.
A = 3^11 = (1)(3^11)
B = 3^12 = (3^1)(3^11) = (3)(3^11)
So, the coefficients must increase by 2 each time, which means . . .
C = (5)(3^11)
D = (7)(3^11)
E = (9)(3^11) = (3^2)(3^11) = [spoiler]3^13 = B[/spoiler]

Cheers,
Brent
Hello Brent - I am having a hard time understanding the below
"if we can take equally-spaced values and rewrite them as products with like terms, the coefficients will increase (or decrease) the same amount"

In other words- does the problem above represent liner or exponential sequence? Looking at the constant increase of multiple of 3 , i assume this is an exponential sequence? If that is the case then E should be 3^15
This is because i am plugging in the value of exponential sequence-
Let me know
Thanks
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