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Challenge#2 (Numbers/Exponents)

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Challenge#2 (Numbers/Exponents)

by aneesh.kg » Tue Jan 29, 2013 9:00 am
C#2:
If A, B, C and D are evenly spaced on the number line as shown below
A....B....C....D
and B = 3^13 and D = 3^15, then what is the value of A?

(A) 3^12
(B) 4(3^13)
(C) - 4(3^13)
(D) - 3^12
(E) - 3^14

OA after sometime.
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by Brent@GMATPrepNow » Tue Jan 29, 2013 9:42 am
Great question, Aneesh!
Multiple approaches (including one very fast approach) is the hallmark of a good GMAT math question.

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by rajatvmittal » Wed Jan 30, 2013 8:54 am
IMO E
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by Brent@GMATPrepNow » Wed Jan 30, 2013 8:58 am
aneesh.kg wrote:C#2:

If A, B, C and D are evenly spaced on the number line as shown below
A....B....C....D
and B = 3^13 and D = 3^15, then what is the value of A?

(A) 3^12
(B) 4(3^13)
(C) - 4(3^13)
(D) - 3^12
(E) - 3^14
Here's one approach.

First, we can make things much easier on ourselves if we first recognize that:
D = 3^15 = (3^2)(3^13) = 9(3^13)

Why did I do that?
Well, now both of the two given values have like terms.
B = 3^13 and D = 9(3^13)

At this point, we can "ignore" the 3^13 for a while. In fact, let's say that x = 3^13
So, we have B = x and D = 9x
At this point, we can determine the value of C

If the numbers are evenly spaced, then it must be true that D-C = C-B
In other words, 9x - C = C - x
Rearrange to get: 10x = 2C
Solve to get: 5x = C

So, our numbers are: A=?, B=x, C=5x, D=9x
As you can see, we add 4x to each value to get the next value.
So..... A= -3x

At this point, we'll replace x with 3^13 to see that A = -3(3^13)
Check the answer choices . . . not there. Looks like we need to rewrite it.

A = -3(3^13) = -1(3)(3^13) = -1(3^1)(3^13) = [spoiler]-1(3^14)[/spoiler] = E

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by aneesh.kg » Wed Jan 30, 2013 9:45 am
Thank you Brent!

I'd solve this in a similar fashion, albeit without oversimplification. (Maybe you did that for the sake of explaining well)

The difference between D and B is twice the difference between each consecutive element.

D - B = 3^15 - 3^13 = 3^13 * (3^2 - 1) = 8 * 3^13
Difference between consecutive elements = 1/2 of above = 4 * 3^13

A is 4 * 3^13 short of B.
Therefore, A = 3^13 - 4 * 3^13 = 3^13 * (1 - 4) = -3 * 3^13

This is when some people look at the options and get worried on seeing that none of the options read like the answer obtained above.

But, if you look carefully -3 * 3^13 = [spoiler]- 3^14[/spoiler].
[spoiler](E)[/spoiler] is the correct answer.
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by vishugogo » Thu Jan 31, 2013 11:13 am
One more approach algebraically....

all the terms are in A.P. so we can write the following

A = a
B = a+d
C = a+2d
D = a+3d

so D-B =2d
d = 4*3^14

B-A = d
A = 3^13-4*3^13
= -3^14
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by varun289 » Fri Feb 01, 2013 8:38 am
bacause it said evenly spaced

we should take 3~2 = 9.3^13

now even space b/t B and D so C is (1+9)/2=5.3^13

now A = B-diffrenece i.e -3.3^13 = -1.(3^14)= -3^14 , So E

enjoy

good question dear - how u made it ? really u made at ur own
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by sana.noor » Wed May 08, 2013 1:54 am
E, it was a good question
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