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.
Source: self-designed
Challenge#2 (Numbers/Exponents)
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- aneesh.kg
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Aneesh Bangia
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- Brent@GMATPrepNow
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Great question, Aneesh!
Multiple approaches (including one very fast approach) is the hallmark of a good GMAT math question.
Cheers,
Brent
Multiple approaches (including one very fast approach) is the hallmark of a good GMAT math question.
Cheers,
Brent
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Here's one approach.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
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
Cheers,
Brent
- aneesh.kg
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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.
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.
Aneesh Bangia
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
GMAT Math Coach
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- vishugogo
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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
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
- varun289
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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
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