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what is the value of A

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by jain2016 » Mon Apr 18, 2016 10:17 am
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5 12 and 5 13, respectively, what is the value of A?

A) 5^ 11
B) 5^ 10
C) -5^ 12
D) (-7)5^ 12
E) (-12)5^ 13

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by DavidG@VeritasPrep » Mon Apr 18, 2016 10:36 am
jain2016 wrote:The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

A) 5^ 11
B) 5^ 10
C) -5^ 12
D) (-7)5^ 12
E) (-12)5^ 13

OAD
I believe the question should have had C = 5^12 and D = 5^13.

Let's call the distance of each segment: x. So the distance between A and B is x, and the distance between B and C is x, etc. So the gap between A and C is 2x, meaning that A = 5^12 -2x.

Now we need to solve for x. If the distance between D and C is x, then we set x = 5^13 - 5^12.
Factor out 5^12, so that 5^13 - 5^12 = 5^12(5 - 1) = 5^12 * 4.

If x = (5^12) * 4, and A = 5^12 - 2x, then A = 5^12 - 2[(5^12) * 4] = 5^12 - (5^12)*8 = (5^12)(1 - 8) = (5^12)*(-7)

Answer is D
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by ceilidh.erickson » Mon Apr 18, 2016 12:45 pm
David's explanation is perfect, and that's really the only way to solve this one. I just want to add (since I was talking about this problem with a student a few days ago)...

If you ever get an answer on the GMAT that feels way too easy, it probably is!

A shocking number of students pick 5^10 on this one, even though they think "huh, it's probably too easy to go 12 - 1 - 1." Trust that instinct! Any answer that you can get to by doing just 1 or 2 pieces of simple arithmetic can't be the answer. The GMAT is never that nice! Ask yourself - what's the twist in this problem that I missed?

On this problem, it's "equally spaced." Consecutive powers (for any base other than 0, 1, or -1) will never be evenly spaced, so it can't be as simple as just subtracting exponents.
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by GMATGuruNY » Mon Apr 18, 2016 1:22 pm
jain2016 wrote:The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5¹² and 5¹³, respectively, what is the value of A?

A) 5¹¹
B) 5¹�
C) -5¹²
D) (-7)5¹²
E) (-12)5¹³

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The length of each space = CD.

Since A is 3 spaces to the left of D, we get:
A = D - (3)(CD)

= 5¹³ - 3(5¹³ - 5¹²)

= 5¹³ - 3(5¹³) + 3(5¹²)

= -2(5¹³) + 3(5¹²)

= 5¹²(-2*5 + 3)

= 5¹²(-7).

The correct answer is D.
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by Brent@GMATPrepNow » Mon Apr 18, 2016 1:45 pm
Here are two similar questions to practice with:
- https://www.beatthegmat.com/evenly-space ... 63714.html
- https://www.beatthegmat.com/challenge-2- ... 67201.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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