The Integers A, B, C and D are shown on the number line

[atharshiraz]

A question came up on the CAT exams by MGMAT:



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

It is pretty clear that if the integers are equally placed then B should be 5^11 and A should be 5^10.

Yet this is not the answer given by the solutions. It is a complicated number manipulation that tries to fit the answer as a multiple of 5^12.

The correct answer is apparently D. But I think 5^10 ought to be correct. It is straightforward and it doesn't make sense to get the answer in the 5^12 form.

p.s. Would you please email me also when you respond because even though I click notify me when a reply is posted I am not notified (atharshiraz AT gmail) thanks!

[peebee]

The key to this problem is recognizing the term evenly spaced. We know that it must be an arithmetic difference.

If you restate the two numbers as 1 x 5^12 and 5 x 5 ^ 12, we can see the difference between the two is 4 x 5^12. Therefore B would be 1 - 4 = -3 x 5^12 and A would be -3-4 = -7 x 5^12.

I think that's right.

Hope this helps!

[atharshiraz]

The key to this problem is recognizing the term evenly spaced. We know that it must be an arithmetic difference.
Hope this helps!

Well I know how to get the number into the right form (-7x 5^12). My question was why is 5^10 wrong (or incorrect) when it is the most logical and straightforward application. On the exam we will not go through the number manipulation but will go straight for what is obvious right?

Why is 5^10 then incorrect if we apply the evenly spaced argument and come up with the logical answer of 5^10 ?

[peebee]

The key to this problem is recognizing the term evenly spaced. We know that it must be an arithmetic difference.
Hope this helps!

Well I know how to get the number into the right form (-7x 5^12). My question was why is 5^10 wrong (or incorrect) when it is the most logical and straightforward application. On the exam we will not go through the number manipulation but will go straight for what is obvious right?

Why is 5^10 then incorrect if we apply the evenly spaced argument and come up with the logical answer of 5^10 ?

Think of it in Easier Terms:
A - 5^1 = 5
B - 5^2 = 25
C - 5^3 = 125
D - 5^4 = 625

Diff between A and B is 20, between B and C is 100, and finally between C and D is 500. Yes, the geometric multiple between each two numbers is 5, however the problem states that it is a constant between terms.

Similarly, the difference between each of 5^10, 5^11, 5^12 and 5^13 is not a constant number as the problem stipulates.

[atharshiraz]

The key to this problem is recognizing the term evenly spaced. We know that it must be an arithmetic difference.
Hope this helps!

Think of it in Easier Terms:
A - 5^1 = 5
B - 5^2 = 25
C - 5^3 = 125
D - 5^4 = 625

Diff between A and B is 20, between B and C is 100, and finally between C and D is 500. Yes, the geometric multiple between each two numbers is 5, however the problem states that it is a constant between terms.

Similarly, the difference between each of 5^10, 5^11, 5^12 and 5^13 is not a constant number as the problem stipulates.

Got it.

Thank you very much.

[tim]

excellent job peebee; thanks for your help in explaining this one!