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Algebra Sequence & Series

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by and1ms238 » Fri Feb 19, 2010 10:41 am
This problem comes from OG 12 #45.

If r is a constant and an=an for all positive integers n, for how many values of n is an<100?

(1) a50 = 500
(2) a100 + A105 = 2,050

NOTE: an is read as function of n... in essence... f(n)

My questions is what is the GMACs definition of value? I went through this problem assuming that value can be a rational number as well... not just an integer.

The answer is D: each statement ALONE is sufficient. And the reasoning is that n = 1, 2, 3, 4, 5, 6, 7, 8 and 9. My reasoning is that you can not determine the exact values because the EXACT value are infinite... assuming rational numbers. Am I way off? Someone just help me through the reasoning of this problem. I was able to figure out the problem algebraically and get that r = 10.. but just could not grasp my mind around "For How Many Values of N..."

Thank you.
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Source: — Data Sufficiency |
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by papgust » Fri Feb 19, 2010 6:38 pm
If r is a constant and an=r*n for all positive integers n, for how many values of n is an<100?

(1) a50 = 500
(2) a100 + A105 = 2,050


Firstly, you have transcribed the question incorrectly. It is an = r*n.

ok, so coming to the question. For how many values of n is an < 100?

1. a50 = 500

a50 = r * n. You know that n is 50.
a50 = r * 50 = 500. So, r = 10.

Now, calculate the value of an as 100.
a10 = 10 * 10 = 100
This is of the form,
an = r * n

So, for an to be < 100, n can take 9 values because a10 equals 100. Question asks for < 100.

Sufficient.

2. a100 + A105 = 2,050

Same logic as statement I. Sufficient to answer.

Hence, D
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by and1ms238 » Fri Feb 19, 2010 8:23 pm
Yes, I understand how to get there. In my practice, I calculated that correctly. But I was under the impression that *value* in the question's stem " for how many values of n is an<100?" includes all rational numbers.

So my question is: Are all 'values' considered integers? I thought all values included rational numbers. Therefore, I assumed that it would be insufficient since the number of 'values' would be infinite.

Do you understand my question? Sorry if I'm not too clear.
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by shashank.ism » Sun Feb 21, 2010 4:14 am
and1ms238 wrote:This problem comes from OG 12 #45.

If r is a constant and an=an for all positive integers n, for how many values of n is an<100?

(1) a50 = 500
(2) a100 + A105 = 2,050

NOTE: an is read as function of n... in essence... f(n)

My questions is what is the GMACs definition of value? I went through this problem assuming that value can be a rational number as well... not just an integer.

The answer is D: each statement ALONE is sufficient. And the reasoning is that n = 1, 2, 3, 4, 5, 6, 7, 8 and 9. My reasoning is that you can not determine the exact values because the EXACT value are infinite... assuming rational numbers. Am I way off? Someone just help me through the reasoning of this problem. I was able to figure out the problem algebraically and get that r = 10.. but just could not grasp my mind around "For How Many Values of N..."

Thank you.
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by harsh.champ » Sun Feb 21, 2010 4:19 am
and1ms238 wrote:Yes, I understand how to get there. In my practice, I calculated that correctly. But I was under the impression that *value* in the question's stem " for how many values of n is an<100?" includes all rational numbers.

So my question is: Are all 'values' considered integers? I thought all values included rational numbers. Therefore, I assumed that it would be insufficient since the number of 'values' would be infinite.

Do you understand my question? Sorry if I'm not too clear.
Hey just read this part frm the ques:-
If r is a constant and an=an for all positive integers n, for how many values of n is an<100?
It is written that the equation is only valid for all +ve integers.
Hence,the answer would not be infinite.

Hope you get the point.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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