The full solution below is taken from the GMATFix App.
-Patrick
How many solutions?
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Source: Beat The GMAT — Data Sufficiency |
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Patrick_GMATFix
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Since A_n = r*n, we can think of the question as "for how many n's is r*n < 100?" The answer must depend on r. The bigger r is, the fewer r*n will equal less than 100. Rephrase: "What is r?"
The full solution below is taken from the GMATFix App.
-Patrick
The full solution below is taken from the GMATFix App.
-Patrick
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Brent@GMATPrepNow
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I have a feeling that this question is somewhat confusing in its current form.GmatGreen wrote:If r is a constant and A_n = r*n for all positive integers n, for how many values of n is A_n < 100?
1) A_50 = 500
B) A_100 + A_105 = 2,050
The question is talking about the terms in a sequence. The individual terms are defined as follows:
term(n) = (r)(n) for all positive integers n, where r is a constant value.
So, for example, if r = 5, then:
term1 = (5)(1) = 5
term2 = (5)(2) = 10
term3 = (5)(3) = 15
etc.
Of course, we don't know the value of r, which is why this is a data sufficiency question.
Okay, so let's word the question as follows:
Target question: For how many values of n is term(n) < 100?
term(n) = (r)(n) for all positive integers n, where r is a constant value. For how many values of n is term(n) < 100?
(1) term50 = 500
(2) term100 + term105 = 2,050
In other words, how many of the terms in the sequence are less than 100?
IMPORTANT: If we can find out what the ENTIRE sequence looks like, we can easily determine how many terms are less than 100.
Given: term(n) = (r)(n) for all positive integers n, where r is a constant value.
Statement 1: term50 = 500
The given information tells us that term(n) = (r)(n)
So, term50 = (r)(50) = 500
We can solve this to conclude that r = 10
Once we know that r = 10, we know what the ENTIRE SEQUENCE looks like: 10, 20, 30, 40, ....
Once we know what the entire sequence looks like, we can definitely determine how many terms are less than 100.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: term100 + term105 = 2,050
The given information tells us that term(n) = (r)(n)
So, term100 = (r)(50) and term105 = (r)(105)
So, statement 2 tells us that (r)(100) + (r)(105) = 2050
Rewrite as 100r + 105r = 2050
Simplify: 205r = 2050
We can solve this to conclude that r = 10
Once we know that r = 10, we know what the ENTIRE SEQUENCE looks like: 10, 20, 30, 40, ....
Once we know what the entire sequence looks like, we can definitely determine how many terms are less than 100.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
