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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?
(1) The sum of the first 2 terms is 15
(2) The first term of the sequence is 9
(1) The sum of the first 2 terms is 15
(2) The first term of the sequence is 9
02 Jun 2016, 13:42
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Let the first term = a , the second term will be equal to 2a/3. The third term = (2*2*a)/(3*3).
Thus the nth term = (a*2^(n-1))/(3^(n-1)). We are supposed to calculate the 100th term, so n = 100.
Stmt1 : Sum of first 2 terms = a + 2a/3 = 15. One equation one variable. we can solve this. Sufficient.
Stm2 : First term = a = 9. We already know n. Hence putting these values in the general equation of any term will give us the 100th term. Suff.
Hence D.
Thus the nth term = (a*2^(n-1))/(3^(n-1)). We are supposed to calculate the 100th term, so n = 100.
Stmt1 : Sum of first 2 terms = a + 2a/3 = 15. One equation one variable. we can solve this. Sufficient.
Stm2 : First term = a = 9. We already know n. Hence putting these values in the general equation of any term will give us the 100th term. Suff.
Hence D.
04 Jun 2017, 07:11
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Bunuel
Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?
(1) The sum of the first 2 terms is 15
(2) The first term of the sequence is 9
(1) The sum of the first 2 terms is 15
(2) The first term of the sequence is 9
Target question: What is the 100th term of the sequence S?
Given: Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3.
In other words, if term_n = k, then term_(n+1) = (2/3)k
IMPORTANT: once we know the value of ANY term in the sequence, we can determine every other term in the sequence.
Statement 1: The sum of the first 2 terms is 15
Let x = term1
So, (2/3)x = term2
We can write: x + (2/3)x = 15
Since we COULD solve this equation for x, we COULD determine the value of the first term in the sequence, which means we COULD calculate every term in the sequence.
So, we COULD find the value of term100.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT
NOTE: Of course, we're not going to actually calculate the 100th term, since doing so would be a waste of precious time
Statement 2: The first term of the sequence is 9
Now that we know the value of the first term in the sequence, we COULD calculate every term in the sequence.
So, we COULD find the value of term100.
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT
Answer:
Cheers,
Brent
