This question is from GMAT Prep so anyone planning to give the practice exam may avoid to see it here.
For others, Please help me in answering the below question:
a1, a2, a3,..., a15
In the sequence shown, an= an-1 + k, where 2<=n<=15 and k is a nonzero constant. How many terms in the sequence are greater than 10?
1. a1 = 24
2. a8 = 10
Thanks in advance!
Sequence of numbers
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- GMATinsight
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Given: an= an-1 + k where 1<n<16DevB wrote:This question is from GMAT Prep so anyone planning to give the practice exam may avoid to see it here.
For others, Please help me in answering the below question:
a1, a2, a3,..., a15
In the sequence shown, an= an-1 + k, where 2<=n<=15 and k is a nonzero constant. How many terms in the sequence are greater than 10?
1. a1 = 24
2. a8 = 10
Thanks in advance!
Question : How many terms in the sequence are greater than 10?
Statement 1) a1 = 24
k is unknown therefore rest of the terms can't be calculated
INSUFFICIENT
Statement 2)a8 = 10
for any non zero value of k, terms will be greater and 7 terms will be smaller than 10 therefore
SUFFICIENT
Answer: Option B
Last edited by GMATinsight on Tue Jul 22, 2014 6:02 am, edited 1 time in total.
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Statement 1 is clearly insufficient.a(1), a(2),...., a(15)
In the sequence shown, a(n) = a(n-1) + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
1) a(1)=24
2) a(8)=10
Statement 2: a₈ = 10.
If k>0, then the sequence is INCREASING: each term in the sequence is GREATER than the preceding term.
In this case, a₉...a�₅ -- a total of 7 terms -- will be greater than 10.
If k<0, then the sequence is DECREASING: each term in the sequence is LESS than the preceding term.
In this case, a�...a₇ -- a total of 7 terms -- will be greater than 10.
In each case, the number of terms greater than 10 = 7.
SUFFICIENT.
The correct answer is B.
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Target question: How many term in the sequence a1,a2,a3...a15 are greater than 10?a1,a2,a3...a15
In the sequence shown, a(n) = a(n-1)+k, where 2 < n < 15, and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
(1) a1 = 24
(2) a8 = 10
Given: a(n) = a(n-1)+k, where 2 < n < 15
In other words, each term is derived by taking the term before it and adding k
IMPORTANT: Keep in mind that k can be either a positive or negative number. So, the sequence may be increasing (e.g., 5, 7, 9, 11...) or it may be decreasing (e.g., 20, 15, 10, ...)
Statement 1: a1 = 24
The 1st term is 24, but since we don't know the value of k, there's no way to determine the terms in the sequence that are greater than 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a8 = 10
Let's consider the 2 possible cases for k (k is POSITIVE or k is NEGATIVE)
case a: k is POSITIVE
This means that the sequence is INCREASING.
In other words, term1 < term2 < term3, etc.
The 8th term is 10, which means every term after the 8th term must be greater than 10.
So, terms 9, 10, 11, 12, 13, 14 and 15 are greater than 10.
This means that 7 terms in the sequence are greater than 10
case b: k is NEGATIVE.
This means that the sequence is DECREASING.
In other words, term1 > term2 > term3, etc.
The 8th term is 10, which means every term before the 8th term must be greater than 10.
So, terms 1, 2, 3, 4, 5, 6 and 7 are greater than 10.
This means that 7 terms in the sequence are greater than 10
Since BOTH cases yield the SAME answer to the target question, we can be certain that 7 terms in the sequence are greater than 10
Statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent