Sequence \(X\) consists of \(825\) terms, and each term after the first term is \(5\) more than the preceding term.

[M7MBA]

Sequence \(X\) consists of \(825\) terms, and each term after the first term is \(5\) more than the preceding term. What is the \(500\)th term of sequence \(X?\)

(1) The \(515\)th term of sequence \(X\) is \(-98\)

(2) The first term of sequence \(X\) is \(-2668\)

Answer: D

Source: Magoosh

[Brent@GMATPrepNow]

Sequence \(X\) consists of \(825\) terms, and each term after the first term is \(5\) more than the preceding term. What is the \(500\)th term of sequence \(X?\)

(1) The \(515\)th term of sequence \(X\) is \(-98\)

(2) The first term of sequence \(X\) is \(-2668\)

Answer: D

Source: Magoosh

Target question: What is the value of term 500?

Given: Each term after the first term is 5 more than the preceding term.

Statement 1: Term 515 of sequence X is -98.
Since each term is 5 more than the preceding term, we know that
term 514 = -103
term 513 = -108
term 512 = -113
term 511 = -118
etc

As you can see, we COULD keep this pattern going to eventually determine the value of term 500
ASIDE: We'd never actually waste our time finding the value of term 500. We need only recognize that we COULD find the value of term 500
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: term 1 = -2668
Since each term is 5 more than the preceding term, we know that
term 2 = -2663
term 3 = -2658
term 4 = -2653
term 5 = -2648
etc
As you can see, we COULD keep this pattern going to eventually determine the value of term 500
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent