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In a sequence of numbers in which each term is 2 more than

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by AbeNeedsAnswers » Sun Apr 28, 2019 3:16 pm

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In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term?

(1) The last term is 90.
(2) The first term is 2.

B

Source: Official Guide 2020
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Apr 29, 2019 9:55 am
AbeNeedsAnswers wrote:In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term?

(1) The last term is 90.
(2) The first term is 2.
Given: Sequence of numbers is such that each term is 2 more than the preceding term

Target question: What is the value of term_4?

Statement 1: The last term is 90.
We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . .

Consider these two possible cases:
Case a: The last term is term_6. In this case, term_6 = 90. term_5 = 88, term_4 = 86, term_3 = 84....etc. So, the answer to the target question is term_4 = 86
Case b: The last term is term_5. In this case, term_5 = 90. term_4 = 88, term_3 = 86 ....etc. So, the answer to the target question is term_4 = 88
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The first term is 2.
If term_1 = 2, then: term_2 = 4, term_3 = 6, term_4 = 8, . .. etc
The answer to the target question is term_4 = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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by [email protected] » Mon Apr 29, 2019 2:58 pm
Hi All,

We're told that in a sequence of numbers, each term is 2 more than the preceding term. We're asked for the fourth term. Sequence questions often come down to two pieces of information: the "formula" for how the sequence progresses and one (or more) of the terms (so that you can calculate the other terms in the sequence). The prompt tells us the formula (add 2 as you go from term to term), so we just need one of the terms in the sequence to find the value of the 4th term.

(1) The last term is 90.

With the information in Fact 1, we can 'work backwards' to find the preceding terms (88...86...84...82, etc.), but we don't know which one will be the 4th term.
Fact 1 is INSUFFICIENT

(2) The first term is 2.

With the information in Fact 2, we can 'work forwards' from the 1st term to find the 4th term:
2nd term = 2+2 = 4
3rd term = 4+2 = 6
4th term = 6+2 = 8
Fact 2 is SUFFICIENT

Final Answer: B

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