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

Question

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.

DS12602.01
OG2020 NEW QUESTION

ZoltanBP · Accepted Answer

We know that these numbers form an arithmetic sequence with a difference of 2. The original question:  a_4=?

1) If the last term is the 4th term, then  a_4=90 . However, if the last term is the 5th term, then  a_4=90-2=88 . Thus, we can't get a unique value to answer the original question.  \implies   Insufficient

2) We know that  a_1=2 , so  a_4=2+(4-1)\cdot 2=8 . Thus, the answer to the original question is a unique value.  \implies   Sufficient

Answer: B

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=WztQd_w9m4M

Chethan92 · Answer

Difference = 2

From S1:

Last term is 90, but no info about first term.
Hence Insufficient.

From S2:

First term = 2
Next term = 2+2 = 4
4th term = 8
Sufficient.

B is the answer.

BrentGMATPrepNow · Answer

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

Cheers,
Brent

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made, 
Rich

EgmatQuantExpert · Answer

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given
 • In a sequence of numbers, each term is 2 more than the preceding term.

We need to determine
 • The value of the fourth term.

As each term is 2 more than the preceding term, the series is an example of an arithmetic progression.
Hence, to find the value of the fourth term, we need to know either the 1st term or the value of any other specific term.
With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, the last term is 90.
 • However, from this statement we don’t know which term is the last term.
 
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the first term is 2.
As every term is 2 more than the previous term, we can say
 • Second term = 2 + 2 = 4
• Third term = 4 + 2 = 6
• Fourth term = 6 + 2 = 8 
As we can determine the value of the fourth term, we can say statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 2 individually, this step is not required.
Hence, the correct answer choice is option B.

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-Algebra-e1533292163516.png

Pritishd · Answer

1. The formula for the  n^{th}  term of a AP is  first term   + (n - 1) *   common difference 
2. The question provides us the common difference i.e.  2  and value of  n  i.e.  4 
3. Plugging the above values into the formula, we get  first term   + (4 - 1) * 2 =   first term  +  6 
4. In order to answer the question we need to find the value of the  first term

Observing the options, we see that option B provides the value of the first term.

Ans.  B

MHIKER · Answer

(1) We know increment but we don't know the first term. Insufficient
 
(2) We know increment and the first term. sufficient.

The answer is B

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=lGOVkWbYhwU

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine the 4th term of a sequence. Notice that this is an arithmetic sequence since each term is 2 more than the preceding term, and thus 2 is the common difference of the sequence. In any arithmetic sequence, we can find the nth term as long as we know the value of any term in the sequence and its position in the sequence.Since here we know d = 2, then to find the 4th term, all we need to know is another term in the sequence provided that we know its position in the sequence.

Statement One Alone:

Even though we know the last term is 90, however, we don’t know the number of terms in the sequence. For example, if the sequence has 10 terms, then we have a_10 = 90. However, if the sequence has 100 terms, then we have a_100 = 90. The former example will yield a different value for a_4 (the fourth term) than the latter example. Therefore, statement one alone is not sufficient.

Statement Two Alone:
 
Since we know the first term is 2, we can determine the fourth term. That is, if we let n = 4 and m = 1 and use the formula for the nth term of a sequence: a_n = a_1+ d(4 - 1), we have:

a_4 = a_1 + 2(4 - 1)

a_4 = 2 + 6

a_4 = 8

We see that the 4th term is 8. Statement two alone is sufficient.

Answer: B

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