If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th

Given: term1 = 0 and term2 = 1

Target question: Does term5 equal 2?
Once we scan the two statements, we can probably jump straight to
.
.
.
Statements 1 and 2 combined
There are several possible sequences that satisfy BOTH statements. Here are two:
Case a: {0, 1, 2, 0, 2,...}. In this case, the answer to the target question is YES, term5 IS 2
Case b: {0, 1, 2, 0, 0,...}. In this case, the answer to the target question is NO, term5 is NOT 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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Given:
I -- 0
II -- 1

1 stm: the fifth term is 0 or 2. insuff
2 stm: the third term is 2. nothing about the fifth term, or the method how we calculate terms. insuff

IMO both statements are not sufficient as well
I will bet on E

Hi All,

We're told that the 1st term of a sequence is 0 and the 2nd term is 1. We're asked if the 5th term in the sequence is 2. To properly answer any sequence question, we need to know the underlying pattern or formula behind it.

(1) Each odd-numbered term is either 0 or 2.

Fact 1 limits the possible values for the 5th term - it can only be 0 or 2. However, we don't know which one it is, so the answer to the question could be NO (if the 5th term is 0) or YES (if the 5th term is 2).
Fact 1 is INSUFFICIENT

(2) The 3rd term is 2.

Fact 2 gives us another term to work with (so we know that the sequence begins with 0, 1, 2...), but this tells us nothing about how the sequence "works", so we cannot deduce the values of any other terms in the sequence.
Fact 2 is INSUFFICIENT

Combined, we know...
Each odd-numbered term is either 0 or 2.
The 3rd term is 2.

Even combined, we still don't know what the 5th term is; with two possible values (and 2 different corresponding answers), the answer could be YES OR NO.
Combined, INSUFFICIENT

Final Answer:

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

We are given that the 1st term of a sequence is 0, and the 2nd term is 1, and we need to determine whether the 5th term is 2.

Statement One Alone:

Each odd-numbered term is either 0 or 2.

Since each odd-numbered term is either 0 or 2, the 5th term could be 0 or 2. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The 3rd term is 2.

The fact that the 3rd term is 2 does not tell us anything about the 5th term. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

With the two statements, we see that the 5th term is either 0 or 2. The two statements together are still not sufficient to answer the question.

Answer: E
_________________

For statement 2

1st is 0
2nd is 1

and 3rd is 2

so we have 1-0=2-1= 1

so it is an AP with First term a = 0 and d = 1 ?

so we calculate 5th term of this series ....

Could you correct me on this doubt ...

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Hi m1033512,

Since we do not know the 'formula' behind this sequence, the information in Fact 2 is not enough to conclusively prove how the sequence works. By extension, we don't know for sure what the 5th term would be.

If the first three terms are 0, 1 and 2, then it's POSSIBLE that we're dealing with an Arithmetic sequence that increases by 1 (meaning the next few terms would be 3, 4, 5, 6, etc). However, it's also POSSIBLE that we're dealing with a variation on a Fibonnaci sequence. For example, what if each term - after the second term - is equal to twice the sum of the prior two terms. In this situation, the sequence would be:

1st = 0
2nd = 1
3rd = (2)(0+1) = 2
4th = (2)(1+2) = 6
5th = (2)(2+6) = 16

Thus, Fact 2 is INSUFFICIENT.

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

Knowing the first term is 0, second is 1 and third is 2, doesn’t make the sequence an AP since we don’t know anything about the rest of the terms. For example, if the fourth term is 100, then it’s definitely not an AP.
_________________

If a3=2 then don't you think 0,1,2 will form an A.P? then answer should be B

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• In a given sequence, the 1st term is 0 and the 2nd term is 1.

We need to determine

• In that sequence, whether the 5th term is 2 or not.

As we do not have any information about the other elements present in the sequence or the pattern followed within the elements, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, each odd numbered term in the sequence is either 0 or 2.

• Hence, the 5th element can be either 0 or 2.
• But we can’t definitely say whether it is 2 or not.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the 3rd term is 2.

• However, from this statement we do not get any pertinent information about the 5th term.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

From both statements 1 and 2 together, we get

• The 5th element can be either 0 or 2.
• The 3rd element is 2.

However, even after combining the statements, we cannot conclude whether 5th element is 2 or not.

Hence, the correct answer choice is option E.


_________________

Hi gmat8998,

Unfortunately, having 3 terms in a sequence is not enough to define the sequence. Since we do not know the 'formula' behind this sequence, the information in Fact 2 is not enough to conclusively prove how the sequence works. By extension, we don't know for sure what the 5th term would be.

If the first three terms are 0, 1 and 2, then it's POSSIBLE that we're dealing with an Arithmetic sequence that increases by 1 (meaning the next few terms would be 3, 4, 5, 6, etc). However, it's also POSSIBLE that we're dealing with a variation on a Fibonnaci sequence. For example, what if each term - after the second term - is equal to twice the sum of the prior two terms. In this situation, the sequence would be:

1st = 0
2nd = 1
3rd = (2)(0+1) = 2
4th = (2)(1+2) = 6
5th = (2)(2+6) = 16

Thus, Fact 2 is INSUFFICIENT.

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

Answer: Option E

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Hi Bunuel, avigutman, CrackVerbal, I marked A in this question. My thinking was that since sequence has to be arranged in a particular order - ascending or descending - we can only have 2 as the value of the 5th term.

I understand sequences follow a certain pattern, but are they not arranged in ascending or descending order?

Thank you!

Hi CrushTHYgmat,

While Arithmetic and Geometric sequences typically increase or decrease in some type of consistent fashion, that does NOT mean that all sequences consistently increase or decrease. For example, consider the following:

f(n) = (-1)^n

This sequences is -1, +1, -1, +1, -1, +1 etc. and it clearly does not consistently increase or decrease. When it comes to DS questions, you have to consider more than just the 'obvious' answer - and in prompts such as this one, you have to be careful about your assumptions (as an incorrect assumption can easily lead you to assume that one of the incorrect answers is correct).

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

Contact Rich at: Rich.C@empowergmat.com

Fibonacci Series is 0 1 1 2 ...
Here we have 0 1 2 ....
Therefore I think it is not possible for this series to be Fibonacci Series.
After reading the other posts I understand a Sequence means it cannot be assumed it's in AP GP until we have solid evidence. Here we have 3 elements which are still not enough it seems. My question is. Can a series be -> 0 1 2 0 1 2 ? Or 0 1 2 67 100 ... No pattern at all? Doesn't the word sequence means there has to be some pattern.

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