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Math Expert V
Joined: 02 Sep 2009
Posts: 60646
If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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Difficulty:   15% (low)

Question Stats: 74% (01:05) correct 26% (01:16) wrong based on 437 sessions

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

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

DS11602.01
OG2020 NEW QUESTION

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Senior Manager  P
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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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
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

DS11602.01
OG2020 NEW QUESTION

#1
not sure whether 5th term is 2 or 0 insufficeint
#2
3rd term is 2 ; so 5th term cannot be found no info given
from 1 &2
we cannot determine 5th term;IMO E
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4228
Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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1
Top Contributor
Bunuel wrote:
If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

DS11602.01
OG2020 NEW QUESTION

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

Cheers,
Brent
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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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

GMAT assassins aren't born, they're made,
Rich
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

DS11602.01
OG2020 NEW QUESTION

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.

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# Scott Woodbury-Stewart

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Joined: 25 Feb 2019
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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ScottTargetTestPrep wrote:
Bunuel wrote:
If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

DS11602.01
OG2020 NEW QUESTION

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.

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 ...

Posted from my mobile device
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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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
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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m1033512 wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

DS11602.01
OG2020 NEW QUESTION

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.

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 ...

Posted from my mobile device

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.
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# Scott Woodbury-Stewart

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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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Bunuel if a3=2 then don't you think 0,1,2 will form an A.P? then answer should be B
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If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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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.

_________________

Originally posted by EgmatQuantExpert on 14 May 2019, 05:32.
Last edited by EgmatQuantExpert on 14 May 2019, 23:31, edited 1 time in total.
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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gmat8998 wrote:
Bunuel if a3=2 then don't you think 0,1,2 will form an A.P? then answer should be B

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
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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Bunuel Hey!
Didn't really think about a Fibonnaci.I thought that only AP/GP/HP is tested here Manager  B
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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From the question stem we have first term = 0, 2nd term=1.

Statement 1 clearly insufficient.

Statement 2: third term is 2. We now have
0,1,2,

I see a pattern here. From second term onward,each term is preceding term+1.

What am I missing ?
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Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th  [#permalink]

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if we have 4th is it suffice or not ? and does c correct ?
_________________ Re: If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th   [#permalink] 30 Sep 2019, 04:52
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