Data Sufficiency

25 integers are written on a board. Are there at least two consecutive integers among them?

1: If any single value in the list is increased by 1, the number of distinct values in the list does not change.

2: At least one value occurs more than once in the list.

OA: C

P.S: Got it wrong (I chose E). So,would request explanation from Experts.

As Brent notes in his post below, the wording in statement 1 is ambiguous.
I believe that the following represents the intent of the problem:

25 integers are written on a board. Are there at least two consecutive integers among them?

1: If any single value in the list is increased by 1, the number of distinct values in the list does not change.

2: At least one value occurs more than once in the list.[/color]

Each of the cases tested below is composed of integers in ASCENDING ORDER.
{1, 1, 1...1, 1, 2} implies the following 25 integers:
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2}.

Statement 1: If any single value in the list is increased by 1, the number of distinct values in the list does not change
Test one case that also satisfies statement 2.
Case 1: {1, 1, 1...1, 1, 2}, for a total of two distinct values
Here, if 1 increases to 2, or if 2 increases to 3, the list will still contain two distinct values.
In this case, the list contains at least two consecutive integers, so the answer to the question stem is YES.

Test one case that doesn't also satisfy statement 2.
Case 2: {1, 3, 5...45, 47, 49}, for a total of 25 distinct values
Here, if any integer in the list increases by 1, the list will still contain 25 distinct values.
In this case, the list does not contain at least two consecutive integers, so the answer to the questions stem is NO.
INSUFFICIENT.

Statement 2: At least one value occurs more than once in the list
Case 1 also satisfies statement 2.
In Case 1, the list contains at least two consecutive integers, so the answer to the question stem is YES.
Case 3: {1, 1, 1...1, 1, 1}
In this case, the list does not contain at least two consecutive integers, so the answer to the questions stem is NO.
INSUFFICIENT.

Statements combined:
Case 1 satisfies both statements.

Try adjusting Case 1 so that it does NOT contain at least two consecutive integers.
Case 4: {1, 1, 1...1, 1, 3}, for a total of two distinct values
Not viable:
If one of the 1's increases to 2, then the number of distinct values will increase from two to three, violating the constraint in statement 1.
Implication:
To satisfy both statements, the list MUST contain at least two consecutive integers, so the answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.

GMATGuruNY wrote:

RBBmba@2014 wrote:25 integers are written on a board. Are there at least two consecutive integers among them?

1: If any single value in the list is increased by 1, the number of distinct values in the list does not change.

2: At least one value occurs more than once in the list.

Statement 1: If any single value is increased by 1, the number of distinct values in the list does not change
Test one case that also satisfies statement 2.
Case 1: {1, 1, 1...2}, for a total of two distinct values
Here, if 1 increases to 2, or if 2 increases to 3, the list will still contain two distinct values.
In this case, the list contains at least two consecutive integers, so the answer to the question stem is YES.

This is fine. A quick question although - how many 1s you've considered here ? I think, 24 number of 1s. Right ? If yes, then in the below Case 4, there are also 24 number of 1s, I guess. Then how statement 1 is NOT valid in this Case 4 ?

GMATGuruNY wrote:
Statements combined:
Case 1 satisfies both statements.

Try adjusting Case 1 so that it does NOT contain at least two consecutive integers.
Case 4: {1, 1, 1...3}, for a total of two distinct values
Not viable:
If one of the 1's increases to 2, then the number of distinct values will increase from two to three, violating the constraint in statement 1.
Implication:
To satisfy both statements, the list MUST contain at least two consecutive integers, so the answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.

It should also satisfy statement 1, like Case 1. ONLY difference between Case 1 & 4 is, I think, Case 1 contains one "2" and Case 4 contains one "3". Rest of the part of both of these two cases is having same data i.e. 24 number of 1s. Right ?

Please clarify.

Brent@GMATPrepNow wrote:I'm not a big fan of this question. In my opinion, it's somewhat ambiguous.
I first read statement 1 to mean that we are increasing every value by one. Of course, this would have no effect on the number of distinct values in the list (in any situation), so I had to re-read statement 1 to see if there's another possible interpretation.
It seems that the author's intent is for us to add 1 to a single value in the list.
This intent could be phrased as "If ANY value in the list is increased by 1, the number of distinct values in the list does not change."

Cheers,
Brent

Brent - I got trapped in the same line! If statement 1 were to mean that we are increasing every value by one then, I think, both the statements combined it'd be NOT possible to reach to a DEFINITE conclusion, hence OA would be E. Right ?

RBBmba@2014 wrote:

GMATGuruNY wrote: Statement 1: For every value in the list, if the value is increased by 1, the number of distinct values in the list does not change
Test one case that also satisfies statement 2.
Case 1: {1, 1, 1...2}, for a total of two distinct values
Here, if 1 increases to 2, or if 2 increases to 3, the list will still contain two distinct values.
In this case, the list contains at least two consecutive integers, so the answer to the question stem is YES.

This is fine. A quick question although - how many 1s you've considered here ? I think, 24 number of 1s. Right ?

Correct.
I've added the following clarification to my post above:
Each of the cases tested below is composed of integers in ASCENDING ORDER.
{1, 1, 1...1, 1, 2} implies the following 25 integers:
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2}.

As per Brent's post, I've also reworded Statement 1, which now reads as follows:
If any single value in the list is increased by 1, the number of different values in the list does not change.

If yes, then in the below Case 4, there are also 24 number of 1s, I guess.Then how statement 1 is NOT valid in this Case 4 ?

Case 1: {1, 1, 1...1, 1, 2}
Here, there are TWO distinct values (1 and 3).
Option A:
If one of the 1's increases by 1 to yield a 2, we get the following list:
{1, 1, 1...1, 1, 2}.
In the resulting list, there are still TWO distinct values (1 and 2).
Option B:
If the 2 increases by 1 to yield a 3, we get the following list:
{1, 1, 1...1, 1, 3}.
In the resulting list, there are still TWO distinct values (1 and 3).
Thus, Case 1 satisfies the constraint in statement 1:
If any single value in the list is increased by 1, the number of different values in the list does not change.

Case 4: {1, 1, 1...1, 1, 3}
Here, there are TWO distinct values (1 and 3).
Option A:
If one of the 1's increases by 1 to yield a 2, we get the following list:
{1, 1, 1...1, 2, 3}.
In the resulting list, there are THREE distinct values (1, 2 and 3) -- VIOLATING the constraint that if any single value in the list is increased by 1, the number of different values in the list does not change.
Thus, Case 4 does NOT satisfy statement 1.

ONLY difference between Case 1 & 4 is, I think, Case 1 contains one "2" and Case 4 contains one "3". Rest of the part of both of these two cases is having same data i.e. 24 number of 1s. Right ?

Correct.

Yes, now OA will be C as the question is reworded. Thanks Guys!

Test one case that doesn't also satisfy statement 2.
Case 2: {1, 3, 5...45, 47, 49}, for a total of 25 distinct values
Here, if any integer in the list increases by 1, the list will still contain 25 distinct values.
In this case, the list does not contain at least two consecutive integers, so the answer to the questions stem is NO.
INSUFFICIENT.

Hi Mitch ,

Everything is cleared just one thing.

we have {1, 3, 5...45, 47, 49} if 1 increases to 2 or 47 increases to 48 , then in this case, the list contain at least two consecutive integers. So how how come this statement is insufficient?

Please advise and correct me if I am wrong.

Many thanks in advance.

SJ

jain2016 wrote:Hi Mitch ,

Everything is cleared just one thing.

we have {1, 3, 5...45, 47, 49} if 1 increases to 2 or 47 increases to 48 , then in this case, the list contain at least two consecutive integers. So how how come this statement is insufficient?

Please advise and correct me if I am wrong.

Many thanks in advance.

SJ

Statement 1:
The list of values in Case 1 is {1, 1, 1...1, 1, 2}.
Since this list contains at least two consecutive integers, the answer to the question stem is YES.
The list of values in Case 2 is {1, 3, 5...45, 47, 49}.
Since this list does NOT contain at least two consecutive integers, the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, statement 1 is INSUFFICIENT.

Hi Mitch ,

Thanks for your reply, but I still have a doubt.

Case 1: {1, 1, 1...1, 1, 2}, for a total of two distinct values
Here, if 1 increases to 2, or if 2 increases to 3, the list will still contain two distinct values.
In this case, the list contains at least two consecutive integers, so the answer to the question stem is YES.

In the above case we increased the 1 to 2 or 2 to 3 , so this shows that the list contain at least two consecutive integers. Answer to the question is YES.

Case 2: {1, 3, 5...45, 47, 49}, for a total of 25 distinct values
Here, if any integer in the list increases by 1, the list will still contain 25 distinct values.
In this case, the list does not contain at least two consecutive integers, so the answer to the questions stem is NO.
INSUFFICIENT.

Here, in the above case we did not increase any number such as 2 to 3 or 45 to 46. Why?

Please advise.

Thanks ,

SJ

Question stem:
Among the 25 INTEGERS WRITTEN ON THE BOARD, are any two consecutive?

jain2016 wrote:

Case 1: {1, 1, 1...1, 1, 2}, for a total of two distinct values
Here, if 1 increases to 2, or if 2 increases to 3, the list will still contain two distinct values.
In this case, the list contains at least two consecutive integers, so the answer to the question stem is YES.

In the above case we increased the 1 to 2 or 2 to 3 , so this shows that the list contain at least two consecutive integers. Answer to the question is YES.

The portion in red uses the wrong list to answer the question stem.
When we answer the question stem, we must use the original 25 INTEGERS WRITTEN ON THE BOARD.

In Case 1, the original 25 INTEGERS WRITTEN ON THE BOARD are {1, 1, 1...1, 1, 2}.
As shown in my post above, this case satisfies statement 1.
Since {1, 1, 1...1, 1, 2} includes at least two consecutive integers -- the two integers in blue -- the answer to the question stem is YES.

Case 2: {1, 3, 5...45, 47, 49}, for a total of 25 distinct values
Here, if any integer in the list increases by 1, the list will still contain 25 distinct values.
In this case, the list does not contain at least two consecutive integers, so the answer to the questions stem is NO.
INSUFFICIENT.

In Case 2, the original 25 INTEGERS WRITTEN ON THE BOARD are {1, 3, 5...45, 47, 49}.
As shown in my post above, this case also satisfies statement 1.
Since {1, 3, 5...45, 47, 49} does NOT include at least two consecutive integers, the answer to the question stem is NO.

Hi Mitch ,

Many thanks for your reply. All clear now.


Thanks,

SJ