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

Don't be intimidated by the "25" integers - nothing else in the problem deals with 25 specifically, so we can reduce this number to something manageable (like 3) to find an answer.

(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.

{1,2,3} --> {2,3,4}:
{2,4,6} --> {3,5,7}:

In either case, the number of distinct values doesn't change. Therefore INSUFFICIENT.

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

{1,1,2} or {1,1,3}; both tell us nothing. INSUFFICIENT.

Taking them both together:

{1,1,2} --> {2,2,3}: number of distinct values doesn't change.
{1,1,3} -->{2,2,4}: number of distinct values doesn't change.

Therefore both options together are still insufficient.

Answer: E

We may write 25 integers as:2,2,2,15,10,7,4,4………………………………………..
1. Increase each value by 1 we will have 3,3,3,16,11,8,5,5……………………….; we cannot answer Y/N as we have minimum 2 consecutive integers or not; Not sufficient
2. In the mentioned list we have 2 & 4 which is appearing more than once, but with this also we cannot say that we have minimum 2 consecutive integer in the list or not; Not sufficient
1+2: including both pointers as well, we can not be sure of minimum 1 value in the list; Not sufficient

Hence answer is E

It's clear that I was wrong with this one... but my interpretation of statement 1 is different than all of yours. Would appreciate some help to understand why I am wrong in my interpretation!

"For every value in the list, if the value is increased by 1, the number of distinct values in the list does not change"<- I thought this was sufficient simply because if all of the numbers were consecutive, adding one to any value would decrease the number of distinct values. Therefore the values in this list would not be consecutive since adding 1 to any given number wouldn't change the amount of unique values. Clearly the statement according to all of you means that each value would increase, which would render this statement irrelevant.

I guess what I'm trying to ask is how, given what is written in statement 1, did you conclude that it meant that all of the values would increase , and not just any which one increased independently?

Thanks to anyone who can clarify! I often seem to get pedantic about what questions mean in my head, and its affecting my performance

Reading another very similar post (a-list-contains-twenty-integers-not-necessarily-distinct-d-172751.html) it seems that we may be misinterpreting the first option. I took it to mean that every value would be increased, but I think you may be on to something by saying that if ANY value were to increase (in which case, it should be worded as "If any single value in the list is increased by 1, the number of different values in the list does not change").

If we are interpreting it like you have, then refer to the other topic - the answer is C.

Ahh I see how the wording is different yes, thanks!

Let’s first review the information given to us here:

25 integers are written on the board – we don’t know whether they are all distinct. We want to know if there is any pair of consecutive integers among them.

Let’s look at the statements:

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.

It is easy to fall for statement 1 and think that it is sufficient alone. Say, if any single value is increased by 1 and it doesn’t match any other value already there in the list, it means that there are no consecutive integers, doesn’t it? Well, no! But we will talk about that in a minute. Let’s first look at why we might think that statement 1 is sufficient.

Say, the numbers are: 1, 5, 8, 10, 35, 76 …

If you increase 1 by 1, you get 2 and the list looks like this:

Now the numbers are 2, 5, 8, 10, 35, 76 …

Note that the number of distinct integers is the same.

Had there been two consecutive integers such as 1, 2, 8, 10, 35, 76 …

If we increase 1 by 1, the list would have become 2, 2, 8, 10, 35, 76 … – this would have decreased the number of distinct integers.

You might be tempted to say here that statement 1 alone is sufficient. What you might forget is that when you increase a number by 1, one distinct integer could be getting wiped out and another taking its place! It may not occur to you that the case might be different when one value occurs more than once, but statement 2 should give you a hint. Obviously, statement 2 alone is not sufficient but let’s analyze what happens when we take both statements together.

Since statement 1 doesn’t tell you that all values are distinct, statement 2 should make you think that you need to consider the case where one value occurs more than once in the list. In that case, is it possible that number of different values in the list does not change even though there is a pair of consecutive integers?
Say the numbers are 1, 1, 2, 8, 10, 35, 76 …

Now if you increase 1 by 1, the list would look like 1, 2, 2, 8, 10, 35, 76 …

Here, the number of distinct integers stays the same even when you increase a number by 1 and you have consecutive integers! In this case, if there were no consecutive integers, the number of distinct integers would have increased. Hence if the numbers are not all distinct and the number of distinct numbers needs to stay the same, there must be a pair of consecutive integers.

This tells you that statement 1 is not sufficient alone but both statements together answer the question with a ‘Yes’.

Answer (C)

Takeaway – Just as when you get an easy (C), you must check whether the answer could be (A) or (B), when you feel that the answer is an easy (A) or (B), you might want to check whether the other statement gives some relevant data and is necessary.

Thanks that is an awesome Explanation!! I first of all though you add one to all the numbers, its just the way I interpreted the Question.
My question is for statement two. And I agree with your explanation entirely!
Here is another list
1, 1, 5, 7, 10, 50...
Now like you said If we add 1 to 1, we get 2 and we get an increase in the number of distinct integers. And so if we had 2 in this series we wont increase the number of distinct integers. But what if we add one to 50, it becomes 51. We wipe out 50 and the number of distinct integers still remain same. And we dont have a set of consecutive integers. I am missing something here.
Thanks a lot!

Hi chetan2u
I have attempted this Question three times now.
Each time i have picked E.
I have seen the solution above.
And somehow i feel i am correct.
Can you please look into my solution =>


We need to see if the set has atleast a pair of consecutive integers.

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.
Set => {3,3,3...3}
New set after addition will be=> {4,4,4..4}
In both cases the "number" of distinct values is 1
Hence The answer is NO

Set => {1,2,3,4..}
New set => {2,3,4..}
Hence the "number" of distinct values will not change.
Hence Insufficient

Statement 2=>
At-least two same elements

Set={3,3,3..3} => NO
Set=> {2,3,3,3,3..}=> YES

Hence insufficient


Combing them =>
Set => {3,3,3,3...}
New set after addition will be => {4,4,4,4}
Hence the "number" of distinct values will not change.

NO

Set => {2,2,3,3,3,3..}
New set after addition =>{3,3,4,4,4,4,4} =>Hence the "number" of distinct values will not change.

YES


Hence E


What am i mission here?
Also, i feel the word "Number of Distinct values" may be ambitious.

Regards
Stone Cold

Hi Bunuel,
But "For every value in the list,if the value is increased by 1" is to add 1 to every element in this list,isn't it?
Pardon me if I'm wrong

If instead of taking number 1, 1, 2, 8, 10, 35, 76 …, we take 1, 1, 5, 8, 10, 35, 76 … then this does not satisfy the requirement. Please clarify.

Hi,

When the numbers are 1,1,2,8,10...
You increase one of the 1 by 1
So new set is 1,2,2,8,10...
Number of distinct integers does not change and this is what the combined info from two statements tells us..

But let me take the set given by you 1,1,5,8,10.....
Now increase one of the 1 by 1
New set 1,2,5,8,10...
Here the distinct number of integers increases by one, as a new number 2 is added while no other integers is getting erased..
Thus this set is not a valid set as it is against the info of statement I..

This is the very reason that there will always be a consecutive integer to satisfy the two statements..

Hope it clarifies your query..

Hi stonecold and sleepynut ,
The reason you are getting E is because of the interpretation of statement I..
The way it is written, it means whenever ANY one value is increased...

The way you are interpreting the sentence, the statement would be
For every value in the list, if each value is increased by 1, the number of distinct values in the list does not change.

Yes it could have been better had the wordings were
If any value in the set is increased by 1, ...... :- there is no ambiguity here
This is what you should see in the actual GMAT..

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