A list contains twenty integers, not necessarily distinct.

Question

A list contains twenty integers, not necessarily distinct. Does the list contain at least two consecutive integers?
 
(1) If any single value in the list is increased by 1, the number of different values in the list does not change.
 
(2) At least one value occurs more than once in the list.

shank001 · Accepted Answer

ill reduce the numbers to 5

(1) If any single value in the list is increased by 1, the number of different values in the list does not change.
suppose the numbers are 1, 3, 5, 7, 9
 a) If we increase any of the above numbers by 1 then the number of distinct value does not change.
 The values are not consecutive.

b) suppose the numbers are 2, 2, 3, 6, 9
 If we increase the value of 2 by 1 then the list will become 2, 3, 3, 6, 9
 The number of distinct values still remains same. But the numbers are consecutive. 
 For this to happen two numbers need to be consecutive.

Two different answers, therefore 1 is not sufficient.

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

Both together will give us condition  b  discussed above.
Hence both are sufficient together.

Ans: C

KarishmaB · Answer

Even though shank001 has provided a great solution above, I would like to give my thoughts on this question.

Here, it is easy to fall for statement 1. At first, it seems as if statement 1 is sufficient. Say, if any single value is increased by 1, it doesn't match any other value already there in the list, it means that there are no consecutive integers. What you might forget that when you increase a number by 1 is that one distinct integer is getting wiped out and another is taking its place!
 
But your statement 2 should give you a hint. 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 5, 5, 6, 9, 20, 50, 57, 87 ... etc
Now if you increase 5 by 1, you get 6 and number of distinct integers stays the same! In this case, if there are no consecutive integers, the number of distinct integers will increase. Hence if the numbers are not all distinct and the number of distinct numbers needs to stay same, there must be a pair of consecutive integers.

This tells you that statement 1 is not sufficient alone and you need both statements to answer the question.

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 (A) or (B), you might want to check whether the other statement is necessary to establish any one statement alone.

honchos · Answer

Karishma (1) gives YES and NO so Insufficient
 (2) Insufficient

Even (1) and (2) together Gives yes and NO situation So answer should be E.

Suppose 1,3,3, 5, 7, 9,11, 13,15,17,19,21,23,25,27,29,31,33,35,37.

from (1) and (2) IF WE INCREASE 3 then we may get consecutive Number, but it is not essential. The condition is of May so (1) and (2) also Gives Yes and No situation hence the answer is E.

shank001 · Answer

If we increase 3 to 4, then the first statement is violated - the number of distinct values should remain same after increasing value by 1.
To satisfy both stmt one and stmt two, we need to make sure that increase by 1 does not create a new number in the list.
this can be achieved only when there are two consecutive numbers on the list.

hope this helps.

manpreetsingh86 · Answer

hi lets shorten this set that you have considered. Suppose we have only first 6 elements in the set.
i.e . 1,3,3,5,7,9

now number of different elements in the set are 5 (1,3,5,7,9) 
 
if i increase 3 with 1 then number of different element in the set becomes 6 (1,3,4,5,7,9) which violates the statement 1

but if we increase 1,5,7 or 9 with 1, number of different elements remains same. therefore we can safely conclude that we definitely have at least 2 consecutive integers in the set.

KarishmaB · Answer

Actually the first statement says that if ANY number is increased by 1, the number of distinct values does not change. So the number of distinct values should stay the same for EACH value in the list. So when we increase the 3 by 1, the number of distinct values should not change. Hence the set given by you above is not possible. 
It must be
1,3,3, 4, 7, 9,11, 13,15,17,19,21,23,25,27,29,31,33,35,37

honchos · Answer

Right Karishma,

But If I would have seen this question directly on Gmat. I would have opted E.

Karishma any advice, last time when I gave my examination on December 10 2013 I scored Q50 V36, 710.

Any advice How to take somewhere between 750-770

KarishmaB · Answer

With a Q50, most of your effort should be directed toward Verbal. Just continue practicing some Quant questions regularly so that your skills don't rust. 
As far as Verbal is concerned, I assume you are average to above average in 2 question types and quite good in the third one. To hit V42, you need to be quite good in 2 of the three and average to above average in the third. Pick up one of CR, SC and RC and work extra hard in that to ensure that you are very good in at least two of the three question types.

Patronus · Answer

Hi  VeritasPrepKarishma ,

I used the following approach and marked E as the answer:

Statement 1) If any single value in the list is increased by 1, the number of different values in the list does not change.

Here, I used 2 sample Sets:
A = {10,2,3};# of different values = 3
B = {10,2,2};# of different values = 2

Option 1: A(+1) = {11,2,3}; # of different values = 3
 Option 2: A(+1) = {10,3,3} ; # of different values = 2 Discarded because does not satisfy the condition of different values
Option 2: A(+1) = {10,2,4};# of different values = 3
Are the numbers consecutive? YES.

But before I say, 1) is sufficient, I went to Set B.

Option 1: B(+1) = {11,2,2}; # of different values = 2
 Option 2: B(+1) = {10,2,3}; # of different values = 3 ; Discarded because does not satisfy the condition of different values
Are the numbers consecutive? NO.

Therefore, Insufficient.

Statement 2: At least one value occurs more than once in the list.  
Set B = {10,2,2} satisfies the condition here, so I took that. But it does not have 2 consecutive integers. So, the answer to the question is NO.
and also, C = {10, 2,2,3,3}. It has 2 consecutive integers. So, YES.
Insufficient

Statement 1) and 2) together: 
B = {10,2,2}; # of different values = 2
And, B(+1) = {11,2,2}; # of different values = 2
Are the numbers consecutive? NO.

C = {10, 2,2,3,3}; # of different values = 3
C (+1) = {11,2,2,3,3}; # of different values = 3
Are the numbers consecutive? YES.

Still insufficient.

Please explain where did I go wrong? Thanks.

KarishmaB · Answer

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

No matter which single value you increase by 1, the number of different values in the list will not change.

So if you have a set (10, 2, 4) - 3 distinct values, No consecutive numbers
Increase 10 by 1, you get (11, 2, 4) - 3 distinct values
Increase 2 by 1, you get (10, 3, 4) - 3 distinct values
Increase 4 by 1, you get (10, 2, 5) - 3 distinct values
Satisfies.

So if you have a set (10, 2, 2, 3) - 3 distinct values, Consecutive numbers
Increase 10 by 1, you get (11, 2, 2, 3) - 3 distinct values
Increase either 2 by 1, you get (10, 2, 3, 3) - 3 distinct values
Increase 3 by 1, you get (10, 2, 2, 4) - 3 distinct values
Satisfies.

Statement 1 is not sufficient because the set may or may not have consecutive numbers. Both type of sets could satisfy the condition that number of distinct values always remains the same.

This is how you check which set does or does not satisfy our condition.

kynir · Answer

Hi  VeritasPrepKarishma ,

When you consider statement 1 and statement 2 together, there can be two scenarios:

(i) 2, 2, 3, 7, 9 ---> 2, 3, 3, 7, 9
 In this case if we increase 2 by one digit, both the statements are satisfied.

(ii) 2, 2, 4, 7, 9---> 2, 2, 5, 7, 9 
If we read the statement 1 carefully, they have mentioned that ' If  any  single value in the list is increased by 1, the number of different values in the list does not change. '
So if we increase 4 here, the number of distinct numbers still dont change.

Since we get both yes and no as an answer, how can both the statements be sufficient??

chetan2u · Answer

Hi,

ANY here means " if you pick up ANY value, it should not change the number of different values" MEANS each value should satisfy this condition.. 
(ii) 2, 2, 4, 7, 9---> 2, 2, 5, 7, 9 
 here the moment you increase 2,you will have the number of different values increased by 1..
But when you increase any single distinct value which does not have any of its neighbour number in the list, the number will remainthe same..

KarishmaB · Answer

You cannot choose the value you increase by 1. It should hold for every value in the set. 
When you increase a 2 by 1 in the case of 2, 2, 4, 7, 9, you will get 2, 3, 4, 7, 9. This increases the number of distinct numbers from 4 to 5.

"If any single value is increased by 1..." means it is applicable for every value in the list.

jlsevasion · Answer

English is not my first language, so this is probably the main issue I have with this question. However, when I read the sentence "If any single value in the list is increased by 1, the number of different values in the list does not change" it is clear to me that what they are saying is:

that if in the original list there were 3 different values , after adding one to each value you should get 3 different values (regardless whether those numbers were in the original list - you only care about the number of different value within the set not when compared with the original set)

1,3,5 has 3 different values --> 2,4,6 has also 3 different values
1,2,4 has also 3 different values --> 2,3,5 has also 3 different values (the fact that 2 is in the original set and the resulting set is not relevant)

Please help! Am I crazy when I understand the problem this way. Is it poorly written or poorly understood

jo5h · Answer

VeritasPrepKarishma

Considering the sequence to be {1,2,3,5,2,6} number of distinct integres is 5
1.
 Increase the value 1 integer, i am increasing the value of 2 by 1 thus the number of distinct integers is (1,2,3,5,3,6)
Insufficient as no 2 consecutive numbers are present

Increase the value 1 integer, i am increasing the value of 2 by 1 thus the number of distinct integers is (1,3,3,5,2,6)
Sufficient as 2 consecutive numbers are present

Therfore, BCD
2.
 For Atleast 1 value to occur more than once,
{1,2,3,5,2,6} Insufficent 
{1,2,3,3,5,6} Suffiencet

C==> Insufficient

Therefor the answer should be E. But, i find from the above explanations as the answer to be C. Please help me out

KarishmaB · Answer

In all the cases you have considered, you do have 2 consecutive integers. For the statements to be insufficient, you need to find a case in which data from both stmnts hold but there are no consecutive integers. That is not possible. There will always be consecutive integer pair and hence the two statements are sufficient.

aquaria · Answer

I answered E as well, and while I understand why C is the answer, I feel C is contingent on a few assumptions:

The prompt asks if there are  consecutive integers . Which in my opinion can mean two things:

1) Numbers that are next to each other on the number line (e.g. 1, 2, 3, 4) - in hindsight, the question is obviously referring to this definition of "consecutive".

2) But you could argue that this can also mean something like (1,1,5,5,3,3,3) where the same number is listed  consecutively  (i.e. one after the other) but are not necessarily in numerical order.

C assumes that the numbers are listed in numerical order (e.g. 1,1,2,3,6,9), which is the regular definition of consecutive. What if the set was (1,3,6,1,9,2)? Then the second definition of "consecutive" would come into play.

Maybe I was thinking way left field, but I feel the prompt (simple as it was), was worded in a way that needed readers to bring in outside assumptions. It may have been pretty obvious and straightforward for some, but I guess this is a case where overthinking it can get you into trouble.

I mean  are we always to assume that any number set in the GMAT will always be listed in numerical order?  I know it's a silly question, but we're already taught to assume that all lines in a given figure are actually straight (unless specified) and that figures are as accurate as can be, so it's just one more assumption specific to the GMAT that we need to keep in mind.

uzumakinaruto444 · Answer

hello,
i have a doubt....in your solution, in condition (a) above, if we increase 1 by 1, we'll have 2,3,5,7,9 which'll be consecutive 2 and 3 integers. then, shouldnt the answer be E?

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A list contains twenty integers, not necessarily distinct.

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A list contains twenty integers, not necessarily distinct.

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