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A list contains twenty integers, not necessarily distinct.

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A list contains twenty integers, not necessarily distinct. [#permalink] New post 17 Jun 2014, 09:42
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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.
[Reveal] Spoiler: OA

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Last edited by honchos on 24 Jun 2014, 08:17, edited 1 time in total.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 17 Jun 2014, 10:20
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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

Last edited by shank001 on 18 Jun 2014, 10:59, edited 1 time in total.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 18 Jun 2014, 02:24
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honchos wrote:
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.


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.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 18 Jun 2014, 11:02
VeritasPrepKarishma wrote:
honchos wrote:
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.


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.


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.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 18 Jun 2014, 11:16
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.


honchos wrote:
VeritasPrepKarishma wrote:
honchos wrote:
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.


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.


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.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 18 Jun 2014, 11:26
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(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.


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.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 18 Jun 2014, 19:08
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honchos wrote:
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.


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
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 22 Jun 2014, 21:15
VeritasPrepKarishma wrote:
honchos wrote:
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.


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


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
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 23 Jun 2014, 00:20
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honchos wrote:
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


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.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 19 Jul 2015, 11:18
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.
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Re: A list contains twenty integers, not necessarily distinct. [#permalink] New post 20 Jul 2015, 22:09
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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.


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.
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Re: A list contains twenty integers, not necessarily distinct.   [#permalink] 20 Jul 2015, 22:09
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