rakeshd347 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.
OA soon.
OA is
C Guys all of you got it wrong. This is one of the tough one from MGMAT DS. It is rated 600-700 level from MGMAT. I doubt it if its that level because its very tricky.
Here is the OE from MGMAT.
This problem is annoying because of the number of terms in the list; it's hard to wrap your head around 20 integers. Check the statements to see whether you can think through the problem using a smaller list, or whether it really is necessary to stick with a list of 20. In the case of both statements 1 and 2, the full size of the list doesn't matter; you can think the problem through using an easier list (say, 10 or even 5 numbers) that still represents the basic principles in question.
(1) NOT SUFFICIENT: If the list consists of the numbers 2, 4, 6, 8, 10, then all of the values are different. If any value is increased by 1, the list will still consistent of five different values, so this scenario satisfies the statement. This list does not contain two consecutive integers, so the answer to the question is no.
If, on the other hand, the list consists of four "1"s and a "2", then there are only 2 different values (1 and 2). If any of the 1's is increased, the result is 2, which is already in the list, so there are still two different values. If the 2 is increased, then the list will contain four 1's and a 3, and so the list will still contain only two distinct values. In this case, the original list does contain two consecutive integers (1 and 2), so the answer to the question is yes.
Because there are two conflicting answers to the question (no and yes), this statement is not sufficient.
(2) NOT SUFFICIENT: A list containing four 1's and a 2 contains two consecutive integers (1 and 2). If the list contains four 1's and a 3, then it doesn't contain any consecutive integers. Because there are two conflicting answers to the question, this statement is not sufficient.
(1) AND (2) SUFFICIENT: Statement 2 indicates that at least one value occurs twice; call that value a.
Statement 1 indicates that increasing any value in the list by 1 will not change the number of distinct values in the list. In this case, then, increasing one of the a values by one, to a + 1, will still leave you with a in the list (since there are at least two a values) as well as a + 1. The value of a + 1, then, must already have been in the original list; if it wasn't, then you would have just added a new value without getting rid of an old value, and statement 1 forbids this.
For example, if the original list is {1, 1, 2, 4, 6}, then a = 1 and there are four distinct values in the list. Changing one of the 1's to 2 makes the list {1, 2, 2, 4, 6} and there are still four distinct values. This list does contain two consecutive integers (1 and 2).
If the original list were {1, 1, 3, 5, 7}, then a = 1 and there are four distinct values in the list. Changing one of the 1's to 2 makes the list {1, 2, 3, 5, 7}, but now there are 5 distinct values in the list! This is not allowed, according to statement 1.
As a result, whatever a is, a + 1 must also be in the original list. The original list must contain at least one pair of consecutive integers.
The correct answer is (C).
