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# A list contains twenty integers, not necessarily distinct. Does the list

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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.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.

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First statment: This statement seems to be an easy fall statement. At first it seems fairly obvious that if on increasing a value  by 1, the number of distinct integers do not change. But that would be true only if all the numbers are distinct. Here it is clearly mentioned, NOT necessarily distinct. For example  if the list has following numbers 1,1,2,5,... rest all distinct. If the number 2 is increased by 1, still the number number of distintct integers are same, but not consecutive. NOT SUFFICIENT

The second statment at first may seem without clue. But it turns that this is a similar case to the previous it is NOT SUFFICIENT to answer the question.

Now let us test the answer for both statements combined. The key is here think of set, dont do it your brain. Don't tax your brain.
Suppose the number set we choose is 7, 7, 8, 10, 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.

Both statement combined are sufficient.

answered Jul 27, 2014 by Guru (5,628 points)
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Jyotsna Mehta