A certain list consists of several consecutive integers. Are there an

Question

A certain list consists of several consecutive integers. Is there an odd number of integers in the list?

(1) The product of the integers in the list is negative

(2) The sum of the integers in the list is even

chetan2u · Answer

(1) The product of the integers in the list is negative
The numbers are consecutive.
a) If there is 0 in the list, the product will be 0
b) If there are only positive numbers, the product is positive.
c) If there are only negative numbers, the product can be positive or negative. Positive, when there are even numbers of integers as each pair of negatives will give a positive sign. Negative, when odd number of integers are there as one negative number will be left after making pairs.
Answer is YES
Sufficient

(2) The sum of the integers in the list is even
1, 2, 3.....YES
2, 3, 4, 5....NO
Insufficient

A

sambhav1895 · Answer

Why option A...Pls explain .....even numbers in the list can also generate product of the terms negative.

stne · Answer

Dear  sambhav1895 ,

Because the list contains only negative terms hence there cannot be an even number of terms, as in such a case product would be positive and NOT negative.

Explanation of why the list contains only consecutive negative terms below:

Please note : The list consists of CONSECUTIVE integers.

Consecutive integers can be of the form 
.......1 2 3 4 5 6 7 8........
....-8 -7 -6 -5 -4 -3 -2 -1 .......
...-3 -2 -1 0 1 2 3 4 5 6...
Etc

(1) The product of the integers in the list is negative

Now if the consecutive list is of the form ..-3 -2 -1 0 1 2 3 4 5 6... then the product of the terms will be zero.
Hence we know that 0 is not in the list.

Next if there are only positive consecutive terms in the list of the form.... 1 2 3 4 5 6 7 8.. then the product of the terms will be positive and NOT negative.
Hence we can say that the list does NOT consist of only positive terms .

Now we know that the list does NOT contain zero also list does not contain only positive terms .
Hence consecutive list must be of the form ......-8 -7 -6 -5 -4 -3 -2 -1 (i.e. list consists of only negative consecutive terms)

Now if there are even number of negative terms such as -8 -7 then product of the terms will be positive.
If there are odd number of negative terms such as -8 -7 -6 then product will be negative.

Hence for a list of only negative terms there must be an odd number of negative terms for the product to be negative.

A is SUFF.

Hope it's clear.

QuantMadeEasy · Answer

Step 1: Understanding statement 1 alone 
(1) The product of the integers in the list is negative
Product of consecutive integers is negative only when there are odd number of negative integers involved.
Eg: -1*-2*-3 = -6
Sufficient

Step 2: Understanding statement 2 alone 
(2) The sum of the integers in the list is even
When Odd number of integers: Sum is 1+2+3 = 6, even
When Even number of integers: Sum is 2+3+4+5 = 14, even
Insufficient

A is correct

A certain list consists of several consecutive integers. Are there an

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GMAT Data Sufficiency (DS) Questions

A certain list consists of several consecutive integers. Are there an

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