taniachauhan
lakshya14
taniachauhan
Bunuel
A certain list consist of several different integers. Is the product of all integers in the list positive?
(1) The product of the greatest and smallest of the integers in the list is positive.
Two cases:
A. all integers in the list are positive: in this case product of all integers would be positive;
OR
B. all integers in the list are negative: now, if there is even number of integers, then product of all integers would be positive BUT if there is odd number of integers, then product of all integers would be negative.
Not sufficient.
(2) There is an even number of integers in the list.
Clearly insufficient. {-2, 2} - answer NO; {2,4} - answer YES.
(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.
Answer: C.
Hope it's clear.
WHAT IF THE LIST HAS 4 NUMBERS LIKE ---> (-),(+),(-),(-)?
THE RESULT IS NEGATIVE???
From statement (1), we got to know that either, the set has all even even positive numbers or negative numbers.
I AM SO SORRY IM STILL NOT GETTING IT.
SO AS PER STATEMENT 1, THE PRODUCT OF SMALLEST AND LARGEST DIGIT SHOULD BE POSITIVE.
NOW ASSUME, WE HAVE A LIST OF n NUMBERS, WHICH ARE ARRANGED (JUST FOR UNDERSTANDING)
NOW, IF n=2, BOTH NUMBERS ARE EITHER NEGATIVE OR POSITIVE TO MAKE SURE OUR STATEMENT 1 IS CORRECT AS GIVEN .
IF n=3 or n=5, THE FIRST AND LAST DIGIT IS EITHER BOTH -VE OR BOTH +VE. BUT WHAT IF IN BETWEEN WE HAVE (+,-,+)
THUS, IT WILL BE LIKE
(-SMALEST) *+*-*+* (-LARGEST) ??
Statement (1) says, The product of the greatest and smallest of the integers in the list is positive. Which means there are "n" integers, but the product of the smallest and the reatest is positive.
Now, the product of 2 integers can only be positive iff both the integers are either positive or negative. If both of them are negative then the last integer in the set would be a negative integer and the list of set would be over in negative range. Same stands for positive integers. Because of statement (1), we cannot mix "positives" and "negatives".
M= {a, b, c, d, e, f, g} let the smallest be "a" and the greatest be "g".
Now with statement (1), a x g = positive, if "a" is positive then "g" has to be positive to make the product positive, and also since set M is in ascending order.
Now, if a x g = negative, and this time "a" is negative, then in order to make the product positive, we need our greatest integer "g" to be negative only. Also, notice "g" is our greatest number in the list , which means thats the end of the list and we can't go to the positive side of the number line, which would make the greatest number a positive with "a" still remaining negative, giving a negative product. This will violate the statement (1).
Hope that's clear.