Set P consists of 56 integers. Is the product of all the integers in

Question

Set P consists of 56 integers. Is the product of all the integers in set P negative?

(1) Exactly half of the integers in set P are negative.
(2) Exactly half of the integers in set P are positive.

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zhanbo · Answer

(1) Only
28 integers are negative with the other 28 nonnegative.
If all the other 28 integers are positive, the product of all the integers in set P is positive
If the other 28 integers contain one or more 0's, the product of all integers in set P is 0.
We can answer "No" to the question 
Is the product of all the integers in set P negative?
Sufficient.

(2) Only
28 integers are positive with the other 28 nonpositive.
If the other 28 integers contain one or more 0's, the product of all the integers in set P is 0.
Otherwise, the product of all the integers in set P is positive.
We can answer "No" to the question 
Is the product of all the integers in set P negative?
Sufficient.

The answer is thus  (D) .

This question is a bit tricky. I originally chose (C).
Only when I wrote this reply did I realize the correct answer is (D).

Archit3110 · Answer

target is product of all integers in set P -ve ( 56 terms)
#1
Exactly half of the integers in set P are negative.
which is 28 ; rest 28 terms may be all +ve or one of term may be 0 ; but target value is NO
sufficient
#2
Exactly half of the integers in set P are positive.
so we can have either 28 -ve terms then answer is no or 27 -ve terms and 1 0 then also target answer is no
sufficient
option D

sanchitb23 · Answer

Given: Set has 56 Integers
Question: is Product of Integers -ive or +ive

Statement 1: Exactly half of the integers in set P are negative.
This means 56/2=28 Integers are -ive, ie. Even Number of Integers are -ive, As Product of Even Number of -ive Integers is Always Positive
Hence, Product of -ive Integers will be Positive, so If any integer is 0 or not, Answer will never be Negative,  Statement 1 is Sufficient

Statement 2: Exactly half of the integers in set P are positive.
This means 56/2=28 Integers are +ive
Which Alternatively means Even number of -ive Integer.
If there is any 0 in the mix, Easy Answer-> Product is not Negative
If not, We'll follow the Logic in Statement 1 ;  Hence Statement 2 is also Sufficient

Therefore, Answer is D

Set P consists of 56 integers. Is the product of all the integers in

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GMAT Data Sufficiency (DS) Questions

Set P consists of 56 integers. Is the product of all the integers in

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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