Question

01. The product of 2021 integers is less than zero. What could be the number of positive integers in the collection? a) 1022 b) 1513 c) 2021 d) 1999​

Answer 1

a. 1022

there should more no. of negative no. to get negative answer

Answer 2

Given,

The product of $\[2021\]$ integers is less than zero.

To find,

The number of positive integers in the collection.

Solution,

Understand in order to get the resultant product negative the number of negative terms in a multiplication system should be more than the $\[\begin{array}{l} \Rightarrow 2021 - 1999\\ \Rightarrow 22\end{array}\]$positive terms.

Examine option (a).

So, the number of negative terms is

$\[\begin{array}{l} \Rightarrow 2021 - 1022\\ \Rightarrow 999\end{array}\]$

Examine option (b).

So, the number of negative terms is

$\[\begin{array}{l} \Rightarrow 2021 - 1513\\ \Rightarrow 508\end{array}\]$

Examine option (c).

So, the number of negative terms is

$\[\begin{array}{l} \Rightarrow 2021 - 2021\\ \Rightarrow 0\end{array}\]$

Examine option (d).

So, the number of negative terms is

$\[\begin{array}{l} \Rightarrow 2021 - 1999\\ \Rightarrow 22\end{array}\]$

Therefore, the maximum negative terms are in option (a).

Hence, the correct option is (a) i.e. $\[1022.\]$