Question

A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is:
A) 1
B) 5
C) 7
D) 3

Answer 1

Hint: Here the question is related to the algebraic equation. We try to write the given data in the form of algebraic expression and then we can determine the unknown variable. To solve this we use simple arithmetic operations and hence we obtain the required solution for the question.

Complete step by step solution:
The question is in the phrasal form, so by reading the question, first we write in the form of numerical and then we are going to solve the algebraic equation or expression.
Now consider the given question we have a positive integer added to the number 1000. let we take the positive integer as x so it is written as \[x + 1000\]. This sum is greater than, this represents we use the\[\text{>}\] symbol. Then we have the sum will be greater than the number when it is multiplied by 1000, so in the RHS we write \[1000x\]
Now the inequality is written as
\[ \Rightarrow x + 1000 > 1000x\]
This will represent the given question. Now take the x to the RHS, when it moves to RHS the sign will change. It will change to a negative sign.
Therefore we have
\[ \Rightarrow 1000 > 1000x - x\]
On subtracting x from 1000x we have
\[ \Rightarrow 1000 > 999x\]
To determine the value ox we divide the above inequality by 999
So we have,
\[ \Rightarrow \dfrac{{1000}}{{999}} > x\]
On dividing the number, we have
\[ \Rightarrow x < 1.001..\]
Since the solution is a positive integer the solution will be 1.
Hence, option (A) is correct.

Note:
The important thing here is writing the phrasal form of the question into numeral form. When we write the given question in the numeral form it will be in algebraic expression. The concept of sign conventions is implied here while solving. While dividing we should know the tables of multiplication.