Question

The product of the successor of 999 and predecessor of 1001 is-
A. one lakh
B. one billion
C. one million
D. one crore

Answer 1

Hint: The concepts of numbering systems and basic multiplication will be used here. The successor of a number is the next integer to the right of the given number when represented on the number line. It can be obtained by adding 1 to the given number. Similarly, a predecessor is the number obtained by subtracting 1 to the given number, and is represented to the left of the given number on a number line. We will find the successor and the predecessor of the given numbers and multiply them to get the answer.

Complete step-by-step answer:

We need to find the product of the successor of 999 and predecessor of 1001. We will start by finding the successor of 999. This can be done by simply adding 1 to 999. The successor of 999 is-
S = 999 + 1 =1000
Now that we have the successor, we will proceed by finding the predecessor of 1001. This can be done by subtracting 1 from 1001 as-
P = 1001 - 1 = 1000
As we can see, the successor, S, of 999 and predecessor, P, of 1001 is the same number-1000. It is asked that we need to find the product of S and P, that is, we need to multiply 1000 by itself. This can be done as-
$1000 \times 1000 = 1000000$
The naming of this number can be done in two ways- using the Indian Numbering System or the International Numbering System. We will name the number in both the ways, and match them with the correct option.
In the Indian system, the first comma is placed after three digits, and the subsequent commas after two digits, starting from the right. So, the commas can be placed as-
10,00,000
In the Indian system the nomenclature is as follows-
One = 1
Ten = 10
Hundred = 100
Thousand = 1,000
Ten Thousand = 10,000
One lakh = 1,00,000
Ten Lakh = 10,00,000
According to this nomenclature, we can see that the number obtained is equivalent to ten lakhs.

In the International system, all the commas are placed after three digits, starting from the right. So, the commas can be placed as-
1,000,000
In the International system the nomenclature is as follows-
One = 1
Ten = 10
Hundred = 100
Thousand = 1,000
Ten Thousand = 10,000
Hundred Thousand = 100,000
One Million = 1,000,000
According to this nomenclature, we can see that the number obtained is equivalent to one million.
Both the nomenclature computed are correct, so we will find that value which is available in the options as well. We can see that option C is one million, hence it is the correct option.

Note: A common mistake here is that students check the answer in one type of numbering system. This often leads to a confusion, or a wrong answer. For example, if a student used only the Indian system here, he/she would get confused because it is not present in the options. Also, another common error is that the students often exchange the terms successor and predecessor, and use them in a reversed manner, that is, they subtract 1 while finding successor and add 1 while finding predecessor.