Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
Remember that the notation [12] means there is a bar over the 12, indicating that the decimal is nonterminating.
Now, let’s start the problem by factoring out 10^2 from (10^4 – 10^2). This gives us:
(10^4 – 10^2) (0.00[12])
10^2 (10^2 – 1)(0.00[12])
We can distribute 0.00[12] with the two quantities in the parentheses. This gives us:
10^2(0.[12] – 0.00[12])
100(0.[12] – 0.00[12])
12.[12] – 0.[12] = 12
Alternate solution:
The number .00[12] is the number .00121212… if we write it without the bar notation. By the distributive property, we have
(10^4 – 10^2) (.00[12]) = 10^4(.00[12]) – 10^2(.00[12]
Without the bar notation, we write this as 10^4(.00121212…) – 10^2(.00121212…)
Multiplying a number by 10^4 indicates that we move the decimal point four places to the right, giving us:
10^4(.00121212…) = 12.1212…
Similarly, multiplying a number by 10^2 indicates that we move the decimal point two places to the right, giving us:
10^2(.00121212…) = 0.1212…
Now, if we subtract the two quantities, we have
10^4(.00121212…) – 10^2(.00121212…) = 12.1212… – 0.1212… = 12 (because the .1212… gets canceled out by the subtraction).
