Here's the whole series of QC tips:
Tip #1: Dealing with Variables
Tip #2: Striving for Equality
Tip #3: Logic over Algebra
Tip #4: Comparing in Parts
Tip #5: Estimation with a Twist
In my last post, we solved the following question:
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Our approach was to first recognize that two of fractions are approximately
Now if we had used these approximations, we would have been left with:
This would have made us conclude (incorrectly) that the answer is C.
To solve this question using approximation, we applied a twist. We recognized that
And so on.
With these little twists, we were able to simplify the two columns as:
From here, it was clear that the correct answer is B
Okay, now let's see if you can apply this approximation with a twist to solve the following question:
Aside: before you read my solutions, see if you can find additional ways to solve this question.
Okay, first we'll solve the question using approximation with a twist, and then we'll solve it using different approaches.
First, let's approximate as follows:
From here, we can drop 4 zeroes from each number to get:
At this point, I'll apply a nice rule that says:
In other words, the product of two numbers is equal to the product of twice one number and half the other value.
So, in Column A, we'll double
From here, when we compare the products in parts, we can see that Column A must be greater than Column B, so the answer is A.
As you might have guessed, the two original products are too large to work on a calculator. For example,
There are, however, some ways to work around this constraint and still use the calculator.
For example, you could divide each number by
this point, the products will still fit into the display of the onscreen calculator and you would clearly see that Column A is greater.
Another possible approach is to perform the same steps we performed earlier, but stop when we get to:
Originally, we applied that handy rule where we double one number and halve the other. However, we could also use the calculator at this point.
So, we get:
Once again, we can see that the answer is A.