Strategy#5 Estimation with a Twist
In the last post we discussed the following question
Attachment:
q1.png [ 9.63 KiB | Viewed 2964 times ]
Our approach was to first recognize that two of fractions are approximately 1/2 and two are approximately 1/3.
Now if we had used these approximations, we would have been left with:
Attachment:
q2.png [ 2.13 KiB | Viewed 2964 times ]
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 213/428 is a little bit less than 1/2, which we denoted as 1/2-. We also noticed that 3007/9101 is a little bit less than 1/3, which we denoted as 1/3-.
And so on.
With these little twists, we were able to simplify the two columns as:
Attachment:
q3.png [ 2.21 KiB | Viewed 2963 times ]
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:
Attachment:
q4.png [ 3.52 KiB | Viewed 2959 times ]
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.
Approximation with a twist:
First, let’s approximate as follows:
Attachment:
q5.png [ 3.05 KiB | Viewed 2956 times ]
From here, we can drop 4 zeroes from each number to get:
Attachment:
q6.png [ 2.86 KiB | Viewed 2956 times ]
At this point, I’ll apply a nice rule that says: \(A*B=2A*{1/2}B\)
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 45+ and halve 64+ to get:
Attachment:
q7.png [ 2.56 KiB | Viewed 2959 times ]
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.
Alternative approach #1
As you might have guessed, the two original products are too large to work on a calculator. For example, (641,713)x(451,222)=289,555,023,286 and this number is too large for the GRE’s onscreen calculator. As such, the calculator would display an error message if you tried to perform this calculation.
There are, however, some ways to work around this constraint and still use the calculator.
For example, you could divide each number by 1000 to get:
Attachment:
q8.png [ 3.12 KiB | Viewed 2957 times ]
point, the products will still fit into the display of the onscreen calculator and you would clearly see that Column A is greater.
Alternative approach #2
Another possible approach is to perform the same steps we performed earlier, but stop when we get to:
Attachment:
q9.png [ 2.8 KiB | Viewed 2957 times ]
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.
(64)x(45)=2880 and (90)x(32)=2880. This means that (64+)x(45+)=2880+ and (90-)x(32-)=2880-.
So, we get:
Attachment:
q10.png [ 2.14 KiB | Viewed 2954 times ]
Once again we see the answer is A.