GMAT Tip: Keep the Concept in Mind
GMAT Quantitative questions can be difficult because of how questions are worded, relationships that have to be identified, and moves in logic that produce the right answer. But, sometimes, a quantitative question is difficult simply because you’re being tested on the same concept over and over again, and they’re hoping to just wear your brain out, in hopes you forget.
Let’s look at a great example of the GMAT making us chase our tail:
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?
- 20 / sqrt (3)
- sqrt (150)
- sqrt (300)
This is a word problem, so the best way to start this question is to decipher what we are being asked to solve, which turns out to be “what is the diagonal of the screen?”
In breaking the question down line by line, we should realize we are being 1) asked about a square and 2) asked about the area. What are we given? The diagonal of the monitor – 20 inches.
P.S. have you ever seen a perfectly square monitor?
That aside, having a square with a diagonal should give us another hint that we will be utilizing 45-45-90 special triangle relationships. Wow, a lot of information to keep organized!
How are we going to get to our end point, the diagonal of screen? We should recognize that we need to subtract the portions of the diagonal that may up parts of the frame.
We’ll start by finding one side of the screen – if we utilized our special right triangle, then the side length of the entire monitor is 20/sqrt(2).
Pro tip: don’t simplify square roots until the very end, unless it is essential to taking a next step in your problem. Answer choices won’t necessarily have to be fully simplified and often, not simplifying along the way saves you time… believe it or not!
Now that we’ve found the length of a side, we’ll find the area of the entire monitor:
S^2 = (20/sqrt(2))^2 = 400/2 = 200
Now, this is where we need to remember the concept we are being asked to understand – squares, but also relationships between squares. Many students will get stuck and forget the relationship between the frame and the screen – 3:1 as stated in the word problem.
A great way to keep moving forward is to return to the problem, constantly reassessing to make sure you are taking the right steps. If the relationship is 3:1, then let’s call the area of the frame A. So, if the area of the screen + area of the frame = area of the monitor then:
3A + A = 200
A = 50
3(A) = 150
We are done, right? Unfortunately, like with many other GMAT Quantitative questions, while we are tired, there is still more to go!
They’ve asked us to solve for the diagonal of the screen. Working backwards with the area question, the length of the side of the screen is the sqrt(150). Using the Pythagorean theorem, we solve for the hypotenuse, which will be the length of the diagonal:
[sqrt(150)]^2 + [sqrt(150)]^2 = d^2
d = sqrt(300)
The correct answer is (E).
There are A LOT of steps to this problem. Beyond staying organized in your calculations, make sure you are constantly remembering what the GMAT is asking you to assess and find – keep the concept in mind.