The GMAT Quant section only tests concepts that you have seen until high school mostly. There are no integrals, derivatives, trigonometry questions or anything that requires a cientific calculator. So why doesn't everyone score 51, the highest score?
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The GMAT Quant percentiles
The first thing to understand is that not all of the scores are distributed equally. According to GMAT statistics, the median score is at about 44, and the biggest jumps happen from score 48 to 51 as you can see in the following chart:
Score | Percentile |
---|---|
51 | 96% |
50 | 85% |
49 | 74% |
48 | 67% |
47 | 60% |
46 | 57% |
45 | 54% |
The Quant factors
There are a couple of factors that separate students that are at level 45 from students at level 48 or 51.
Level 45 student:
- Understands most formulas bus hasn't memorized them, and still needs a cheatsheet while solving exercises.
- Is not used to using a stopwatch to measure time, and usually takes about 3 to 5 minutes in medium level questions.
- Relies heavily on operations, writing everything down carefully so as to not make any mistake.
- Usually runs out of time in the mock exams and has to guess around 8 questions.
- Studies about an hour a day, mostly trying new exercises, even online.
Level 48 student:
- Has memorized mostly all the formulas and properties and can recognize them fairly quickly.
- Is used to using a stopwach and takes an average of 2 minutes in medium level questions.
- Uses operations and shortcuts trying to not write so much.
- Might be a little tight on time at the end and mabe has to guess 2 or 3 questions.
- Studies about 2 hours a day, reviewing formulas and a mix between new exercises and past exercises.
Level 51 student:
- Has mastered the formulas and properties, and can quickly identify which one is needed by picking up patterns or key words.
- Easy questions are done using only the time necessary, which is usually 30 seconds. Medium questions average 1:30 minutes and hard questions are done with patience, taking as long as needed (up to 5 minutes).
- Writes what is necessary. Usually the first lines written represent a "second or third" step. The first step has been done mentally.
- Even though he or she takes as long as necessary on the hard questions, the easy and medium questions compensate enough so that at the end there is time left over, usually less than 10 minutes.
- When studying, there is a focus on "how can I do this faster?", not just answering correctly and moving on to the next question. There is a lot of reflexion and writing down patterns in the notebook.
Sample question
In the following example I will show how a student from each level solves the question differently.
The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2 to 1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?
a) \(\frac { 3 }{ 4 } K\)
b) \(\frac { 2 }{ 3 } K\)
c) \(\frac { 1 }{ 2 } K\)
d) \(\frac { 1 }{ 3 } K\)
e) \(\frac { 1 }{ 4 } K\)
Level 45 solution (about 4 minutes)
First identify the formula \(Area=\frac { b\times h }{ 2 }\)
In order to find the height, use the Pythagorean theorem. If we call the side \(L\), than dividing the triangle in two gives me a base of \(\frac { L }{ 2 }\). Using the formula the height is \(\frac { L }{ 2 } \sqrt { 3 }\).
Let's say the large triangle has side \(2x\) and the small triangle has side \(x\).
The area \(K\) of the large triangle would be \(K=\frac { (2x)(x\sqrt { 3 } ) }{ 2 }\). Simplifying: \(K={ x }^{ 2 }\sqrt { 3 }\)
The shaded area is the large area minus the small area, therefore:
\(\frac { (2x)(x\sqrt { 3 } ) }{ 2 } -\frac { (x)(\frac { x }{ 2 } \sqrt { 3 } ) }{ 2 }\)
\({ x }^{ 2 }\sqrt { 3 } -\frac { { x }^{ 2 }\sqrt { 3 } }{ 4 } =\frac { 3({ x }^{ 2 }\sqrt { 3 } ) }{ 4 }\)
â€‹Replacing \(K\):
\(\frac { 3 }{ 4 } K\)
Level 48 solution (about 2 minutes)
First identify the direct formula for area of equilateral triangles of side \(L\): \(Area=\frac { { L }^{ 2 }\sqrt { 3 } }{ 4 }\)
Let's say the large triangle has side \(2x\) and the small triangle has side \(x\).
The area \(K\) of the large triangle would be \(K=\frac { { (2x) }^{ 2 }\sqrt { 3 } }{ 4 } ={ x }^{ 2 }\sqrt { 3 }\)
The shaded area is the large area minus the small area, and we can replace \(K\) wherever it appears:
\(\frac { { (2x) }^{ 2 }\sqrt { 3 } }{ 4 } -\frac { { x }^{ 2 }\sqrt { 3 } }{ 4 } =\frac { 3 }{ 4 } { x }^{ 2 }\sqrt { 3 } =\frac { 3 }{ 4 } K\)
Level 51 solution (about 40 seconds)
(Mostly in his or her mind) First recognize the most efficient property: proportional figures have areas that are in the same relation as the sides, but squared. If the sides have a proportion of 2 to 1, the areas have a proportion 4 to 1. Therefore the shaded region is \(\frac { 3 }{ 4 }\) the area of the large triangle \(K\).
Answer: \(\frac { 3 }{ 4 } K\)
Conclusion
What really separates the students that score well versus those that don't is not so much the formulas, but other factors such as using efficient properties, operating less and having the agility that is gained from a lot of practice and reflection.
Whatever your current level, now you have a clear idea of what is expected at a higher level, so you can work towards achieving that new level. Also, if you want more in depth training, you can check out my complete GMAT Quant course here.