Mathematics Problems in SAT: Examples With Tricks

Mathematics Problems in SAT: Examples With Tricks

At the first glance, the maths problem at SAT looks very complicated but breaking down the problem might bring the solution pretty quickly.


((783783783)+(3783783634)+(3783634634)+(634634634))(783+634)(783+634)) = ?

  1. 1365
  2. 1417
  3. 5677
  4. 1

Now, this problem might seem to be very difficult to solve at first glance. It might take minutes to solve even by the calculator.

But upon a second look we see that if:

a = 783 and

b = 634

Then the problem can be re written as :

(a3+3a2b+3ab2+b3)(a+b)2 = ?


Now by expansion it is quite evident that

(a+b)3 = (a3+3a2b+3ab2+b3)


Substituting, we get

(a+b)3/ (a+b)2 = a+b


So, by substituting we get,

783 + 634 = 1417 …. (B)


So, the previous problem showed that the actual technique would have taken minutes even by the use of calculator. Also solving seemed a bit complicated but just by using a few formulae the complexity of the problem was reduced to none. The problem could be solved almost without the use of any calculator. In this way if the given problem is understood step by step and is then analyzed then the problem could easily be broken down into smaller units which can be solved easily.


Detailed Synopsis:

  1. The first step is identifying the type of problem. In this case, it is algebra. Since there exists a lot of constants we may try to replace them by variables.
  2. The second step is assigning variable to those constants. Here two variables namely ‘a’ and ‘b’ are used.
  3. Now these variables are put into the equation, and we have a newer equation.
  4. Then some standard equations are used, and the values of our equations are compared.
  5. The standard equations are converted into the given format so that they fit into the equation.
  6. This equation is then solved with respect to the question and boiled down to an easier version.
  7. Reverse substitution is used and the actual values replace the variables..
  8. These are then solved according to the laws of algebra, and then we have the answer.



Check out this SAT math question.

What is the area of the following square, if the length of BD is 3?


  1. 5
  2. 6
  3. 7
  4. 8
  5. 9


Now the given problem might seem to have given very less data to calculate the solution. But this crucial data can be used to calculate other data that in return could calculate the desired result.

For instance if we actually draw the line which is given then that divides the two opposite angles in exact half giving 45-45-90 triangle whose one side and 3 angles are known and other edges can be calculated. The main trick here is to find out what exactly is required to calculate the answer. In this case, it was the area of a square. We know it to be (side)2 but the value of the side is not known, but the value of the diagonal is, so somehow this value must be manipulated to get the length of the side of the triangle.


Detailed Synopsis:

  1. Draw the diagonal mentioned in the question BD and write the length of the edge.
  2. We then get the right angled and angles CDB = BDC = 45o.
  3. Using the 45°-45°-90° special triangle ratio n:n:n
  4. If the hypotenuse is 3, then the legs must be 3.
  5. Now it is known that the side of the square is 3 which was the requirement to calculate the answer.
  6. Area of square = s2 = 32 = 9…. (E)

Thus analyzing every problem with tiniest possible accuracy, firstly determining what is actually being asked, then determining what logic could be applied so that the problem could be reduced to an easier version or determining the dependencies required to calculate the answer in the case of geometry. Remembering the formulas can prove to be a blessing in this scenario. Then those formulas could be applied in a step by step fashion and then the answer can be calculated with ease. So no matter how impossible the problem looks at the first glance the solution can be obtained by solving one smaller problem at a time.

Jay Regan

Jay Regan, a SAT prep coach by profession and a hobby blogger by passion. He has joined the online industry to help the students located all over the world. With his vast experience in tutoring and writing; he is ready to help guide "less-achieving" students. After walking an extra mile in SAT tests, especially in Math, he has designed an easy-learning process.

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