The SAT, one of the most loathed and feared tests for high school students, can feel impossible to conquer. For many ambitious young people, above 700 on math is the holy grail of scores: you hear that it can be achieved but actually reaching it seems impossible. Dear friend: fear not! The grail has been found and there are concrete steps that can be taken to help you achieve above a 700 on the math portion of SAT.
For those who are only attempting to score in the 600 range, the good news is you can miss a few problems and get there, but for those really attempting to ANNIHILATE the math portion of the SAT you cannot skip questions. This is especially true of hard math problems. The trick with hard problems is to forget for a moment that they are supposed to be hard and to just WORK. This does not mean you should assume that the problem is easier than it is and pick an overly simple answer, but it does mean believing that you have the skills to approach a problem and DOING IT! Take the problem below which would appear at the end of the SAT math section.
There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure in inches of the width of the foil covered prism?
1) Don’t give up before you start!
I can feel your skin crawling as fear sets in, but believe in yourself! Let’s start working like we do with any other problem. This problem is at the end for a reason. You should have finished everything else already so all you need to focus on is this problem. Don’t worry about the time at this point. You will waste more time worrying than you have to spare. Start working! And start with what you know!
2) Start with what you know
We know: 1 in cubes is the same as inches cubed (volume in inches cubed is essentially a measure of how many cubes that are 1in x 1in x 1in that can fit in a 3D shape). We also know that the 128 cubes are completely covered by other cubes so that none of their sides touch the outside. This means that there is essentially a bigger prism completely covering a smaller prism. Its like when you used to play with blocks (I know you did!) and you would completely enclose a block in other blocks to make an exact replica only bigger. So we have a rectangular prism that is 128 inches cubed. Finally, we also know that one side is twice as big as the other two.
3) Draw a picture (if possible)
Let’s try to draw what this might look like. If we had a cube that was 2 x 2 inches cubed, one side would look like this:
In order to cover it completely on all sides we would have to have a cube that had one more cube on each side. So the new face would look like this
So we essentially know that the final figure will have sides that are two greater than the sides of the interior structure, (again, this would enclose a smaller rectangular prism). Huzzah! We are getting somewhere.
4) Use general equations to get specific answers
Using the equation of a rectangular prism and the information that our smaller prism has a length that is two times the width and height we can start writing equations:
L x W x H = Area of a rectangular prism
Let’s make L = x That would mean that H = x also and W = 2x and we can plug that into our equation to get:
(x)(2x) (x) = 160 or (2x^3) = 128 —-> x = 4
5) ANSWER THE QUESTION
We are SO close to the end, but we need to answer the question being asked. Now the length and height of the smaller prism is 4 in (which is an answer choice) but that is NOT what the question asks. The width of our smaller prism is twice the length or 8 in. This is also NOT what the question asks! We know from our previous calculations that all the measurements of the final figure are two greater than the smaller so the dimensions of the larger prism would have to be L= (x+2), H= (x+2) and W = (2x+2). Thus our final answer is 2(4) + 2 = 10. WOOHOOO we DID IT!!
To score above a 700 on the math portion of the SAT you don’t need to be a genius, you just need to believe that you have the tools necessary and then USE them! You can do this; now, all you have to do is prove it to yourself. Good luck test destroyer!
David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.