Percentages Part C

Hello and welcome to the last part in percentages. Percentages are really straight forward but the wording of the problem can be a little confusing at times. Some problems you can do mentally, some questions you can solve in a few seconds by the use of a calculator and some questions require you to think more than the previous questions.

Now I will look at the last question posted in ‘Percentages Part A’. The last question is actually easier than the question about the house, but there is a reason why this question is one of the last questions you will most likely encounter in the exam. The reason is a result of the answer choices and the requirements for this question. For average test takers, when they reach this question, usually they have a few seconds remaining. With my guidance on how to approach the S.A.T you will have at least two minutes remaining! Let’s look at the question;


60% of x is 30% of y. if w = 4x, what percentage is (x + y)/w?

a) 15%
b) 25%
c) 60%
d) 74%
e) cannot be determined from the information above

When you are running low on time students tend to build up an anxiety fear and their brains are out of focus and are easily distracted by eye catchers. When time is low some students take the risk and guess answers. Let’s look at the answer choices.

Why choice a) 15%? This is to distract you as ½ of 60% is 30% hence ½ of 30% is 15%. (THIS IS INCORRECT!)

Why choice b) 45%? This is to distract you as ½ of (60% + 30%) = 45%. NOTE: X and Y are not percentages, they are unknown numbers!

Why choice c) 60% ? This is a distracter! This is because, under pressure, 90% of students guess the answer c.

Why choice d) 75%? This is the actual answer but this is a well placed answer for this question. This is a trap for students that who underestimate and over think in Mathematics. Advance students in Mathematics scan each choice, like what I have just done, to choose an appropriate answer when time is low. (x + y)/ 4x can be misinterpreted for (30% + 60%)/ 120% (THIS IS INCORRECT!). Some Math students know that this is wrong but they think of how the average person will attempt it and you must do that also so that you won’t waste time looking at ridiculous choices hence saving you time!

Why choice e)? This is because there are no values given. (NOTE: YOU WILL ENCOUNTER THIS ANSWER A LOT ON THE S.A.T.)

Those are the reasons why this question is hard. It’s because of the time you will most likely have to do this question that really brings out the difficulty. This question is a dependant question. Y and W depends on X, because of this, no matter what number you choose for X, you will always get the correct answer as long as you do it properly. You can choose any value for X but when working with percentages it is much more economical, in reference with time, to use the number 100. No matter what value for X you choose you will get 75% as the answer. This concludes straight forward percentages. There are also more questions involved in percentages but they are a combination of other topics such as Geometric Progression (G.P.)! The question about the house involves G.P. and that will be the topic of my next post. Thank you for reading and I wish you all the luck in your future exams!