This tip for improving your SAT score was provided by David Greenslade at Veritas Prep.
The SAT, unlike most tests that high schools administer, is nearly entirely multiple choice. This means the answer is right in front of students on the pages of the test booklet as they take the test. Most students, not surprisingly, start working immediately when they read the question in an attempt to maximize their time to work on each question. This is not wrong, per se, but clues are often contained in the answer choices that can elucidate what the test is asking and how to find the answers. Here is an example SAT question:
“The price of a new gaming system was g dollars and James bought the system with a coupon for c percent off. The store also gave James and additional s percent off the discounted price as a promotion. What represents the price in dollars for the gaming system?”
(a) g (100-1/c)(100-1/s)
(b) g ((1- c) (1- s) /100)
(c) g ((1- c+s)/100)
(d) g (c/100)(s/100)
(e) g (1-c/100)(1-s/100)
The SAT likes to leave things in theoretical terms to test a student’s ability to work with variables and apply concepts to nonconcrete problems. The good news is that this technique also leaves a lot of clues that can be very helpful in determining the final answer. All the answer choices start the same way: They multiply the price of the console by something. This is pretty intuitive, as discounts are generally found by starting with the initial price. The answers also all have 1s, 100s, or both somewhere in the equation, which is a big clue. The question gave the discounts as percents, which means the percents must be divided by 100 to become usable decimals or fractions (90% = 9/10 or 0.9).
Knowing this, answer choice A can be essentially eliminated, but why all the 1s? It is difficult to look at these choices and figure out what those might be attempting to convey (or how they are intended to confuse) without doing a little more work. Theoretical questions can easily be simplified by inserting concrete numbers into the variables. Imagine g = $125 (a good deal, I know) and the coupon, c, is 20% off and the promotion, s, is an additional 10% (what a bargain). So to make 20% a fraction, it is divided by 100 to become 20/100 or 2/10. If this is simply multiplied by the price, the result is
$125 x 2/10 = $25.
That seems far too low a price for 20 percent off. What is actually happening is the price is being reduced by $25, or 20 percent, so the final price will be 20 percent less, or 80 percent of its initial value. This is where that 1 comes in: If $125 is multiplied by 1-2/10 (or 8/10), the result is
$125 x 8/10 = $100 ($25 less than $125).
So it can then be inferred that when taking a discount, the initial value of the product is multiplied by 1 minus the percent discount divided by 100 (1 – % discount/100).
To take an additional discount, as is asked in the question, the new price (the product of the price and the discount) would then be multiplied by 1 minus the percent discount divided by 100 again.
Price (1-1st % discount/100)(1-2nd % discount/100)
The only answer choice that accurately reflects this is answer choice (e).
Answer choices are extremely useful in helping to determine the answer to a problem. The question above can also be checked using the answer choices. Simply plug in the values chosen for the different variables and see if answer choice (e) gives a correct result. All the other choices will give results that do not equal the real derived answer. So use the answer choices; they are there to help if you know how to find the clues.
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