6.7 SAT Math - Guess and Check

There are certain SAT math problems in which you will need to simply throw in numbers to see what works – these are very similar to Must/Always and Solve the Relationship problems, except that, because of the limits imposed by the question, only certain numbers will work.  There is no shortcut around these problems; you just have to try a series of numbers until you find an answer.

-SAT Math Hint:  These questions are testing your ability to stay neat, organized, and patient.  Don't jump around when trying numbers, but keep to system so that you're remembering all possibilities.

Example Problem

16. In a set of nine different numbers, which of the following CANNOT affect the median?

(A) Increasing the smallest number only
(B) Increasing the largest number only
(C) Decreasing the largest number only
(D) Increasing each number by 10
(E) Doubling each number

Choose nine numbers and find the median.  Then go through each answer choice and do that to your numbers.  Keep in mind that your goal here is still to break patterns, so if you chose 2, 3, 4, 5, 6, 7, 8, 9, 10, don't simply increase the smallest number by one or two; increase it by 50.  Try to make changes that will eliminate the answer choice, not prove it to be sometimes true.

-SAT Math Tip: If you consistently get two answer choices as possibilities, take a close look at your numbers or what you've been doing.  On this particular problem, many students get torn between B) and D) because, with answer choice D), the ones place hasn't changed, and therefore the order of numbers and the median number appear almost the same – the median prior to the change was 6, and it is now 16.  But is 6 the same number as 16?  No.  D) has changed the actual median, even if it didn't change the order of the numbers.  So the answer here is B).

Here's another Guess and Check:
8. If x and y are prime, which of the following could be the list of factors of xy?

(A) 1, 3, 5
(B) 1, 2, 3, 5
(C) 1, 2, 3, 7, 42
(D) 1, 2, 9, 18
(E) 1, 2, 11, 22

Pick two prime numbers for x and y and multiply them together, then list the factors.  Use that information to help you start eliminating answer choices.

-SAT Math Hint: If you notice something that you find odd about the majority of the answer choices, in this case perhaps that they are asking about prime numbers and yet every answer contains 1, which you know is not prime, make sure you are clear in what the question is asking.  If the majority of answer choices contain a number that you don't think should be there, you might be misreading the question.

Did you get an answer?  The answer is E).  It is the only answer choice in which the list of factors contains two prime numbers, 1, and the product of those two numbers.