Following the previous two week's discussions, this note continues with examples of "quality" questions on standardized tests. By quality, I suggest that though even in a constrained test environment, the questions prompt thought by pushing beyond guess-and-check strategies and obvious distractors.
For example, consider these questions taken from sample tests in review manuals for the SAT, CBEST, ACT, Miller Analogies Test, and a Firefighter's Exam:
[Question #1] In a recent survey of 250 people, 130 preferred Softie paper towels to Kleenup paper towels, 100 had no preference, and the remainder preferred Kleenup. What percent of those survey preferred Kleenup paper towels? A student answered 40%. Which statement best describes why the answer given is not reasonable?
(A) Only 20% of those surveyed preferred Kleenup
(B) 130 is 52% of 250
(C) 100 people had no preference and 100 is 40% of 250
(D) Only 20 people preferred Kleenup and 20 is 8% of 250
(E) Insufficient information to determine the percent
[Question #2] Harvey started a savings account. At the beginning of the year he put $284 in the account and left it for one year. At the end of the year he hyad earned 10 1/4% interest. How much money did he have in his savings account at the end of the year? A student answered $313.11. Which statement best describes why the answer given is reasonable?
(A) The answer must be greater than $284
(B) $313.11 is almost $30 greater than $284
(C) #313.11 rounds to $310 and $310 - $284 = $26; to the nearest ten $26 rounds to $30
(D) 10% of 284 is $28.40; $284 + $28.40 = $312.40; the answer will be a little more than $312.40
(E) Because he should get at least $313 if he leaves his money in a savings account for an entire year
[Question #3] Clerk A sorts B letters per hour, clerk C sorts D letters per hour. The D letters which clerk C sorts exceed those which clerk A sorts by 10 letters per hour. Measured in number sorted per 8-hour day, clerk C exceeds A by:
(A) D-10B ...
(B) 8(D-B) ...
(C) D+C-A+B ...
(D) C+D-A+B ...
[Question #4] Assume that you have moved into new quarters and you are to arrange the packing cases against the walls. There are eleven cases which must be placed against two walls, one wall three yards wide and the other two yards wide. Five of the cases are each 18 inches wide and six of the cases are each 15 inches in width. Cases are to be placed on the floor only. In order to fit them into the available space you should place...
(A) Four of the wider cases against the smaller wall and the rest against the larger wall
(B) Four of the narrower cases against the smaller wall and the rest against the larger wall
(C) All the narrower cases against the larger wall and all the wider cases against the smaller wall
(D) All the larger cases against the larger wall and all the narrower cases against the smaller wall
I suggest that these questions are of quality, in that they can make the responder think. Can you see why? Also, what do you think are the "correct" answers...according to the given resource texts?
Note: T.R. (Bellingham) writes: "My comment on your fourth 'quality' or thoughtful question this week is that if the walls are adjacent, the problem can't be solved."...I agree though did not think such!
Hint: Compare your answers and thoughts with others...
Solution Commentary: The associated resources gave these answers, if you care...and are they correct?
[#3] B....but given the nature of the question, I wonder if anyone would choose responses C or D?
[#4] A...but, are there other possibilities?