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## When Test Questions Fail

Following last week's discussion, this note continues with examples of "potential" errors is on standardized tests. By potential, I suggest that either more than one of the given responses could be a possible answer (in a multiple choice format!) or an incorrect response is used as the answer.

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] Which of the following expressions is equal to x/[x+(1/x)]?
(A) x/(x+1) ... (B) 1+x2 ... (C) 1/(1+x2) ... (D) x2/(x2+1) ... (E) None of the above.

[Question #2] 1 : 1/4 :: 8 : __________
(A) 4 ... (B) 32 ... (C) 2 ... (D) 1/2 ... (E) 16

[Question #3] TRIANGLE : EQUILATERAL :: ___________ : quadrilateral
(A) Square ... (B) Rectangle ... (C) Isosceles ... (D) Circle ... (E) Right Triangle

[Question #4] James is arranging a display of coffee tins on a table 40 inches wide and 42 inches long. How many tins, each six inches in diameter, can be placed on the surface of the table without stacking the tins?
(A) 42 ... (B) 46 ... (C) 47 ... (D) 182 ... (E) 186

[Question #5] Suppose that the number of fires occurring in a particular type of dwelling decreased C percent in July, as compared to June, but then increased C percent in August, as compared to July. Then the number of fires occurring in that type of dwelling during August, as compared to June, is...
(A) Decreased by the percent equal to C squared divided by 100
(B) Unchanged
(C) Increased by percent equal to fraction whose numerator is 100 100 minus C and denominator is 100
(D) Decreased by the percent equal to the fraction C over 100

[Question #6] Suppose that 8 inches of snow contribute as much water to the reservoir system of N.Y.C. as one inch of rain. If, during a snowstorm, an average of 12 inches of snow fell during a six-hour period, with drifts as high as three feet, the addition to the water supply as a result of this snowfall ultimately will be the equivalent of...
(A) 1 1/2" rain ... (B) 3" rain ... (C) 4 1/2" rain ... (D) An amount of rain cannot be determined

I suggest that these questions are poor, in that they can mislead the test-taker. Can you see why? Also, what do you think are the "correct" answers...according to the given resource texts?

Solution Commentary: According to the associated resource texts, the given "correct" answers are:

[#1] D....but why is this incorrect? (i.e. consider domains)

[#2] C...but why could 8/4 (I know this is 2 as well!) or 8/32 be just as correct?...in fact, I could build a case for the correctness of any of the answers given!

[#3] A...but I have no idea why. That is, the analogy seems to be misconstrued....and it is unfortunate that three of the given options relate to triangles. What if a rhombus was a given choice as well?

[#4] The "given" answer is 42, but many things are wrong here. For example, the assumed answer mimics the fact that the tins are placed in rows, ignorant of the idea of circle packing. Also, what about the legal extension of a tin over the edge of the table? And, for many people, what is a coffee tin even?

[#5] A is the given answer, but I claim none of the answers are correct. For example, suppose there were 100 fires in June and C = 50. The how many fires in July? August? I rest my case!

[#6] Somehow, B is the given answer...am I missing something?