“Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved…”
Certainty in this complex and confusing conditions can be hard to come by. Sometimes, we cannot know definitively whether we possess sufficient evidence or understanding to make correct choices, yet still we must choose. Such is the uncertain fate of those who tackle standardized test math!
Math on exams like the SAT and ACT frustrate test takers for a myriad of reasons, from convoluted word problems to complex or unexpected concepts. Sometimes devising the right solution to a problem seems impossible, while, at other times, we don’t even fully understand the problem.
These levels of extreme uncertainly can be considered features of standardized test design, rather than flaws. After all, the test makers channel tremendous knowledge, expertise, and guile to the challenge of helping students get as many questions wrong as possible. Standardized test math very often ingeniously embeds traps within problems and vice versa to the extent that even the strongest math student feels confused and uncertain.
A perfect example of the mind games test makers play can be found in the common math answer choice, “Cannot be determined from the information provided.”
Janice’s family went to the movies last week and bought 4 tickets, 4 sodas, and 1 pack of candy for $58.50. This week her family went again, but this time they bought 4 tickets, 4 sodas, and 3 packs of candy for $63.50. How much does one pack of candy cost?
(A) $5.00
(B) $3.50
(C) $2.50
(D) $2.00
(E) Cannot be determined from the information provided
A mainstay of ACT Math, this pernicious option preys upon the ignorance Charles Darwin commented on in his quote from The Descent of Man. And therein lies its effectiveness. After all, when you are struggling to answer a math problem, you are bound to find solace and perhaps even affirmation in any choice that suggests the flaw lies not in the solver but in the problem itself.
No wonder “Cannot be determined from the information provided” is almost always a TRAP.
You may look at the math problem above and decide that you cannot solve it. Your determination in this case does not mean the problem itself cannot be solved, when a simple system of equations will suffice to unlock the answer. You might not be able to determine the answer from the information provided, but it certainly can determined.
Of course, the diabolical nature of these tests guarantees that no rule is without its exceptions. The “Cannot be determined” choice may be a trap 99% of the time, but that just makes the problem for which it is correct all the more challenging. I reviewed the second test in The Official ACT Prep Guide with a student recently who eliminated that choice out of hand, only to lose the point when the solution really couldn’t be determined from the information provided.
What lesson can we draw from this example, apart from further confirmation of the fiendish imaginations at work designing standardized exams these days? When tackling any problem on tests or in life, resist the temptation to assume that, just because you cannot solve it, a solution does not exist. Dig deeper, test your assumptions, and avoid the seductive solace of the Dunning–Kruger Effect. Nearly every problem can be solved.
Mike Bergin