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Question

 

Dear Mitch,

I read somewhere you that you think it's important for students to keep in mind the fact that it is much easier to pick out the correct answer from a group of choices than it is to come up with the answer yourself.  (I'm talking about the multiple choice questions).   How is a person supposed to pick out the right answer if they don't work out the problem? 

Sincerely,

Nathan Lambert
Las Vegas, NV

Answer

 Dear Nathan,

 Yes, I have said something close to that, and I believe it to be fact -- however – as I will explain, there are exceptions to this rule.

First, though, the concept:

Very often on standardized tests, and in particular the SAT exam, there are a few questions that would require substantial time and effort to work the problem out until arriving at an answer, and then matching your answer with one of the choices and filling in the corresponding oval with your number two pencil. 

And sometimes – but only occasionally – the problem is actually impossible to figure out without more information.

Fortunately, though, it's no worry on a multiple choice question because – not only do you have more information, but you have the correct answer right there on your paper!  (The only glitch, of course, is that it is camouflaged among a number of other choices, all of which are wrong).  It's your job to figure out which one is correct and select it.

How? 

Well, you can take the choice one at a time and plug them in to the original problem to see which one makes the story work out right through till the end. 

NOTE:  YHIS PARTICULAR METHOD WORKS BEST AND MIGHT BE THE FIRST THING YOU TRY WHEN THE QUESTION IS ASKED ALMOST ENTIRELY IN VARIABLES.  (SUCH PROBLEMS OFTEN HAVE VARIABLES ALL THE WAY THROUGH UNTIL THE VERY END WHERE THEY FINALLY GIVE YOU ONE REAL NUMBER, AND PRESUMABLY YOU ARE TO SOMEHOW WORK BACKWARDS.

EXAMPLE:  Mack baked cookies.  When he was finished, he ate seven of them himself, then took half of the remaining ones and gave them to his best friend, Mr. F.  Then Mack ate one more and gave one-third of the ones still remaining to his grandmother. If he gave his grandmother 11 cookies, how many did he have altogether before he began to eat the very first cookie he consumed that day?

Choices:

A) 65

B) 70

C) 75

D) 80

E) 85 

Well, this can certainly be solved algebraically, and it would not be difficult at all.  But sometimes it will be, so here is the method:

Take a choice and try it in the story.  Try the first one, 65.  Story:  He ate 7, so now he is down to 58.  He gave half of the remaining ones to his friend, so now he is down to 29.

He at one more, so now he has 28.  He gives 1/3 of these remaining ones to his grandmother, who then has 11.  Well, one-third of 28 is?

Not great.  28 is not divisible by three, and so one-third could not equal 11 exactly; not the story does not mention breaking any up into pieces, etc.

So you CROSS OFF CHOICE A.  AND NEVER BOTHER RETURNING TO IT; IT DOES NOT WORK SO DO NOT WASTE YOUR TIME WITH IT. 

Try another.  How about choice c?  Here goes:

Begins with 75 and eats 7, so now has 68.

Gives half those remaining ones to friend, so now has 34.

Eats one more and now has 33.

Gives 1/3 of these remaining ones to grandma, so 1/3 x 33 = 11.

The story she says she receives 11 cookies.  So your story works.  And you are correct, the answer is choice c, 75.

NOTE:  I did mention that there is an exception.  There have been some informal studies that show a higher percentage of wrong answers to the same question when it is presented in multiple choice format over the style where the student is expected to simply do the work and come up with the answer.  There are probably a few reasons for this, but I believe the main one is this:  The wrong answer choice are designed to look enticing.  And sometimes, for problems that a person would never get wrong on his or her own is the type that one lazily circles the "obvious" answer.  "Obviously wrong", sometimes. Example:   4 1/2 x 3 1/4 = 

A) 7 2/6

B) 12  1/8

C)  12  2/8

D) 14  5/8

HINT:  The wrong answer (but most popular) is 12 1/8.  Yet when this is not a multiple choice questions, most students who selected the wrong answer get it correct on their own!  Try it, you will see! 

Hope this helps,

Mitch 

P.S. Thank you to those who have written in about our recent typo/error, which was repeated and repeated and repeated.  The PSAT is NOT the first week of October.  It is October 17th, or October 20th, depending upon your school.