TMI? No... Not Enough Information (NEI) or Extraneous Information (EI)?

At a recent sporting event, 25 athletes won one gold medal each. 25 others won a silver medal. 25 won bronze. 40 athletes did not win any medals. How many medals were awarded?

Answers

a) 115
b) Not enough information
c) 75

The answer is "c"

Note: 

You might be tempted to answer... a) (115) because that is 25 x 3 + 40. You see the numbers in the question and you combine them. 

You might be tempted to answer... b) "Not enough information" because the question involves medals awarded to some athletes and then suddenly some athletes aren't getting any medals.

********If you answer "Not enough information" more than twice on a fifty question exam, you should check the questions again. 

3 out of 4 - Again. What if there is no 3rd number?

Here's a quick review...



"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

"A motorcyclist rides 125 miles in 3 hours. At this rate, how much distance will be covered in 5 hours?"

A factory produces 3000 widgets every 45 minutes. How many widgets will be produced in 7 hours?


These questions, I like to call, are "3 out of 4" questions. You are given 3 numbers and you need to find the 4th. How to solve? Make yourself a 4-way relationship box. 


Let's look at question 1 again. 

"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

Your two "measurements" are height (H) and shadow length (SL).

H           SL
10            6
12            ?

Remember MUADO - Multiply Up and Across, Divide by the Other Number.

12 x 6 = 72
72/10 = 7.2

You could have set your box up another way.

H      10    12
SL     6      ?

6 x 12 = 72
72/10 = 7.2

Same answer...


Tricks to watch out for!

In question 3, the two "measurements" are time and widgets. However, the first "time" is in minutes and the second one is in hours. You need to either convert the 45 minutes to .75 hours, or convert the 7 hours to 420 minutes. Then set up your box, remember MUADO, and get yourself the right answer.

So...

What if the question has no 3rd number? 

For example...

You need to answer 40 questions correctly on an exam in order to get the 80% passing mark. How many questions are on the exam?

Where's the 3rd number?

The third number is 100 - the % means 100.

Your two "measurements" are questions answered correctly (Q) and percent (%).

Q           %
40           80
?            100


Another example...

Pat can cut a lawn in 45 minutes? How long will it take Pat to cut 2.5 lawns?

Where's the 3rd number?

The third number is 1 - "a lawn" = 1.

Your two "measurements" are lawns (L) and time (T).

L           T
1           45
2.5         ?

Age Problems - Method 2 - Substitution

Chris is 3 times as old as Pat.               Together their ages add up to 32.                          How old is each of them?

Method 2 - "Game Show" Higher or Lower Method

a) Pat is your "reference" or starting point. Look for the word "as" or "than". (The first sentence could have been written "Chris is 3 times older than Pat.") The word associated with "as" or "than" becomes your reference. 

b) Pick 1 to represent Pat's age. 

c) If Pat is 1, then Chris has to be 3 because "Chris is 3 times as old as Pat."

d) "Together their ages add up to 32..." so...
1 + 3 will not work, as it doesn't = 32. The answer is too low. Pick a higher number to represent Pat's age. 

e) Pick 10 to represent Pat's age. 

f) If Pat is 10, then Chris has to be 30 because "Chris is 3 times as old as Pat."

g) "Together their ages add up to 32..." so...

10 + 30 will not work, as it doesn't = 32. The answer is too high. Pick a lower number to represent Pat's age. 


h) Eventually, by going higher and lower, you'll figure out that Pat is 8. Chris is 24 because Chris is 3 times older than Pat.

i) Check! Always check! "Together their ages add up to 32."       8 + 24 = 32.

Classic "Age" Problems - A couple of ways to solve these questions - Method 1

Chris is 3 times as old as Pat.               Together their ages add up to 32.                          How old is each of them?

Method 1 - 

a) Create an equation. Pat is your "reference" or starting point. Look for the word "as" or "than". (The first sentence could have been written "Chris is 3 times older than Pat.") The word associated with "as" or "than" becomes your reference. 

b) Pick a letter to represent Pat's age. We'll use "x".

c) If Pat is "x", then Chris has to be 3x.

d) "Together their ages add up to 32..." so...
x + 3x = 32

e) Combine your x's. (That's a lot of alimony). 
4x = 32

f) This means 4 times "something" = 32. The answer is 8. One "x" = 8

g) Pat is 8, because Pat is one "x". Chris is 24 because Chris is 3 times older than Pat.

h) Check! Always check! "Together their ages add up to 32."       8 + 24 = 32.