Question 1205139: " I am a three-digit number. My second digit is 4 times bigger than the third digit. My first digit is 3 less than my second digit. What number am I...? "
Found 7 solutions by MathLover1, ikleyn, Edwin McCravy, greenestamps, mccravyedwin, Alan3354, AnlytcPhil:
Answer by MathLover1(20849)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Similarly to as a drop of nicotine kills a horse, this phrasing
" My second digit is 4 times bigger than the third digit "
kills a reader.
This form " My second digit is 4 times bigger than the third digit "
is not used and is PROHIBITED when Math problems are written in English.
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
I am a three-digit number.
_ _ _
My second digit is 4 times bigger than the third digit.
_ 4 1 or _ 8 2
My first digit is 3 less than my second digit.
1 4 1 or 5 8 2
What number am I...? "
141 or 582
Edwin
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I will take a slightly less restrictive position than tutor @ikleyn.
The phrase "4 times bigger than" SHOULD NOT be used in the statement of a math problem, but it is not prohibited.
Both of the tutors who supplied responses showing solutions to the problem got the wrong answers.
The reason for their wrong answers is that they took "4 times BIGGER THAN" to mean the same thing as "4 times AS BIG AS". It does not; those are two different things.
4 times AS BIG AS means the number is 4 times what it was before -- i.e., it is 400% as big as it was.
4 times BIGGER THAN means it has GROWN BY 400%, so now it is 500% as big as it was.
So 4 times BIGGER THAN means 5 times AS BIG AS; if the smaller number is x, then the bigger number is 5x, not 4x.
Using the correct interpretation of "4 times bigger than", since the second digit is 4 times BIGGER THAN the third digit, which means 5 times AS BIG AS the third digit. Then there is only one possibility: the third digit is 1 and the second digit is 5. That then makes the first digit 2.
ANSWER (the only one): 251
Unfortunately, in everyday sloppy English, the two phrases are nearly always used to mean the same thing.
But in a math problem, where the given information has to be absolutely clear in order to find an answer, it is exceedingly bad form to use a phrase like "4 times bigger than" that is open to different interpretations.
Answer by mccravyedwin(407)  (Show Source):
Answer by Alan3354(69443)  (Show Source):
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website!
Let's paraphrase Greenestamps' words:
4 times AS SMALL AS means the number is 4 times less than what it was before --
i.e., it is 400% as big as it was.
4 times SMALLER THAN means it has SHRUNK BY 400%, so now it is 500% as small as
it was.
So 4 times SMALLER THAN means 5 times AS SMALL AS; if the larger number is x,
then the smaller number is  , not  .
So if the stated problem had been:
" I am a three-digit number. My second digit is 4 times SMALLER than the third
digit. My first digit is 3 less than my second digit. What number am I...? "
No, that won't work, since we can't have "negative digits". We have to change
"less" to "MORE".
" I am a three-digit number. My second digit is 4 times SMALLER than the third
digit. My first digit is 3 MORE than my second digit. What number am I...? "
" I am a three-digit number.
_ _ _
My second digit is 4 times SMALLER than the third digit.
_ 1 5
My first digit is 3 MORE than my second digit.
4 1 5
What number am I...? "
415
Merry Christmas, TOOTERS! J.
Edwin, aka Analytic Phil!
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