Mathematical Reasoning Drill 5, Problem 5. How many pencils could Mrs. Morrison have had?
|CAHSEE Math||Mathematical Reasoning|
|Logic and Proofs||Algebraic Proof|
there would be 5 pencils left over. Instead of handing out the pencils on the
first day, she decided to hold off until the size of her class had stabilized.
A few days later, when she actually distributed the pencils, there were 25 students and there
were still 5 pencils left after the equal distribution.
How many pencils could Mrs. Morrison have had?
And here are the potential answers...
OK, so this question is just asking us to plug
in the potential answers one by one and figure out the remainders.
We have to get a number such that the remainder is 5 after dividing by both 25 and by 30.
So… consider A. With 125 pencils and the 25 student alternative, there would be NO
pencils left over – so... we can reject A.
Consider B with 130 – in this case, we’d have remainders of 5 and 10 –
so, not 5 and 5 which is what we seek… so punt B.
Now C: 150. Well, 25 and 30 go into 150 evenly so there’d be NO pencils left for either solution.
Try D: 30 into 155 gives us 150 evenly with 5 leftover;
and 25 into 155 gives us 150 evenly with 5 leftover…
So the answer to this oddball question...
...and this strange woman Mrs. Morrison dot com...
As in, “Don’t tell Mrs. Morrison dot com about computers.”