# CAHSEE Math 5.5 Mathematical Reasoning

Mathematical Reasoning Drill 5, Problem 5. How many pencils could Mrs. Morrison have had?

 CAHSEE Math Mathematical Reasoning Language English Language Logic and Proofs Algebraic Proof Mathematical Reasoning Estimation

### Transcript

00:23

there would be 5 pencils left over. Instead of handing out the pencils on the

00:28

first day, she decided to hold off until the size of her class had stabilized.

00:36

A few days later, when she actually distributed the pencils, there were 25 students and there

00:41

were still 5 pencils left after the equal distribution.

00:45

How many pencils could Mrs. Morrison have had?

00:48

And here are the potential answers...

00:52

OK, so this question is just asking us to plug

00:55

in the potential answers one by one and figure out the remainders.

01:01

We have to get a number such that the remainder is 5 after dividing by both 25 and by 30.

01:08

So… consider A. With 125 pencils and the 25 student alternative, there would be NO

01:13

pencils left over – so... we can reject A.

01:17

Consider B with 130 – in this case, we’d have remainders of 5 and 10 –

01:21

so, not 5 and 5 which is what we seek… so punt B.

01:26

Now C: 150. Well, 25 and 30 go into 150 evenly so there’d be NO pencils left for either solution.

01:35

Try D: 30 into 155 gives us 150 evenly with 5 leftover;

01:41

and 25 into 155 gives us 150 evenly with 5 leftover…

01:46

So the answer to this oddball question...

01:48

...and this strange woman Mrs. Morrison dot com...

01:51

...is D.

01:52

As in, “Don’t tell Mrs. Morrison dot com about computers.”