Summer 2014 questions

 

(click on picture for larger view!)
The solutions also appear at

http://puzzle-mania-for-the-mind.blogspot.com/2014/05/blog-post.html

along with some other puzzles.

I have not done a complete solution to #5

IF YOU CLICK ON A PROBLEM
YOU CAN SEE A LARGER VIEW!

(SCROLL DOWN FOR THE ANSWERS.)

HINT FOR #8

The ANSWER is MORE THAN 30.

#8 Is VERY SIMILAR to:

THE ANSWERS ARE HERE...

(CLICK ON THE PICTURE TO SEE BETTER!)

****************2nd half of the summer********************

The following problems are for Mid-June to July 20th:

(The solutions will appear after July 20th)

#9) How many positive integers are FACTORS of 540?

#10) How many FOUR-DIGIT integers
use each of the digits 1,2,3 and 4

EXACTLY ONCE and are DIVISIBLE by 11?

#11) The senior class at Cincy High School has 200 students.

156 of the students are attending a university in the fall.

67 students will be employed,
and 35 will be employed while 

attending a university.
How many students will NOT WORK or

attend a university?

#12) What is the sum of the 40 smallest multiples of 7?

#13) In the prime factorization of 100!
(one hundred FACTORIAL),

what is the power of 5?

**************************************

#9) How many positive integers are FACTORS of 540?

ANSWER to #9) 24 choices

#10) How many FOUR-DIGIT integers 

use each of the digits 1,2,3 and 4

EXACTLY ONCE and are DIVISIBLE by 11?

ANSWER to #10) 8 four-digit integers

#11) The senior class at Cincy High School has 200 students.

156 of the students are attending a university in the fall.

67 students will be employed, 

and 35 will be employed while 

attending a university. 

How many students will NOT WORK or

attend a university?

ANSWER to #11) 12 students will do neither

#12) What is the sum of the 40 smallest multiples of 7?

ANSWER to #12) 5740

#13) In the prime factorization of 100!

(one hundred FACTORIAL),

what is the power of 5?

ANSWER to #12) the power on 5 is 24

**************************************

#14) ELVIS is in the building!

A problem from the 6th grade contest -

Counting Rectangles

Another 5th/6th grade competition question:

The FORM of your ANSWERS...

You may need for Math Counts ...

Know how to handle a 30-60-90 degree Triangle.

There are notes below

and a video at this LINK

http://knepfle.com/30_60_90_tri.htm

   

Watch a short presetation on the 30-60-90 triangle properties. CLICK HERE

  

SEE BELOW:

Since COMBINATIONS occur frequently,
you may want to practice using the n C r KEY on the TI-83

Please DOUBLE click on video to enlarge!

MEAN MEDIAN MODE

RULES FOR DIVISIBILITY:

A NUMBER IS DIVISIBLE BY_____, IF ______
2 The last digit is even (0,2,4,6,8)
128 is  129 is not
3 The sum of the digits is divisible by 3
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3) No
4 The last 2 digits are divisible by 4
1312 is (12÷4=3)      7019 is not
5 The last digit is 0 or 5
175 is 809 is not
6 The number is divisible by both 2 and 3
114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
 308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
7 If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
8 The last three digits are divisible by 8
109816 (816÷8=102) Yes      216302 (302÷8=37 3/4) No
9 The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10 The number ends in 0
11 If you sum every second digit and then subtract all other digits and the answer is: 0, or divisible by 11
1364 ((3+4) - (1+6) = 0) Yes
3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
12 The number is divisible by both 3 and 4
648    (By 3? 6+4+8=18 and 18÷3=6 Yes.
        By 4? 48÷4=12 Yes) Yes
524      (By 3? 5+2+4=11, 11÷3= 3 2/3 No.
           Don't need to check by 4.) No