Which is not true? Only one even prime; 61 is prime, 196 is

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mumu416

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I want to know what's the answer for this question, because i just had for a test and i don't really know the answer.

Question 1: Which of the following statement is not true?

A. there is only one even prime number
B. 61 is a prime number
C. 196 is a perfect square number
D. 23 is the product of two different integers
E. 127 is a perfect cube.

well, i think that D, E are both possible, i am not really sure...

Question 2: Charlie spent one quater of his money on a book and then gave his brother two third of what was left. He then had $9. How much money did Charlie start with?

A. $27, B. $36, C. $48, D. $44, E. $40
 
mumu416 said:
D. 23 is the product of two different integers

E. 127 is a perfect cube.

well, i think that D, E are both possible answers for this exercise , i am not really sure...

23 = 23 * 1

So, now what do you think about the possibility of choice (D)?

Question 2

Charlie spent of his money on a book and then gave his brother of what was left.

This is not proper English; the sentence makes no sense, to me.
Click to expand...
 
Sorry one mistake

the second question is: Charlie spent one quater of his money on a book and then gave his brother two third of what was left. He then had $9. How much money did Charlie start with?
 
Re: Sorry one mistake

mumu416 said:
Charlie spent one quater of his money on a book and then gave his brother two third of what was left. He then had $9.

How much money did Charlie start with?
Click to expand...


Hello MuMu:

Do you know how to calculate one-quarter of an amount?

Do you know how to calculate two-thirds of an amount?

If you do, then do the following with each of the possible choices to discover which choice is the correct solution.

Take one-quarter of the choice. Take two-thirds of the result. See if you end up with 9.

If you do not know how to calculate such fractional amounts, then tell us.

Cheers,

~ Mark :)

 
Re: Hi, iam new ! 2 questions...

mumu416 said:
E.127 is a perfect cube.
well, i think that D, E are both possible, i am not really sure...
Click to expand...
You don't seem to know what a cube is; it's the product of a number multiplied by itself:
1 * 1 * 1 = 1
2 * 2 * 2 = 8
3 * 3 * 3 = 27
4 * 4 * 4 = 64
5 * 5 * 5 = 125
6 * 6 * 6 = 216

So you can plainly see that 127 is NOT a cube.
 
mumu416 said:
well, i think that D, E are both possible, i am not really sure...
Click to expand...
If I may venture to suggest, it might have been a better use of your time to think about the concepts and attempt the exercises, rather than memorizing the text and all the multiple-choice options...?

To get started, try studying the basic concepts. Grab a dictionary and copy down the definitions of "even" numbers, "odd" numbers, "prime" numbers, "products" of numbers, "perfect squares" (or "square" numbers), and "perfect cubes" (or "cubes"). Then check your textbook for the definitions of these same terms. Compare and contrast, and review the relevant sections in your book and pages in your class notes. Then review the section(s) on factoring numbers, finding prime factorizations, and testing for primality. If you are having difficulty understanding your book and your course materials in any particular area, please specify, and we'll be glad to try to find lesson links so you can learn.

mumu416 said:
Question 2: Charlie spent one quater of his money on a book and then gave his brother two third of what was left. He then had $9. How much money did Charlie start with?

A. $27, B. $36, C. $48, D. $44, E. $40
Click to expand...
At the very least, since you had time to memorize all of the answer options, you have had time to test each of these values. What have you concluded?

Please be complete. Thank you! :D

Eliz.
 
BASIC ALGORITHIM of ARITHMETIC: Any number may be written as a finite product of primes.

Prime number: any integer divisible only by 1 and itself .
examples: 2,3,[4 is not , divisible by 2] 5, 7, 11, 13.....

0 added to any number yields the same number
1 multiplied by any number yields the same number

A) There is only one even prime, All even numbers can be written as 2 x , x an integer. Then all even numbers are divisible by 2

B) 61 is 2 a factor? no; is 3 a factor? no; is 5 a factor? no; is 7 a factor ? no
Then 61 is prime. [You only have to check up to the square root of the number because if there was a factor above the square root it would have had a factor below the square root]

C) is 196 a perfect square?
factor 196
196= 2*98
196=2*2*49
196=2*2*7*7 Yes 196 is a perfect square it is [2*7] squared

D) 23 is the product of two integers? yes 1*23
Any number multiplied by 1 yields itself

e) 127 is a perfect cube?
basic Algorithim shows 127 isnt divisible by any prime up to 13
127 is prime, then cannot be the product of 3 integers.


let M be the money Charlie started with
he spent M/4 on a book and had 3M/4 left
he gave his brother 2/3 of 3M/4 to his brother or M/2 to his brother.
he had left 1/3 of 3M/4 = M/4
but M/4=9
M=36 answer B

Arthur
 
mumu416 said:
Question 2: Charlie spent one quater of his money on a book and then gave his brother two third of what was left. He then had $9. How much money did Charlie start with?
A. $27, B. $36, C. $48, D. $44, E. $40
Click to expand...
Often easier to "back up":

x = initial amount
y = left after book purchased
9 = left after 2/3 to brother

y - 2y/3 = 9 : y = 27

x - x/4 = y = 27 : x = 36
 
arthur ohlsten said:
FUNDAMENTAL THEOREM of ARITHMETIC: Any natural number greater than 1 may be uniquely written as a finite product of prime numbers.

Prime number: any natural number greater than 1 divisible only by 1 and itself ...
Click to expand...


Hi MuMu:

Arthur's main points above are correct; I made some adjustments in red. (I'm not sure if you've learned the word "integer", but you should have learned the definition of "natural number" -- I hope. There's a big difference.)

There are many algorithms for finding the prime factorization of natural numbers greater than 1. (You can find lots of information on the Internet.)

I suggest, for beginning arithmetic students, to COMPLETELY memorize the multiplication table up to (at least) 12 times 12. If you do this, then you can easily find (in your head) all of the prime numbers less than 144. For example, is the natural number 127 one of the products in the multiplication table? If you know your multiplication table, then you know right away that 127 is not found in the multiplication table; this, in turn, tells you that 127 is a prime number because you cannot find two whole numbers that multiply to make 127.

This skill (i.e., determining in your head the prime numbers less than 144) is VERY important to have for future math study because writing numbers as products of prime factors makes it so easy to simplify a whole bunch of stuff (fractions, square roots, etc.).

Cheers,

~ Mark :)

 
THANKS!!!

I now have remembered 1~12times table, thanks!
one thing, i thought that INTEGER is a whole number - 54, -12, -1, 0, 65. etc. or am i wrong?
 
Mark-
Thank you for the corrections.
I am always surprised that so few students know the fundamental algorithim of arithmetic. I always quote it when I am factoring quadratic equations for students.
Sorry on the slip about integers and natural numbers, but I studied number theory in the fifties and find I get 'sloppy' with age.

Arthur
 
mumu416 said:
... i thought that INTEGER is a whole number - 54, -12, -1, 0, 65. etc. or am i wrong?
Click to expand...


Hi MuMu:

(I sure hope that you're not related to WaMu!) ... :wink: ... (Just kidding!)

I find that many people use the term "whole number" inconsistently. Here are accurate definitions:

The set of natural numbers = {1, 2, 3, 4, ...}

The set of whole numbers = {0, 1, 2, 3, 4, ...}

The set of integers = {... -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}

Notice the following.

The set of whole numbers is exactly the same as the set of natural numbers, with one exception. The set of whole numbers contains one extra member: zero.

If you add the opposite of each natural number to the set of whole numbers, then you end up with the set of integers.

When I studied at Seattle Central Community College, all of my instructors were familiar with -- and accepted the name -- "whole number(s)" without incident.

Later, when I studied at the University of Washington, I found it difficult to locate professors who were familiar with the set of whole numbers. I often lost credit on assignments if I wrote the name "whole numbers" on homework or exams because these professors all claim that there is no such set.

I still remember sitting in one professor's office, trying to explain the definition of the set of whole numbers, when he kicked open the door to his office, yelled across the hall to a fellow professor, "Hey Jack -- you ever hear of anything like a set of whole numbers?" Jack replied, "No, I don't think so." After which my professor struck an additional 5 points from my exam (this, in addition to the previous 10 points that I lost), all because I wrote the term "whole".

According to these hardballs, the set of whole numbers does not exist; it is called the set of "non-negative integers". And that was their final answer!

I do not agree; there are dozens of textooks which define the set of whole numbers, and thousands of references.

In summary, it's more important that you -- in your own mind -- understand the differences between natural numbers, whole numbers, and integers. All three sets share common members, but they are not exactly the same sets.

It is not correct to say that two whole numbers multiply to make -54 because there are no negative numbers in the set of whole numbers.

It is not correct to say that two natural numbers multiply to make 0 because there is no zero in the set of natural numbers.

Understand the following.

All natural numbers are whole numbers, but not all whole numbers are natural numbers.

All whole numbers are integers, but not all integers are whole numbers.

Another name for the set of natural numbers is the set of positive integers.

Another name for the set of whole numbers is the set of non-negative integers.

Cheers,

~ Mark :)

 
arthur ohlsten said:
... I am always surprised that so few students know the fundamental algorithim of arithmetic ...
Click to expand...


I am always surprised that so few high-school graduates know the multiplication table up to 12 times 12.

~ Mark :(

 
Mark-
If I remember correctly from number theory at UCLA 1957, the ancient greeks and the middle ages europeon had no concept of zero, or negative numbers.
In fact a mathemetician in the 1600's claimed x+4=0 had no solution and was meaningless.
I believe 0 entered Eureopean math via the Arabs and the Indians.
In the middle ages a European mathemetician said the positive numbers were "natural numbers given by God, and all others from man ".
I know the natural numbers as those from 1 to infinity and not sure of 0. Its been 50 years.
And like most others I use the term integers, for all numbers both positive and negative but you are correct as far as I remember.
Arthur
 
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