Posted by nicole on Monday, September 22, 2008 at 4:32pm in response to math.
Can u please help me with this..this is my sons 6th grade work and im pulling my hair out..i would like to know how to do it so he does not think or his teacher that im an idiot...
Thank You So Much
-The mystery # is a decimal..
-The digit in the 1's place is less then then digit in 10th place..
-No 2 digits are the same..
-The number is less than the # of years in a century...
-The digit in the 10th place is less than the digit in the 1000's...
-There are 2 digits in the whole part..
-There are 5 digits all together...
-The sum of the digits is 20....
-No digit is odd...
-The product of the digits in the ones place and the 100th is zero...
-The sum of the digits in the ones place and the 100th is two...
-The number is greater than 5 dozen...
-The sum of the digits in the decimal part of the # is the same as the digits in the whole part of the number.
-The product of the digits in the 10ths place and the 1000's is equal to 2 dozen...
-The product if the digits in the 100's place and the tens place is zero..
-What is the mystery # ________
10.9186
86.042
To find the mystery number, let's break down each clue and find the information it provides:
1. The mystery number is a decimal.
2. The digit in the 1's place is less than the digit in the 10th place.
Given this clue, we know that the tenth place digit is greater than the ones place digit.
3. No two digits are the same.
This means that all the digits in the number are unique.
4. The number is less than the number of years in a century.
A century consists of 100 years. So the mystery number is less than 100.
5. The digit in the 10th place is less than the digit in the 1000's.
This tells us that the digit in the 10th place is smaller than the digit in the thousands place.
6. There are 2 digits in the whole part.
The whole part of the number has only 2 digits.
7. There are 5 digits in total.
This means the number has 5 digits in total, including both the whole part and the decimal part.
8. The sum of the digits is 20.
The sum of all the digits in the number is 20.
9. No digit is odd.
None of the digits in the number are odd numbers (1, 3, 5, 7, 9).
10. The product of the digits in the ones place and the 100th is zero.
The digit in the ones place multiplied by the digit in the hundredth place equals zero. This means that at least one of them is zero.
11. The sum of the digits in the ones place and the 100th is two.
The digit in the ones place added to the digit in the hundredth place equals two.
12. The number is greater than 5 dozen.
A dozen is equal to 12, so 5 dozen is 60. This clue tells us that the number is greater than 60.
13. The sum of the digits in the decimal part of the number is the same as the digits in the whole part of the number.
The sum of the digits in the decimal part of the number is equal to the sum of the digits in the whole part.
14. The product of the digits in the 10ths place and the 1000's is equal to 2 dozen.
Similar to clue 12, we know that the product of the digit in the 10th place and the digit in the thousands place is equal to 2 dozen (2 * 12 = 24).
15. The product of the digits in the 100's place and the tens place is zero.
The digit in the hundreds place multiplied by the digit in the tens place equals zero. Again, this means that at least one of the digits is zero.
Based on these clues, let's find the mystery number step by step. Starting with the clues that provide specific information:
- Clue 5 tells us that the digit in the 10th place is smaller than the digit in the thousands place. Since the digit in the thousands place cannot be zero (as per clue 15), it must be greater than zero and the digit in the 10th place must be zero.
- Clue 14 tells us that the product of the digits in the 10ths place (zero) and the 1000's is equal to 2 dozen. So the digit in the thousands place must be equal to 2.
- Clue 3 tells us that no two digits are the same. So we have the digits zero and two filled in for the 10th and thousands place respectively: _ _ _ _ 0 _.
- Clue 9 tells us that no digit is odd. Therefore, the remaining digits in the number must be even. The only even digits left are 4, 6, and 8.
- Clue 6 tells us that there are 2 digits in the whole part. Since no two digits can be the same, the remaining two digits must be different, which means one of them must be even and the other one odd. However, clue 9 states that all digits are even, so this clue is contradictory.
Based on this contradiction, it seems like there might be an error or inconsistency in the given clues. Without more information, it is not possible to determine the exact mystery number.
Please note that if there is additional information or if any of the given clues require revisiting, we can reevaluate the solution process.
To find the mystery number, we need to carefully analyze each clue given and use deductive reasoning to narrow down the possibilities.
Let's break down each clue one by one:
1. The mystery number is a decimal.
- This means the number has a whole number part and a decimal part.
2. The digit in the 1's place is less than the digit in the 10th place.
- This tells us that the tens digit is greater than the ones digit.
3. No 2 digits are the same.
- This means that each digit in the number is unique.
4. The number is less than the number of years in a century.
- There are 100 years in a century, so the number is less than 100.
5. The digit in the 10th place is less than the digit in the 1000's.
- This gives us the information that the thousands digit is greater than the tens digit.
6. There are 2 digits in the whole part.
- The whole part of the number has only 2 digits.
7. There are 5 digits altogether.
- This means the number has 3 digits after the decimal point.
8. The sum of the digits is 20.
- We know that the sum of all the digits (both in the whole part and the decimal part) is equal to 20.
9. No digit is odd.
- This tells us that all the digits are even.
10. The product of the digits in the ones place and the 100th is zero.
- This means either the ones digit or the digit in the hundredth place is zero.
11. The sum of the digits in the ones place and the 100th is two.
- This tells us that the sum of the ones digit and the hundredth digit is 2.
12. The number is greater than 5 dozen.
- A dozen is equal to 12, so 5 dozen is 60. The mystery number is greater than 60.
13. The sum of the digits in the decimal part of the number is the same as the digits in the whole part of the number.
- This means the sum of the digits after the decimal point is the same as the sum of the digits before the decimal point.
14. The product of the digits in the 10ths place and the 1000's is equal to 2 dozen.
- The product of the digit in the tenths place and the digit in the thousands place is equal to 24.
15. The product of the digits in the 100's place and the tens place is zero.
- This implies that either the digit in the hundreds place or the digit in the tens place is zero.
Now, let's analyze the given clues together and narrow down the possibilities:
Based on clue 2, the tens digit is greater than the ones digit. Since all the digits are even (clue 9), the options for the tens and ones digit are limited: (2, 4, 6, 8).
Clue 4 states that the number is less than 100, and clue 6 says there are 2 digits in the whole part. Combining these clues, the options for the tens and ones digit are further narrowed down to: (20, 24, 26, 28, 40, 42, 46, 48, 60, 62, 64, 68, 80, 82, 84, 86, 28).
From clue 12, we know that the number is greater than 5 dozen (60). Thus, the possibilities for the tens and ones digit are now limited to: (62, 64, 66, 68, 80, 82, 84, 86, 28).
Clue 5 tells us that the thousands digit is greater than the tens digit. Since the thousands digit must be even, and considering the remaining options for the tens and ones digit, the only possibility for the thousands digit is 8. Therefore, the options for the tens and ones digit are now: (82, 84, 86).
Clue 8 states that the sum of the digits is 20. Let's calculate the sum of the digits for each of the remaining options:
- For 82, the sum is 8 + 2 = 10.
- For 84, the sum is 8 + 4 = 12.
- For 86, the sum is 8 + 6 = 14.
Since none of the options have a sum of 20, we can conclude that there isn't a valid solution that matches all the given conditions. It's possible that there was an error or inconsistency in the clues provided. I would recommend double-checking the clues or seeking clarification from the teacher.