Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Answer:
[tex]A=2044[/tex]
Step-by-step explanation:
Note that [tex]x\in\mathbb{W}[/tex] denotes that [tex]x[/tex] is a whole number.
By definition, consecutive numbers follow each other when we count up (e.g. 1, 2, 3).
Let's consider our conditions:
- A, B, and C are consecutive whole numbers greater than 2,000
- A is a multiple of 4
- B is a multiple of 5
- C is a multiple of 6
Since B is a multiple of 5, the ones digit of B must be either 0 or 5. However, notice that the number before it, A, needs to be a multiple of 4. The ones digit of a number preceding a ones digit of 0 is 9. There are no multiples of 4 that have a ones digit of 9 and therefore the ones digit of B must be 5.
Because of this, we've identified that the ones digit of A, B, and C must be 4, 5, and 6 respectively.
We can continue making progress by trying to identify the smallest possible whole number greater than 2,000 with a units digit of 6 that is divisible by 6. Notice that:
[tex]2000=2\mod6[/tex]
Therefore, [tex]2000-2=1998[/tex] must be divisible by 6. To achieve a units digit of 6, we need to add a number with a units digit of 8 to 1,998 (since 8+8 has a units digit of 6).
The smallest multiple of 6 that has a units digit of 8 is 18. Check to see if this works:
[tex]C=1998+18=2016[/tex]
Following the conditions given in the problem, the following must be true:
[tex]A\in \mathbb{W},\\B\in \mathbb{W},\\C\in \mathbb{W},\\A+1=B=C-1,\\A=0\mod 4,\\B=0\mod 5,\\C=0\mod 6,[/tex]
For [tex]C=2016[/tex], we have [tex]B=2015[/tex] and [tex]A=2014[/tex]:
[tex]A\in \mathbb{W},\checkmark\\B\in \mathbb{W},\checkmark\\C\in \mathbb{W},\checkmark\\A+1=B=C-1,\checkmark\\A=2014\neq 0\mod 6, \times\\B=2015=0\mod 5,\checkmark\\C=2016=0\mod 6\checkmark\\[/tex]
Not all conditions are met, hence this does not work. The next multiple of 6 that has a units digit of 8 is 48. Adding 48 to 1,998, we get [tex]C=1998+48=2046[/tex].
For [tex]C=2046[/tex], we have [tex]B=2045[/tex] and [tex]A=2044[/tex]. Checking to see if this works:
[tex]A\in \mathbb{W},\checkmark\\B\in \mathbb{W},\checkmark\\C\in \mathbb{W},\checkmark\\A+1=B=C-1,\checkmark\\A=2044=0\mod 4,\checkmark\\B=2045=0\mod 5,\checkmark\\C=2046=0\mod 6\checkmark[/tex]
All conditions are met and therefore our answer is [tex]\boxed{2,044}[/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
