Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
Solution
In order to maximize the sum of the numbers, the numbers must have their digits ordered in decreasing value. There are only two numbers from the answer choices with this property: and . To determine the answer we will have to use estimation and the first two digits of the numbers.
For the number that would maximize the sum would start with . The first two digits of (when rounded) are . Adding and , we find that the first three digits of the sum of the two numbers would be .
For the number that would maximize the sum would start with . The first two digits of (when rounded) are . Adding and , we find that the first three digits of the sum of the two numbers would be .
From the estimations, we can say that the answer to this problem is .
p.s. USE INTUITION, see answer choices before solving any question -litttle_master
== Solution 2 ==
In order to determine the largest number possible, we have to evenly distribute the digits when adding. The two numbers that show an example of this are and . The digits can be interchangeable between numbers because we only care about the actual digits.
The first digit must be either or . This immediately knocks out .
The second digit must be either or . This doesn't cancel any choices.
The third digit must be either or . This knocks out and .
The fourth digit must be or . This cancels out .
This leaves us with .
== Solution 3 ==
If we use intuition, we know that the digits will be IN ORDER, to maximze the number. This eliminates textbf{(B)}, textbf{(D)},and textbf{(E)}. Additionally, the 2 two numbers must have 9 or 8 for the first digit to maximize the sum, eliminating textbf{(A)}. This leaves boxed{textbf{(C)} 87431}.
-written by litttle_master purely, not copied from anywhere
== Video Solution by OmegaLearn==
https://youtu.be/HISL2-N5NVg?t=654
~ pi_is_3.14
https://youtu.be/trAjltkbSWo ~savannahsolver
Gilda has a bag of marbles. She gives of them to her friend Pedro. Then Gilda gives of what is left to another friend, Ebony. Finally, Gilda gives of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?
Solution
After Gilda gives % of the marbles to Pedro, she has % of the marbles left. If she then gives % of what's left to Ebony, she has = % of what she had at the beginning. Finally, she gives % of what's left to her brother, so she has of what she had in the beginning left.
The letter M in the figure below is first reflected over the line and then reflected over the line . What is the resulting image?
[figure]
[figure]
Solution
When M is first reflected over the line we obtain the following diagram:
[figure]
When M is then reflected over the line we obtain the following diagram:
[figure]
Therefore, the answer is
~MRENTHUSIASM
==Video Solution (A Clever Explanation You’ll Get Instantly)==
https://youtu.be/tYWp6fcUAik?si=V8hv_zOn_zYOi9E5&t=350
~hsnacademy
==Video Solution 1 by Math-X (First understand the problem!!!)==
https://youtu.be/oUEa7AjMF2A?si=l-XMI73aofM6q4ye&t=320
~Math-X
==Video Solution 2 (CREATIVE THINKING!!!)==
https://youtu.be/lItyKxX_qB8
~Education, the Study of Everything
==Video Solution 3==
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=259
~Interstigation
==Video Solution 4==
https://youtu.be/c-D-bj2htGE
~savannahsolver
==Video Solution 5==
https://youtu.be/Q0R6dnIO95Y?t=182
~STEMbreezy
==Video Solution 6==
https://www.youtube.com/watch?v=6kkJVsOKcuk
~harungurcan
==Video Solution 7 by Dr. David==
https://youtu.be/hh3DbQ9Rd5Y