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Use the mathematical operators + , − , ÷ , × exactly once to fill in the blank boxes. What is the maximum real value that can be obtained?
Give your answer to two decimal places.
The answer is 20.33.
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1 solution
Right. But can you explain why there isn't possible any other bigger value ?
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Yeah, to maximize our value optimally we should place the multiplication sign in the last box because the adjacent numbers are the greatest ones. Then in the second last box we should place plus because it too increases the value unlike division and minus. Now, since 1 and 2 are "small" values, we should check in each case of - and ÷. In case of 1÷2-3+4×5, we get 17.5 but in case of 1-2÷3+4×5 we get 20.33 thus it is the greatest value.
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Perfect , you should add that in the solution to make explicit by what what reasoning you arrived at the result and , more importantly , to prove it is maximum.
I thought the same about maximizing and decreasing the result of the increasing and decreasing operators used and maybe you should say that the answer is made with 2 decimal digits so that there are not unclarities of how to enter the answer once you found it since the result is rather 20,(33) and cute problem.
((1-(2/3)) +4) *5=21.66
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You cannot use parentheses, the language of the question clearly rules out that possibility.
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it does not rule out parenthesis it does not say 'only use' or do not use. It just states that you must use the given operators once. 'Use the mathematical operators + - * / exactly once to fill in the blank boxes. What is the maximum real value that can be obtained?
But you have used parentheses to get your answer because you have multiplied 4x5 and also not stated that BOMDAS is applicable. Your usage is correct but the answer is wrong. The correct answer is 18.33 (ie 1-2 = -1divided by3 = -1/3+4=3 2/3x5=18.33.
well by applying BODMAS rule to your solution comes to -19.66 and not 20.33 1-2/3+4 5 B✔ O✔ D✔=1-0.66+4 5 M✔=1-0.66+20 A✔=1-20.66 S✔=-19.33 ANSWER= -19.33
Integer values are also real values, the question is what is the biggest real number, not the biggest non integer value, ergo The solution is 121 (=1+2 3 4*5)
what about (1+2)x3x4x5=180
The question is not clear. It does not say that you "can't" use an operation more than once. So if you are allowed then 121 is the right answer.
1 − 2 ÷ 3 + 4 × 5 = 1 − 0 . 6 6 + 2 0 = 2 0 . 3 3 .
To maximize our value optimally we should place the multiplication sign in the last box because the adjacent numbers are the greatest ones. Then in the second last box we should place plus because it too increases the value unlike division and minus. Now, since 1 and 2 are "small" values, we should check in each case of - and ÷. In case of 1 ÷ 2 − 3 + 4 × 5 , we get 1 7 . 5 but in case of 1 − 2 ÷ 3 + 4 × 5 we get 2 0 . 3 3 thus it is the greatest value.