Quinary Quantity Part 3

Logic Level 2

$\large \left( \square \ + \ \square \ - \ \square \ \right) \times \ \square \ \div \ \square$

You are given that the numbers $1,2,3,4$ and $5$ are to be filled in the square boxes as shown above (without repetition).

Find the minimum possible value of the resultant number. Give your answer to 3 decimal places.

The answer is -2.667.

3 solutions

Chew-Seong Cheong
Aug 11, 2015

The expression is equivalent to $S = (A+B-C)\times D \div E$ . For minimum $S$ , $A+B-C$ must be minimum, which is $1+2-5=-2$ , $D$ and $E$ be the maximum and minimum with the remaining numbers, that is, $D=4$ and $E=3$ . Therefore, $S_{min} = (-2) \times 4 \div 3 = \boxed{-2.667}$ .

I donno if I am stupid or what. I do believe we have to do this according to BODMAS. and I dont see any brackets in the problem.

SO my answer is

2+3-5*4/1

which gives -15

5*4/1=20

2+3-20=-15

I dont see any brackets in the question. Try typing my answer in any std calculator. Please tell me if I am wrong.

Ritwik Gopi - 5 years, 10 months ago

It is mentioned that: $\color{#D61F06}{\text{By strictly applying the operations from left to right}}$ . The BODMAS problem is Part 4 .

Chew-Seong Cheong - 5 years, 10 months ago

oops my bad

Ritwik Gopi - 5 years, 10 months ago

It said "strictly applying the operations from left to right." Of course you don't use the brackets. Clearly said,clearly done

Caeo Tan - 5 years, 5 months ago

Yes you are

Stefano Prosperi - 4 years, 11 months ago

I also think so gopi

Shaid Hasan Niloy - 5 years, 4 months ago

I thought the answer was -15 too!

Elena Gomes - 5 years, 10 months ago

same result ^^

Felixx Felixx - 5 years, 6 months ago

I agree that $S_{min}=\frac{-8}{3}=\boxed{-2.667}$ . However, I am not sure that $A+B-C$ must be a minimum is so obvious. It is obvious that $A+B-C$ must be negative, which means that C could be 4 or 5, with A and B being a combination of 1, 2, or 3 can provide negative numbers. It just so happens that A+B-C should be a minimum for this problem but I think a complete solution would need to show the above combinations to truly show that S is minimized when $A+B-C$ is minimized, unless there is a principle I am missing here.

The combinations being: A=1, B=2 ,or vice versa, C=4, D=5, and E=3 gives $S=\frac{-5}{3}$

A=1, B =2, or vice versa, C=5, D=4, and E=3 gives $S=\boxed{\frac{-8}{3}}$ , our answer

A=1, B=3, or vice versa, C=5, D=4, and E=2 gives $S=-2$

Scott Ripperda - 5 years, 9 months ago

I found one solution that gives less its 2+3-4 5/1 2+3-4 5 2+3-20 5-20 -15

zain ali - 5 years, 1 month ago

$(2+3-4)5/1 = 5$

Chew-Seong Cheong - 5 years, 1 month ago

I used some python code, and went through the possible combinations. If you use $\boxed{2 3 4 5 1}$ you get -15. I thought that it might be asking for the positive answers online, but if you use $\boxed{1 2 3 4 5}$ you get 0.6? I am very confused, please explain.

massimo 22 - 3 years, 6 months ago

If we consider magnitude the least value is 0.002

Siobhan Doran - 3 years, 1 month ago

My error was assuming that minimum meant the smallest absolute value rather than simply being furthest to the left on the real number line. My first result was 0

Joshua Burton - 5 years, 1 month ago

my answer was also -15

Bhaskar Pandey - 4 years, 3 months ago

It cannot be -15 because you have to do the parenthesis first

Luke Spooner - 2 years, 2 months ago

Kartik Agarwal
Dec 13, 2015

the solution is (1+2-5)*4/3

I agree and I get -3.66...

Larry McCandless - 5 years, 6 months ago

Andrea it equals 0. (2+3=5-5=0)*4=0/1=0.

hi taco - 2 years, 2 months ago

what's about 2+3-5*4/1 ? It's -14

Andrea Virgillito - 4 years, 10 months ago

*-15 obvl :)

Andrea Virgillito - 4 years, 10 months ago

okay....now i've got the ans was -2.667..

Andrea Virgillito - 4 years, 10 months ago

ya ,I also have the same doubt

Adarsh Adi - 4 years, 6 months ago

If u put 2 plus 3 then minus 4 multiple 5 decided to 1 🔚all equal -15#

Ahmed Ammar - 4 years, 3 months ago

Michael Fitzgerald
Apr 20, 2018

from itertools import permutations
from math import isinf

perm = permutations([1, 2, 3, 4, 5])

min_ = isinf
max_ = 0
max_permutation = ''
min_permutation = ''

for i in list(perm):
    x = float(i[0]+i[1]-i[2])*i[3]/i[4]
    if x < min_:
        min_ = x
        min_permutation = i
    if x > max_:
        max_ = x
        max_permutation = i


print 'Min: %0.3f; (%d+%d-%d)*%d/%d\n' %(min_, min_permutation[0], min_permutation[1], \
           min_permutation[2], min_permutation[3], min_permutation[4])

print 'Max: %0.3f; (%d+%d-%d)*%d/%d' %(max_, max_permutation[0], max_permutation[1], \
           max_permutation[2], max_permutation[3], max_permutation[4])

1
2
3

Min: -2.667; (1+2-5)*4/3

Max: 25.000; (3+4-2)*5/1

Quinary Quantity Part 3

The answer is -2.667.

3 solutions

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