How netizen solved this math problem taken from India's Civil Service Commission exam

The math problem or shall we say, perhaps a puzzle or something like it, was asked this way:

"Can you solve _ + _ + _ = 30 using 1, 3, 5, 7, 9, 11, 13 and 15?"

We saw it somewhere on Facebook and the answers were awesome, to a point that people even sparked a debate on how to treat the equation.
Can you solve this UPSC exam math problem
Image: www.mobypicture.com
Mathematical puzzles are sometimes regarded as integral part of recreational mathematics. However, this one comes with rather tricky sides.

As we scoured the Internet to find out how people tackled the above mentioned puzzle, we got these vast ranges of answers:

Jameson Quinn
Obviously, the problem is impossible without some kind of trick; the sum of three odd numbers cannot be an even number. The first trick I can think of is: 15 + 15 + ▢ = 30; the ▢ is a squarish 0. It's possible that they're thinking of some other trick (for instance, a 1 superimposed on a 5 could look like a 6; or, you could add a digit after the 30), but at that point it's just about guessing what's in the head of whoever's grading the answer.
Akshat Sinha (Software Engineer)
Factorial method:
3!+11+13=30
3!+9+15=30
Changing Base method :-
[(3) + (3) + (3) + (3) + (3)] in base 5 =[(6)+(6)+(6)+(6)+(6)]In base 10=(30)In base 10
LEarn BASE Conversion click here:-learn_base_conversion
Addition-Subtraction Method:
a+b+c=a+b+(x-y) where x-y=c
15+(13-11)+(9+7-5+3-1)
15+(13-11)+(9+7-3)
15+(13-9)+(7+3+1)
15+(13-9)+(7+5-1)
15+(13-7)+(5+3+1)
15+13+(3-1)
15+13+(5-3)
15+13+(7-5)
15+13+(9-7)
15+13+(9-5-3+1)
15+13+(11-9-7+5+3-1)
15+13+(11-9 )
15+13+(11-9+7-5-3+1)
15+13+(11-7-5+3)
15+13+(11-7-3+1)
15+13+(11-5-3-1) 
Barnadhya Rwitam Sharma
9,3 + 5,7 + 15 = 30   /   11,3 + 3,7 +15 = 30
Reason:
In some non English speaking countries, they use comma in place of decimal. For example you can take countries like France and Italy. Here is a link to clarify your doubt: Math Forum - Ask Dr. Math
Also, I have used commas to use the characters you have provided in the question itself. 
A. Rielben
There's no combination. It's impossible. Every number in that list is odd.
We know that any even number can be expressed as 2n where n is an integer. Any odd number can be expressed as 2n−1.
Let m, n, and k all be integers. Then the sum of three odd numbers can be written as:
(2m−1)+(2n−1)+(2k−1)
=2(m+n+k−1)−1.
Note that m+n+k−1 is another integer. If we call it N then the result is simply
2N−1
which, as we established, is an odd number. Therefore the sum of three odd numbers is always an odd number.
Shai Simonson
This answer uses one each of 3, 5, 7, 11, and 13.  And two "."s.
5.7 + 11.3 + 13 = 30

Here is another "cute" answer:
11 - 5 + 13 - 3.1 + 15 - .9 = 30
It is still missing the 7.
The numbers are placed around each symbol in the equation below, liberally interpreting the _ as a - sign.
 _+_+_=30 
Pradyumna Achyuthuni
(5)base_9 + (11)base_9 + (13)base_9 = (30)base_9
i.e  5 + 10 + 12 = 27 in decimal system.
Hugh O'Byrne
119+11+9=30.  A more symmetric solution would be 1113+913+713=30.
Josh Manson
You can't.
30 is an even number.
An even plus an even is an even. An even plus an odd is an odd. An odd plus an odd is an even.
The sum of three numbers is the sum of one of them and the sum of the other two.
All of the numbers in your list are odd.
The sum of any two of them will be even.
The sum of one of the numbers in the list and the sum of two numbers in the list will be an odd plus an even which is odd.
30 is an even number which cannot be the sum of an odd and an even.
A lot of people nailed the question quite impressively, in their own ways and means in the field of mathematics. But according to Quora.com member Soumitra Agarwal:
This is a modified form of a UPSC exam question which started with "Can you fill the...." and thus the legit answer was NO. You might be happy to know that only the topper, Gaurav Agarwal,  was the one who was able to answer.
UPSC or Union Public Service Commission is a civil service commission office in India.

Did you imagine that the answer could be as simple as "NO"? The question is answerable by "Yes" or "No" anyway.

Source: Quora

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2 comments :

Anonymous said...

If allow I would put 11+13×(3!)

Anonymous said...

15,731 + 13,159 + 1,11 = 30 -JTK