Don't cancel AB
a 1 + b 1 + 1 = a b ÷ ( a × b )
For single digit positive integers a and b , let a b denote the two-digit integer: 1 0 a + b .
Suppose S a and S b be the sum of all possible values of a and b respectively such that they satisfy the equation above. Find the value of S a + S b .
The answer is 54.
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1 solution
Hey bro, why the interval [1,9] only??"a" can take any value from [1,~)…i did not quite understand..plz do elaborate.thanks
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If a > 9 then , how will a b be a 2 digit number?
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You should explicitly state that \overline{ab} is always a two digit number, or even better, state that a and b may only range over [1..9]. Othewise, I liked that brain teaser ;)
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@Dexxter Quant – I have already stated that a b is a two digit number.You must see the 2nd point of details and assumptions.
Nice problem bro :)
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Thanks! I am happy you solved it :)
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Hahhahahahahah...funny me...lol haha hahahahaha...,sometimes we just surpass the most trivial observation.., sorry for being silly.lol
Great problem.. :D.. did it same way.
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Thanks bhai..
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I must say you're a very good problem poser
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@Rishabh Tripathi – Actually i just read somewhere 6 × 9 + ( 6 + 9 ) = 6 9 which led me to form this generalized problem. Thanks.
You should have mentioned that you want distinct values of a and b.
Ohh, ohh, I forrgot to add that Numbers from 1-9 .How dumb of me -_- Great Problem :) :)
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Mehul tune distance mention karna bhul gaya kya iss problem me?
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Nahi to. Check Karo xD
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@Mehul Arora – Chalak bhai ... Zhut bole kawwa kate .. xD
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@Nihar Mahajan – xD xD xD Ikr. Vese Bade Dino Baad online aaye?
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@Mehul Arora – Ha ... BADE 4 dino bad
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@Nihar Mahajan – Bhai, Aapki Kami Mehsoos Hoti hai xD Sorry for my liberal use of Words xD
Nice solution.
Great problem yaar........
Great problem
But you should specify in problem that Sb= sum of distinct(b) or Just ask for the sum of Sa+b
why couldn't it(Sb) be 81 and hence
Sa+Sb=126!, since Sa=45 !
Multiply both sides by a b to get :
a + b = a b − a b a + b = 1 0 a + b − a b a = 1 0 a − a b 9 a = a b b = 9 (Since a = 0 )
Note: This tells us that value of b is fixed and a can take any value over positive integers from the interval [ 1 , 9 ] .
Hence ,
S a + S b = r = 1 ∑ 9 r + 9 = 5 4