Thefeelgoodfactor's Blog

Random thoughts

24 * 26

on September 1, 2013

The first time someone had asked me to calculate the value of 24 * 26 without actually multiplying these two numbers was probably when I was in fourth or fifth standard, before we had learnt the various mathematical identities and short cuts. (Yeah, I had the honor of studying with such mathematics enthusiasts in school). Obviously, I couldn’t answer it then and my friend never mentioned the shortcut to me. Over time, the various tricks taught showed how simple this question is (or so I thought until recently).

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Most of the interviewers usually have a set of questions which they would usually ask in any interview (regardless of the role/position). My colleague too has one such question – he has asked that one question to all his interviewees so far. To be fair to him, his other questions depend on candidate’s profile, E.g. he has asked questions like Explain FFT (Fast Fourier Transformation) to an E&C engineer, equation of EOQ to an Ops graduate. (Again, lets not bother about the role for which the interviews were being held).

Coming back to the topic, that one question which my friend asks is this : “Calculate 24 * 26 without multiplying them”. And I was surprised with some of the answers given by the candidates –

First Interview:

PM : Calculate 24* 26 without multiplying them

Candidate1 (C1): I don’t know.

PM: Think of the identity (a+b)*(a-b). 

C1: Now I get it. I can solve it now.

PM: So what is the answer?

C1: 24 * 26 = (12+12) * (13+13) 

Second Interview:

PM : Calculate 24* 26 without multiplying them

C2: 24 * 26 = 26 * (26 – 2) = 26* 26 – 26 *2 = 26* 26 – 52

C2 goes on to multiply 26*26.

PM: I asked you not to multiply

C2: I am not multiplying 24 and 26, I am multiplying 26 & 26.     

When I got a chance to interview someone, I decided to ask this question, However, I wanted to be more careful with the way I frame the question. Here’s what happened:

Me: Calculate 34 * 36 without using a pen & paper.

C3: <Blank Expression>

Me: Let me give you a hint. Do you know what is sqr(a) – sqr(b)?

C3: I get it now, (a+b)*(a-b) = sqr(a) – sqr(b). So we can solve it using this shortcut, So, 

34 * 36 = (40 – 6) * (40 – 4)

Me: I like the fact that you were able to break each numbers as sum of two different numbers, but can you help me in identifying what is a & b?

C3: Oh, looks like I made a mistake.

Me: Even I thought so.

C3: It is (35 + 1) * ( 35-1) = sqr(35) – 1.

The candidate didn’t know how to find square of 35, but I decided against pursuing this further.

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We were narrating these incidents to a mutual acquaintance. He has a stellar academic & professional background – IIT graduate, worked with a consulting firm for 3 years before starting his own company. His reaction was: “Yaar, ye tricky savaal hai. 24 * 26 toh shayad mei bol deta, par agar tum mujhse 23 * 27 poochte toh karne mei fight hoti.” 

 

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