Solving multiple choice questions

How would you solve this multiple-choice problem: What is 12345 x 45678?

  1. 201932843
  2. 563894910
  3. 402394820
  4. 384718349
  5. 938491834

It always amazes me when people try and multiply the two numbers. In any objective-type test (multiple choice question), the aim is not to solve the problem — it is to pick the correct answer!

Most people don’t seem to realise the difference.

If I had to solve the problem, I’d look for shortcuts. For example,

  1. All answers have 9 digits. So that’s not going to help.
  2. 12345 ends with a 5. All multiples of 5 end with 5. So the answer is either (2) or (3).
    1. 201932843
    2. 563894910
    3. 402394820
    4. 384718349
    5. 938491834
  3. Multiplying the first digits, 1 X 4 = 4. So the answer’s got to start with a bit more than 4. (3) starts with 40. That’s too low. C’mon, the second number STARTS with 45. So…
    1. 563894910
    2. 402394820

This takes me 10 seconds. Multiplying the two takes me ten times as long.

Let me repeat the point: You DON’T have to get to the answer. You’ve already been given the answer. You just don’t know which one it is. And you don’t have to solve the entire problem to pick the right one.

There are many ways of picking the right answer. One is what I just used: the answer must satisfy some property. In this case, the answer must be a multiple of 5.

In other cases, the answer must be close to something. For example, what’s 37463 x 28438?

  1. 532686397
  2. 1065372794
  3. 2130745588
  4. 4261491176
  5. 8522982352

Well, let’s just multiply the first two digits: 37 x 28. That’s 1036. So the answer’s got to be close. OK, (2) is the answer.

These are not one-off techniques, nor are these applicable only to numbers. You can always pick the right choice without solving the problem.

A weaker, but more general version of the above rule is: you can always eliminate choices without solving the problem.

I’ll blog more on this shortly.

  1. anand says:

    hats off. U made me to think…….

  2. Vinodh says:

    First rule should be to eliminate the options based on the product of the last digits. So, for the second example, it’s easier to eliminate all the other four options based on this rule. Of course, there are easier techniques for generic multiplication/division as well…I have an somewhat interesting technique to calculate squares/products based on simple algebraic formulae…of course they are better used with some practice, but very powerful.

  3. vasudha says:

    HATS OFF TO YOU… THE INFORMATION IS PRETTY GOOD.. YOU MADE ME THINK

  4. jake says:

    its easier and faster to get the answer for the second one by looking at the last digit of the answers. it has to be the same as the last digit of the product of the unit place digits of the numbers being multiplied.

  5. Shreyas says:

    “All multiples of 5 end with 5” – I guess it should be “All multiples of 5 end with 5 or 0” 🙂

  6. Anonymous says:

    CAN YOU PLEASE TELL ME WHERE i CAN FIND MORE TIPS ON SOLVING MCQ? I LIKED GOING THROUH THIS BUT I NEED MORE PRACTICE. THANK YOU

  7. Anonymous says:

    There is a much better way to solve Q2. the last digit of N1 is 3 and the last digit of N2 is 8. 3*8 is 24 so N1*N2 has to end with 4. so the answer should be

  8. GV Rao says:

    I would like to multiply first 2 digits: 45 x 78, and in second case: 3 x 8, which is easy, last digits gives more guess on product.

  9. Sri Lankan Friends says:

    hmmm very interesting

  10. ali says:

    good but should be more efficent via understanding

  11. deepak says:

    phaltu trick sab hai…
    issss se kahi behtar tricks mere paas hai….
    sirf tukka maar ke IIT me aa gaya hu YES I AM IN IIT…