8/3/2019 Find the Second Last Digit in a Number

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Nike caused controversy with its advertising campaign during the 1996 Olympics by using theslogan, You Dont Win Silver You Lose Gold. Nikes use of this slogan drew harshcriticism from many former Olympic Silver medalists. In a way, it did undermine the importanceof the second position but in Math things are often very different. Figuring out the second lastdigit is often tougher than figuring out the last digit in the particular type of Quantitative Abilityquestions I am going to write about. It is unlikely but definitely not impossible that in CAT you

get a straightforward question that asks you to find out the second last digit of a number(abcpqr). It did happen in CAT 2008. In few cases, you will be able to do it by forming a cycleand observing the pattern. Those will be the easier cases. Read on if you wish to do the samefor the not-so-easy cases.

The question becomes really simple if the last digit in abcpqr is 0 or 5 because if it 0, thesecond last digit will be 0 and if it is 5, second last digit will be 2 or 7 (which can be easilyfigured out by observing the cyclicity). All the other questions can be divided in two broadcategories,

a) Last digit is odd

b) Last digit is even

I recommend that before using any of the concepts given below, you should try and see if apattern exists.

Let us consider our number is abcpqr where a, b, c, p, q and r are digits and c is not 0 or 5.

Concept 1: What to do when the last digit is odd?

The second last digit always depends on the last two digits of the number so anything beforethat can be easily neglected. We first convert the number in such a way that the last digit ofthe base becomes 1. The second last digit of the number will then simply be,

Last digit of (Second last digit of base) X (Last digit of power)

Let us look at few examples,

Eg 1a: Second last digit of 3791768 = Last digit of 98 = 2

Eg 1b: Second last digit of 1739768 = Second last digit of 39768 = Second last digit of SecondLast digit of 1521384 = Last digit of 2 4 = 8

Eg 1c: Second last digit of 9317768 = Second last digit of 17768 = Second last digit of (174) 192 =Second last digit of (21) 192 = Last digit of 2 x 2 = 4

Concept 2: What to do when the last digit is even?

The second last digit always depends on the last two digits of the number so anything before

that can be easily neglected.

8/3/2019 Find the Second Last Digit in a Number

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We need to remember the following ideas:

**2 raised to power 10 will always end in 24.

24 raised to an even power will always end in 76 and to an odd power will always end in 24.

76 raised to any power will always end in 76.

Now we can use these to find out the second last digit. We reduce the number in such a waythat the last two digits of the base become 76.

Eg 2a: Second last digit of 1372482

Second last digit of 72482

Second last digit of 72480 x 722

Second last digit of (7210

)48

x (**84)

Second last digit of 2448 x (**84)

Second last digit of 76 x 84

Second last digit of 6384 = 8

Eg 2b: Second last digit of 48307 = (483) 102 x 48 = (****92) 102 x 48

Second last digit of 92100 x 922 x 48 = 76 x (**64) x 48

Second last digit of (****72) = 7

Eg 2c: Second last digit of 15484 = Second last digit of (54) 84

Second last digit of (545) 16 x 544 = (***24) 16 x (542) 2

Second last digit of 76 x (2916) 2

Second last digit of 76 x 56

Second last digit of 4256 = 5

I hope that after reading this post you will be at ease in figuring out the second last digit insuch type of questions. I also hope that you will not mind winning silver medals either.