7/29/2019 rules to follow

1/2

Remainder Theorem

We have to take care about the following things while finding remainder:

1. 'x' when divided by 'x' the remainder will be 0.

2. 'x + a' when divided by 'x' the remainder will be a.

3. 'x - a' when divided by 'x' the remainder will be -a' i.e. '-a + x'.4. (mx + a)^n when divided by 'x' the remainder will be a^n.

5. (mx - a)^n when divided by 'x' the remainder will be (-a)^n.

Here we will always express numerator in terms of denominator

Example: A number when divided by 7 and 11 gives 4 as remainder in each case. Find the largest 3-digit

number of such type.

Ans. General form of such a number = (LCM of 7 and 11) k + 4

= 77 k + 4 where k is any whole number

Now largest 3-digit number of the form (77k+4) is for k = 12

i.e. 7712 + 4 = 928.

Last Two Digits

For finding the last 2-digits in any calculation like (ab)^n

Where 'ab' is a 2-digit number and n is any number, we will first find out the unit's digit and then

the ten's digit.

We will convert all the calculations in which we have unit digit of the base as 1.

1. So lets start with those calculations which have 1 as unit digit in baseNow if the base has 1 as the unit digit then we can say that the unit digit of the result will also be

1.

Now tens digit will be the product of tens digit of base and unit digit of power.

Rule of allegation

This rule helps us in solving questions where two varieties (of different prices) are mixed to get a

new variety with a new Average price.

Quantity of cheaper Price of Dearer - Average price--------------------------- = ---------------------------------------------------------

Quantity of dearer Average pricePrice of cheaper

Example: In what ratio should tea at the rate Rs. 40/kg be mixed with tea at the rate Rs. 27/kg,

so that mixture may cost Rs 30/kg?Using the above formula

7/29/2019 rules to follow

2/2

Quantity of cheaper / quantity of dearer = (4030)/ (30-27) = 10/3

So, the two should be mixed in the ratio 10:3.

In case of liquids, there is another formula which can be used in various questions.

In a vessel containing x litre of a one liquid (say pure milk), if y litres is withdrawn and replaced

by another liquid (say pure water), and this is repeated n times, then:

Milk left in vessel after nth operation = x [1-y/x] n

Example: In a vessel full of 5 litres of milk, five times 250 ml is taken and replaced with water,what is the concentration of milk left in the vessel

As per the formula, Milk left in vessel after nth operation = x [1-y/x] n

Milk left = 5(1-0.25/5)5 (remember to covert ml into litres)

Solving, Milk left = 3.86 litresThe concentration is 3.86/5 x 100 = 77.3 %