Accenture Divisibility Quiz-1

(x³ + 4x² + 6x - 2) ÷ (x + 5), find remainder

Find the value of x: x + 5 = 0 x = -5

Find the remainder: Sub x = -5 to find the remainder: x³ + 4x² + 6x - 2 = (-5)³ + 4(-5)² + 6(-5) - 2 = -125 + 4(25) + (-30) - 2 = -125 + 100 - 30 - 2 = -57

Let us take exponents 0, 1, 2, 3,  ....one by one to "17"

For example, if we take exponent "0" for 17, we get 17⁰ = 1

Here 1 is less than the divisor 16 and 1 can not be divided by 16.

If the dividend is less than the divisor, then that dividend itself to be considered as "Remainder"

So, if 17⁰  is divided by 16, we get the remainder "1"

13^{36} = (13^3)^{12} = 2197^{12} = (2196+1)^{12} when ((2196+1)^{12}  is divided by 2196, all terms in the expansion are divisible by 2196 except 1^{12}, so the remainder will be 1.

Divisor = 999

quotient = 366

Remainder = 103

Define x: Let the number be x

Solve x: x ÷ 999 = 366 remainder 103 x = 999 x 366 + 103 x = 365737

let larger no.is x and smaller no.is y. now we get from question is that (x-y)=1365...(1),6y+15=x...(2).Now from equation (1)-(2)we get y=270,x=1635.therefore the smaller no. is y=270.

For a no. to be divisible by 8, the last 3-digits of that no. should be divisible by 8...

Here 6x2 should be divisible by 8... Try for all possible value from 0 to 9... x = 3 => 632 which is perfectly divisible by 8... Ans : 3

For a no. to be divisible by 24, it should be divisible by both 8 nd 3... since 24=>8*3

In the given options , 3125736 is divisible by both 8 and 3... So its also divisible by 24... Ans : (4) 3125736

15411 when we Divide 15207 by 467, we get 263 as remainder. 467-263=204.

Either subtract 263 from 15207 or add 204 in 15207 to get a number divisible by 467.

The number nearest to 15207, which is divisible by 467 = 15207+ 204=15411 check ...15411/467=33

7936 => 2^2 * 2^2 * 2^2 * 2^2 * 31^1 To make it as a perfect square, we have to multiply 7936 with 31... Hence the reqd no. is 7936*31 = 246016 Ans : 246016

rem=16,divisor=16*5=80,quotient=80/20=4; no.=divisor*quotient+rem=80*4+16=336 is the right answer