Divisibility Quiz-1

Given that : \frac{2}{3}^rd of the oranges are not edible out of 3,75,569

no. of edible oranges= \frac{2}{3}\times 75,569

= 2,50,379

=  3,75,569 - 2,50,379

= 1,25,189

Similarly no. of edible apples = \frac{3}{5} \times 2,45,589

=1,47,353

=2,45,589 - 1,47,353

= 98,236

 

Total nouber of fruits which the owner can sell =  1,25,189 +  98,236

= 2,23,425

 

n divided by 8 yields a remainder equal to 3 is written as follows

n = 8 k + 3 , where k is an integer.

add 5 to both sides of the above equation to obtain

n + 5 = 8 k + 8 = 8(k + 1)

The above suggests that n + 5 divided by 8 yields a remainder equal to zero.

Let the three consecutive numbers be n, n+1, and n+2. So
according to question,
\frac{n+n+1+n+2}{5}= 51
3n+3 = 51\times 5
n = 84
Thus the largest among them is n+2 = 86

X=4x+2
Y=4y+1
X+Y=4(x+y)+3
As seen above, if we divide X+Y by 4, the remainder will be 3.

The given number = 526897

\frac{526897}{7}=75271

which is divisible by 7

LCM of 25, 70 and 35 is 350

Now 350 = 5 x 7 x 2 x 5

To make it perfect square, it must be multiplied from 2 x 7.

So required no. = 5 x 5 x 7 x 7 x 2 x 2 = 4900

Correct Option :- D

Explanation:-

Every multiple of 9 (9, 18, 27, 36, etc.) has the property that its digits will always add up to a multiple of 9.
For example, the number 4,968 is a multiple of 9 (552 × 9), and its digits add up to 27 (3 × 9).
Because of how the problem is stated, with four-digit numbers, the sum of the digits will always be 9 or 18 or 27.
Adding 1 + 8 or adding 2 + 7 (as specified in the problem) again gives 9.

We just need to find the remainder when 21549876 is divided by 46

The remainder will be 26 after dividing 21549876 by 46

Hence 26 is the least number which should be added to 21549876 to make it completely divisible by 46

L.C.M of 2,3 and 5 is 30

so on dividing the largest 7 digit number i.e: 9999999 by 30 we get a remainder 9

So largest number which is divisible by 2,3 and 5 is 9999999-9= 9999990

For any number to be co prime with 51 it should not be a multiple of 3 and 17

Number of integers less than 1,00,000 which are multiples of 3 = floor(1,00,000/3) = 33,333

Number of integers less than 1,00,000 which are multiples of 17 = floor(1,00,000/17) = 5882

Number of integers less than 1,00,000 which are multiples of 51 = floor(1,00,000/51) = 1960

Number of integers less than 1,00,000 which are multiples of 3 or 17 = 33333 + 5882 - 1960 = 37,255

Number of integers less than 1,00,000 which are not multiples of 3 or 17 = 1,00,000 - 37,255 = 62,745