Cognizant Divisibility- Quiz-1

When n is divided by 8, the remainder is 3 may be written as

n = 8 k + 3

multiply all terms by 6

6 n = 6(8 k + 3) = 8(6k) + 18

Write 18 as 16 + 2 since 16 = 8 * 2.

= 8(6k) + 16 + 2

Factor 8 out.

= 8(6k + 2) + 2

The above indicates that if 6n is divided by 8, the remainder is 2.
The answer is C.

Explanation:-

The sum of three consecutive odd natural numbers each divisible by 3 is 72.

To find : What is the largest among them?

Solution :

Let x , x+3 , x+6 are three consecutive numbers divisible by 3

According to question,

Substitute the value of x in consecutive numbers,

x=21,

x+3=21+3=24,

x+6=21+6=27

Therefore, The largest number among them is 27.

A=7x+3
B=7y+5
A-B=7(x-y)-2
A-B=7(x-y)-7+7–2 [by adding -7 and +7]
A-B=7(x-y-1)+5
As seen above, if we divide A-B by 7, the remainder will be 5.

The given number =7x86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+x
(Sum of the odd places)- (Sum of even places) =
Number (exactly divisible by 11)
23-(9+x) = divisible by 11
14 - x = divisible by 11.
X must be 3, to make given number divisible by 11.

Explanation:-

Numbers less than 100 divisible by 2 are 10, 12, 14, 16,...,98.

Total numbers divisible by 2 are 45

Remaining numbers are 11, 13, 15, 17, 19...99 = 45

Numbers divisible by 3 in the above numbers are 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93 and 99.

Total numbers divisible by 3 are = 15

Remaining integers = 45-15 = 30.

Numbers divisible by 5 in the remaining numbers = 25, 35, 55, 65, 85, 95

Total numbers = 6

Remaining 30-6 = 24.

So 24 numbers are not divisible by 2, 3 and 5.

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. These all divisible by 9 and 3Ans.

time taken= distance travelled / speed
time taken = 345/50
time taken=6.9hours

Here as per condition let us consider third number = x,

then 2nd number = 2x
and 3rd number = 4x,

Given that (4x+2x+x)/3 = 77,

7x = 3x77,

x = 3 x 11 = 33,
first number = 4x = 4 x 33 = 132

So 9x/12x=9/12
time =distance /speed
4=360/9x
so x=10
12x=120
Time taken by car b =360/120=3 hour

Explanation:-

3/7 of oranges are sour to eat.

Total no. of oranges = 3,80,205

Sour oranges = 3/7 of 3,80,205

= 3 × 54315 = 162945

Oranges that can be sold = total no. of oranges - sour oranges

= 3,80,205 - 1,62,945

= 2,17,260