Quiz-1

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

Two-digit positive integers less than 100 are from 10 to 99. So, there are total 90 integers.

Suppose, U is the set of all integers from 10 to 99 and A, B, C are the sets of multiples of 2, 3, 5, respectively.

So, n(U)=90

n(A)= 90/2=  45

n(B)= 90/3= 30

n(C) = 90/5= 18

Number of integers which are divisible by both 2 and 3 : n(A ∩ B) = 90/6= 15

Number of integers which are divisible by both 3 and 5 : n(B ∩C) = 90/15 = 6

Number of integers which are divisible by both 2 and 5 : n(C∩ A) = 90/10= 9

and the number of integers which are divisible by all 2, 3 and 5 :

n(A∩ B∩ C) = 90/30= 3

n(A U B U C)

= n(A)+n(B)+n(C)-n(A∩ B)-n(B∩C)-n(C∩A) + n(A∩B∩C) =45+30+18-15-6-9+3 =66

So, the number of integers which are not divisible by 2, 3 and 5 will be:

n(U)- n( A U B U C)

= 90-66

=24

 

The simple answer of your question is 3 and 9.

Step-by-step explanation:

For example,
Take any randomly 5 digit number , we take 12345.
so, 12345 - (1+2+3+4+5) = 12330
12330 is a multiple of 9 and 3 both.

Lets we take another example.
We take 11111
so, 11111 - (1+1+1+1+1) = 11106
11106 is a multiple of 9 and 3.

Hence, generalizing this, we get
The correct answer is 3 or 9

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 1st 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

Given that :
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
so 2,17,260 oranges can be sold by the farmer.

 

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.