Deloitte Divisibility Questions and Answers Quiz-1

Given that :

\frac{3}{7} of oranges are sour to eat. Total no. of oranges = 3,80,205

Sour oranges = \frac{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 \times 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.

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)= \frac{90}{2}=  45

n(B)=\frac{ 90}{3}= 30

n(C) = \frac{90}{5}= 18

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

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

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

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

n(A∩ B∩ C) = \frac{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:

Hey Mate,

The simple answer of your question is 3 and 9.

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.

 

time taken= distance travelled / speed
time taken = \frac{345}{50}
time taken= 6.9 hours

Let the three numbers be = x, y, z

\frac{x + y + z}{3} = 77
x + y + z = 231 ...(1)

According to question, equations formed:

x = 2y

y = 2z

.°. x = 4z

Put these in (1):

4z + 2z + z = 231

z = 33

x = 4z
x = 132

 

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