CLEAR
Toprankers-Info

+91 7676564400

Mobile App

Get it on Google Play
Discussions
Select Date
Tags:

Articles

Discussions
Submit Discussion
Ankur Malik

· started a discussion

· 1 Months ago

describe (Question: 184397.0 )

describe question

Question:

How many pairs of X and Y are possible in the number 763X4Y2, if the number is divisible by 9?

Options:
A) 8
B) 9
C) 10
D) 11
Solution:

Ans: (d) Sum of x and y = (0, 5), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0), (5, 9), (6, 8), (7, 7), (8, 6), (9, 5)


Rule of Divisibility by 9 : The sum of digits of Number should be divisible by 9 then only the number itself will be divisible by 9.


e.g.  

Number 729 

Sum of Digits = 7+2+9 = 18 (as 18 is divisible by 9, Number 729 will be divisible by 9)


Here,

The given number is 763X4Y2

sum of number = 7+6+3+X+4+Y+2 =22+X+Y

Now, X can be any number between 0 - 9 

also Y can be any number between 0 - 9


so, Possible values of  X+Y is any number between 0 -18 


Hence, Sum of digits (22+X+Y) will be between 22(22 + 0 where both X and Y is 0) and 40 (when both X and Y is 9).


Now, in the range of 22 and 40, only 27 and 36 are divisible by 9.

Hence, X+Y must be 5 or 14.


Thus the possible combinations are


For, X+ Y = 5

X=0, Y =5

X=1, Y=4

X=2, Y=3

X=3, Y=2

X=4, Y=1

X=5, Y=0


For X+Y=14

X=5, Y=9

X=6, Y=8

X=7, Y=7

X=8, Y=6

X=9, Y=5


Possible pairs are 11.

Knowledge Expert

· commented

· 1 Months ago

Rule of Divisibility by 9 : The sum of digits of Number should be divisible by 9 then only the number itself will be divisible by 9.

e.g.
Number 729
Sum of Digits = 7+2+9 = 18 (as 18 is divisible by 9, Number 729 will be divisible by 9)

Here,
The given number is 763X4Y2
sum of number = 7+6+3+X+4+Y+2 =22+X+Y
Now, X can be any number between 0 - 9
also Y can be any number between 0 - 9

so, Possible values of X+Y is any number between 0 -18

Hence, Sum of digits (22+X+Y) will be between 22(22 + 0 where both X and Y is 0) and 40 (when both X and Y is 9).

Now, in the range of 22 and 40, only 27 and 36 are divisible by 9.
Hence, X+Y must be 5 or 14.

Thus the possible combinations are

For, X+ Y = 5
X=0, Y =5
X=1, Y=4
X=2, Y=3
X=3, Y=2
X=4, Y=1
X=5, Y=0

For X+Y=14
X=5, Y=9
X=6, Y=8
X=7, Y=7
X=8, Y=6
X=9, Y=5

Possible pairs are 11.
-logo
We at aim to provide most comprehensive content & test for practice which is carefully divided into various chapters and topics to help you focus on your weak areas.Our Practice mock test gives you unmatched analytics to help you realize your strong areas,time management and improvement areas.Our Short & Crisp notes on each topic will help you to quickly revise the topic along with the tips & tricks of the exams.
More About
-Info
-Info

Mobile App

Get it on Google Play
About Us Campus Ambassador Careers Contact Us Refund Policy

All Rights Reserved Top Rankers

User Policy
Disclaimer
Terms & Conditions