How many three digit integers can be divided by 4 to produce a new integer with the same ten,s digit and units digit as the original integer
Answers
Given : three digit integers can be divided by 4 to produce a new integer with the same ten,s digit and units digit as the original integer
To Find : How many such number possible
Solution:
Dividing three digit number by 4 result in two digit or 3 digit number :
Let say three digit integer XYZ
Value 100X + 10Y + Z
Case 1 :
Divided by 4 to get YZ ( two digit number )
Value = 10Y + Z
=> (100X + 10Y + Z)/4 = (10Y + Z)
=> 100X + 10Y + Z = 40Y + 4Z
=> 100X = 30Y + 3Z
100X ens with 0
30Y end with 0
hence 3Z must end with 0
so Z = 0
=> 100X = 30Y
=> 10X = 3Y
=> X = 3 , Y = 10
Hence no such number
Case 2 :
Divided by 4 to get AYZ ( three digit number )
Value = 100A + 10Y + Z
=> 100X + 10Y + Z = 400A + 40Y + 4Z
=> 100(X - 4A) = 30Y + 3Z
100(X - A) ends with 0
30Y end with 0
Hence 3Z ends with 0
=> 100(X - A) = 30Y
=> 10 ( X - 4A) = 3Y
X - 4A = 0 is the only solution
A = 1 , X = 4
A = 2 , X = 8
400 & 800 are two three digit numbers which when divided by 4
produce a new integer with the same ten,s digit and units digit as the original integer
400/4 = 100
800/4 = 200
2 numbers are possible
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Answer:
Given: three digit integers can be divided by 4 to produce a new integer with the same ten,s digit and units digit as the original integer
To Find : How many such number possible
Solution:
Dividing three digit number by 4 result in two
digit or 3 digit number:
LTE
Let say three digit integer XYZ
Value 100X + 10Y + Z
Case 1:
Divided by 4 to get YZ (two digit number)
Value = 10Y + Z
=>(100x+10Y+Z)/4= (10Y + Z)
<=>100X + 10Y + Z=40Y+4Z
⇒>100X = 30Y +3Z
LTE
100X ens with 0
30Y end with 0
hence 32 must end with 0
so Z = 0
=> 100X = 30Y
=>10x=3Y
→>> X = 3, Y = 10
Hence no such number
Case 2:
Divided by 4 to get AYZ (three digit number)
Value = 100A + 10Y + Z
=>100(X-4A) = 30Y + 3Z
100(X - A) ends with O
30Y end with 0
Hence 32 ends with O
=> 100(X -A) = 30Y
=> 10 (X-4A) = 3Y
X-4A=0 is the only solution
A=1.X=4
A=2, X=8
LTE
400 & 800 are two three digit numbers which when divided by 4
produce a new integer with the same ten,s digit
and units digit as the original integer
400/4 = 100
800/4 = 200
2 numbers are possible
Learn more:
how many five digit positive integers that are divisible by 4 can be...
https://brainly.in/question/17495885
how many positive integer are between 10 and 2016 are divisible by ...
https://brainly.in/question/12980649