Math, asked by qasimzia, 1 month ago

how many three-digit integers can be divided by 4 to produce a new integer with the same ten's digit and unit's digit as the original integer

Answers

Answered by Anonymous
19

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

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