make two 4 - digit numbers using each of the digits 1,2,4, and 5 such that the numbers made are divisible by 132.
Answers
Given : 4-digits numbers using each the digits 1,2,4 and 5 such that the numbers made are divisible by 132
To find : Two such numbers
Solution:
132 = 2 * 2 * 3 * 11
=> 132 = 4 * 3 * 11
Divisible by 2 so last digit should be even 2 or 4
a number is divisible by 4 if sum of two digits are divisible by 4
last two possible digits are
12 , 52 , 24
1 + 2 + 4 + 5 = 12 sum is divisible by 3
So now remaining divisibility by 11
Subtract the last digit from a number made by the other digits. If that number is divisible by 11 then the original number is, too.
Ending with 12
5412 & 4512
541 - 12 = 539 then 53 - 9 = 44 divisible by 11
5412 is divisible by 132
5412/132 = 41
4512
451 - 2 = 449 then 44 - 9 = 35 not divisible by 11
Ending with 52
1452 & 4152
145 - 2 = 143 then 14 - 3 = 11 divisible by 11
1452 is divisible by 132
1452/132 = 11
4152
415 - 2 = 413 then 41 - 3 = 38 not divisible by 11
Ending with
1524 & 5124
152 - 4 = 148 then 14 - 8 = 6 , not divisible by 11
5124
512 - 4 = 508 then 50 - 8 = 42 not divisible by 11
1452 & 5412 are two 4-digits numbers using each the digits 1,2,4 and 5 such that the numbers made are divisible by 132
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Answer
1452. and 5412 are two 4 digit rational numbers using each the digit 1,2,4,5 such that the numbers are divisible by 132
Step-by-step explanation:
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