Fellow nairalanders please help me with this question, would gladly appreciate. (Answer and proof needed)

Question: A boy changes the pin of his phone from 0000, he forgot it but he remembers that when he multiply by 4 the result is the number in reverse. Find the number

I've got one

Ask goggle

@OP. Aren't you a GENIUS?

timonski:
@OP. Aren't you a GENIUS?

even geniuses need help bro.

GeniusDavid:
Fellow nairalanders please help me with this question, would gladly appreciate. (Answer and proof needed)

Question: A boy changes the pin of his phone from 0000, he forgot it but he remembers that when he multiply by 4 the result is the number in reverse. Find the number

This is a question under number theory.

The number is 2178.
2178 * 4 = 8712.
You're looking for a number ABCD such that ABCD * 4 = DCBA.
Where ABCD = ! 0 because he changed it from 0000.
Since the number is 4 digits, you an write it with a place value of a thousand, ie. 1000A + 100B + 10C + D
(1000A + 100B + 10C + D) * 4 = 1000D + 100C + 10B + A
You can see that the maximum value of ABCD is 2499, because anything higher, Eg 2500 * 4 = 10,000 which is a 6-digit number and thus cannot satisfy our conditions.

By the rules of divisibility, Whole numbers are divisible by 4 if the number formed by the last two individual digits is evenly divisible by 4.
So since DCBA has to be divisible by 4 because we multiplied ABCD by 4 to get it it follows that BA is divisible by 4.

Also because the maximum value of ABCD is 2499, A can either be 1 or 2.
We conclude that A is 2 because it is divisible by 4 (a number that divides 4 evenly cannot end in an odd number), because AB is divisible by 4.

So we have A = 2.

Also, D = 8 because A =2, 2 * 4 = 8.

Recall we can write ABCD as 1000A + 100B + 10C + D
Multiplying it by 4 we get 4000A +400B +10C +4D
which is equal to 1000D + 100C + 10B + A
4000A + 400B + 40C + 4D = 1000D + 100C + 10B + A
Substituting A =2, D = 8 we get:
390B -60C = -30
or simplifying: 13B -2C = -1.
The possible values of C and B in which they would both be single and positive are: 1,7.
It follows that since the largest value for ABCD is 2499, B is odd and either 1 or 3.
Since we have calculated B to be 1, the value of C is 7.

Concluding we have:
A=2;
B=1;
C=7;
D=8.

ABCD = 2178.
To test we multiply it by 4 and this gives 8712 which corresponds to DCBA.

That's all.

Karmanaut:

This is a question under number theory.

The number is 2178.
2178 * 4 = 8712.
You're looking for a number ABCD such that ABCD * 4 = DCBA.
Where ABCD = ! 0 because he changed it from 0000.
Since the number is 4 digits, you an write it with a place value of a thousand, ie. 1000A + 100B + 10C + D
(1000A + 100B + 10C + D) * 4 = 1000D + 100C + 10B + A
You can see that the maximum value of ABCD is 2499, because anything higher, Eg 2500 * 4 = 10,000 which is a 6-digit number and thus cannot satisfy our conditions.

By the rules of divisibility, Whole numbers are divisible by 4 if the number formed by the last two individual digits is evenly divisible by 4.
So since DCBA has to be divisible by 4 because we multiplied ABCD by 4 to get it it follows that BA is divisible by 4.

Also because the maximum value of ABCD is 2499, A can either be 1 or 2.
We conclude that A is 2 because it is divisible by 4 (a number that divides 4 evenly cannot end in an odd number), because AB is divisible by 4.

So we have A = 2.

Also, D = 8 because A =2, 2 * 4 = 8.

Recall we can write ABCD as 1000A + 100B + 10C + D
Multiplying it by 4 we get 4000A +400B +10C +4D
which is equal to 1000D + 100C + 10B + A
4000A + 400B + 40C + 4D = 1000D + 100C + 10B + A
Substituting A =2, D = 8 we get:
390B -60C = -30
or simplifying: 13B -2C = -1.
The possible values of C and B in which they would both be single and positive are: 1,7.
It follows that since the largest value for ABCD is 2499, B is odd and either 1 or 3.
Since we have calculated B to be 1, the value of C is 7.

Concluding we have:
A=2;
B=1;
C=7;
D=8.

ABCD = 2178.
To test we multiply it by 4 and this gives 8712 which corresponds to DCBA.

That's all.

Thanks boss

GeniusDavid:
Thanks boss

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Check out this particular example on this topic, i found it veeeeeeeeeeeeeeeeeeery helpful . It actually shows the rule fo "11"

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http://9jababa.com/junior-mathematics-where-are-the-maths-gurus/
Check it out

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