Depth challenge year 4

[hana]

The digits in Darcey's 2-digit and 1-digit number are all different to the digits Asha has used.

Darcey's 2-digit and 1-digit numbers have 2 odd digits and Asha's have 2 even digits.

Darcey's 2 digit-number is double that of Asha's.

Asha's 1-digit number is double that of Darcey's.

What are their missing numbers?

Is there more than one possibility?

 

[Zam]

View attachment 37667The digits in Darcey's 2-digit and 1-digit number are all different to the digits Asha has used.

Darcey's 2-digit and 1-digit numbers have 2 odd digits and Asha's have 2 even digits.

Darcey's 2 digit-number is double that of Asha's.

Asha's 1-digit number is double that of Darcey's.

What are their missing numbers?

Is there more than one possibility?

The correct answer is: Darcey's 2-digit number is 46, and Asha's 2-digit number is 23. Darcey's 1-digit number is 6, and Asha's 1-digit number is 4.

Explanation: According to the given information, Darcey's 2-digit number is double that of Asha's, so if we let x be Asha's 2-digit number, then Darcey's 2-digit number would be 2x. Similarly, Asha's 1-digit number is double that of Darcey's, so if we let y be Darcey's 1-digit number, then Asha's 1-digit number would be 2y.

From the given information, we know that the digits in Darcey's 2-digit and 1-digit numbers are all different from the digits Asha has used. This means that x and y cannot have any common digits. Also, Darcey's 2-digit number has 2 odd digits and Asha's has 2 even digits, so x must be an odd number and 2x must be an even number. Similarly, Asha's 1-digit number is double that of Darcey's, so y must be an even number and 2y must be an odd number.

The only pair of numbers that satisfies all these conditions is x = 23 and y = 4. Therefore, Darcey's 2-digit number is 2 * 23 = 46, and Asha's 2-digit number is 23. Darcey's 1-digit number is 4, and Asha's 1-digit number is 2 * 4 = 8.

 

[Kingfireboy]

Yeah spot on.