1) It is a five-digit whole number. 2) It is a palindrome. 3) Its tens digit is the cube root of a one-digit number. 4) The product of its hundreds digit and its ones digit is 54. 5) The sum of its hundreds digit and its ones digit is 15. 6) It is divisible by 4. 7) The sum of its 100s digit and its tens digit is 10. 8) The product of its hundreds digit and its tens digit is 9. 9) Its ten thousands digit is 6. 10) Its thousands digit is 1.
just work with the clues. The number's digits are
abcde
palindrome means it is
abcba
tens digit must be 1 or 2, so b=1 or 2
a2c2a
a1c1a
c*a = 54, so c=9 and a=6 or vice-versa
92629
62926
91619
61916
c+a=15 well, we already knew that with the 9 and 6
divisible by 4 knocks out the odd ones, and we are left with
62926
61916
c+b=10
Our number must be 61916
The rest is just redundant.
Thank you thank you thank you. thank you for explaining it with the answer. that helps to understand it. :)
To find the five-digit whole number that meets all the given conditions, let's break down each condition and solve it step by step:
1) It is a five-digit whole number.
Since it is a five-digit number, it must be somewhere between 10,000 and 99,999.
2) It is a palindrome.
A palindrome is a number that reads the same forward and backward. To find a five-digit palindrome, we need to consider the middle digit since it will be the same when reversed. Therefore, our number will look like this: ABCBA. The first and last digits (A and A) will be the same, and the middle digit (C) will be determined later.
3) Its tens digit is the cube root of a one-digit number.
The cube root of a one-digit number can be 1, 2, or 3. Let's consider these options.
4) The product of its hundreds digit and its ones digit is 54.
The only digit pairs whose product is 54 are (6, 9) and (9, 6). Since the sum of the hundreds and ones digit is 15, we can determine that the correct pair is (9, 6).
5) The sum of its hundreds digit and its ones digit is 15.
From the previous condition, we already know that the pair is (9, 6). Therefore, the sum of the hundreds and ones digit is 9 + 6 = 15.
6) It is divisible by 4.
To determine if a number is divisible by 4, we only need to check its last two digits. The possible values for the last two digits (A and A) are (46, 46), (64, 64), (26, 26), and (69, 69). The only pair that satisfies the condition is (64, 64).
7) The sum of its 100s digit and its tens digit is 10.
Given that the tens digit should be the cube root of a one-digit number, the possibilities for the 100s and tens digit are (1, 9), (2, 8), and (3, 7). The only pair that gives a sum of 10 is (2, 8).
8) The product of its hundreds digit and its tens digit is 9.
The only pair of digits that satisfies this condition is (1, 9).
9) Its ten-thousands digit is 6.
According to this condition, the number must start with a 6.
10) Its thousands digit is 1.
As per this condition, the thousands digit should be 1.
By putting all the conditions together, we can conclude that the five-digit whole number that satisfies all the given conditions is 61,964.