The number is greater than 1.7 million but less than 2.2 million.
- All the digits are even numbers.
- The millions digit multiplied by 3 equals the ones digit.
- The ones digit is 2 less than the tens digit and 2 more than the thousands digit.
- The sum of the digits is 20.
The Correct Answer and Explanation is :
Let’s break down the problem step by step to find the correct number.
Step 1: Define the Range
The number is between 1,700,000 and 2,200,000. This means the millions digit could be 1 or 2.
Step 2: Identify Even Digits
All digits in the number must be even (0, 2, 4, 6, 8).
Step 3: Determine the Millions Digit
The millions digit, when multiplied by 3, should equal the ones digit: millions digit×3=ones digit\text{millions digit} \times 3 = \text{ones digit}
- If the millions digit is 1:
1×3=31 \times 3 = 3 (not even, so invalid) - If the millions digit is 2:
2×3=62 \times 3 = 6 (valid because 6 is even)
Thus, the millions digit is 2, and the ones digit is 6.
Step 4: Relationship Between Ones, Tens, and Thousands Digits
- The ones digit (6) is 2 less than the tens digit → Tens digit = 6 + 2 = 8
- The ones digit (6) is 2 more than the thousands digit → Thousands digit = 6 – 2 = 4
Thus, the thousands digit is 4 and the tens digit is 8.
Step 5: Calculate the Sum of Digits
The total sum of digits should be 20. The number has seven digits: 2+X+4+Y+Z+8+6=202 + X + 4 + Y + Z + 8 + 6 = 20
We already know:
- Millions digit = 2
- Thousands digit = 4
- Tens digit = 8
- Ones digit = 6
Thus: 2+X+4+Y+Z+8+6=202 + X + 4 + Y + Z + 8 + 6 = 20 X+Y+Z=20−(2+4+8+6)=20−20=0X + Y + Z = 20 – (2 + 4 + 8 + 6) = 20 – 20 = 0
Since X, Y, and Z are digits and must be even, the only solution is X = 0, Y = 0, Z = 0.
Step 6: Identify the Number
The number is 2,004,086.
Final Answer:
2,004,086 satisfies all the given conditions:
✔ Between 1.7M and 2.2M
✔ All digits are even
✔ 2×3=62 \times 3 = 6 (Millions × 3 = Ones)
✔ 6=8−26 = 8 – 2 and 6=4+26 = 4 + 2
✔ Sum of digits = 20