In a four-digit number, the product of thousands digit and units digit is zero while their difference is 7. Product of the middle digits is 18 . The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is __________.
Explanation:
Let the number be 'abcd'. [a, b, c, d and single digit positive integers.]
Given,
a × d = 0 a cannot be 0 since the given number has to be a 4 digit number, hence d = 0
Also, a - d = 7 ⇒ a = 7
Also, b × c = 18 ...(1)
The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit ⇒ a - d = b - c = 7 ...(2)
From (1) and (2), we get b = 9 and c = 2.
∴ The number is 7920.
Hence, 7920.
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