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Question 7 : 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 __________.


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Explanatory Answer

Given is a 4-digit number, Since the product of thousands digit and unit digit is zero.
One of them has to be zero. Thousandth Digit cannot be zero, since it is a 4-digit number
So, unit digit has to be zero.
__ __ __ 0

Given thousands place and unit place difference is 7
7 __ __ 0
Product of middle digits is 18
So, the possibilities are 3 × 6 or 6 × 3 or 2 × 9 or 9 × 2
Thousandth digit is more than unit digit by 7

Then the hundredth digit should be more than tens digit by 7. (since given thousandth digit is as much more than the unit digit as the hundreds digit is more than tens digit)

So it has to be 9 and 2
7 9 2 0

The answer is 7920

 

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