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Number Theory Level 3

1 A B C D E ‾ × 3 = A B C D E 1 ‾ \large \overline{1ABCDE} \times 3 = \overline{ABCDE1}

The above shows a product of a 6-digit integer with 3 to produce another 6-digit integer.

What is the value of A × B × C × D × E A\times B\times C \times D \times E .

2240 2560 4500 3200 2420 1200 3600

Satyabrata Dash by Satyabrata Dash , 20, India

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1 solution

Abhisek Mohanty
Jun 25, 2016

THIS IS REALLY A VERY SIMPLE PROBLEM................. JUST SEE THE UNIT DIGIT 'E' MULTIPLIED WITH 3 GIVES 1. THE ONLY VALUE OF E IS 7. THAT MEANS THE PRODUCT A B C D E SHOULD BE DIVISIBLE BY 7. AND THE ONLY OPTION THAT IS DIVISIBLE BY 7 IS THE LAST ONE..................... I THINK THIS IS OVERATTED DUE TO ITS LOGIC HIDDEN BEHIND OTHERWISE A NORMAN MAN WOULD FIND ALL VALUES OF THE UNKNOWNS AND THEN MULTIPLY WITHOUT EVEN LOOKING AT THE OPTIONS

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