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Gurome's Quant Blog Series – Algebra: Linear Equations A99


The answer to the latest question on Algebra: Linear Equations rules is posted below.

 

Explanation:

Let the digit in the tens place of the number be x and let the digit in the units place of the number be y.

Hence, the number can be written as 10x + y.

Also, sum of the digits of the number is x + y.

We know that dividend = quotient × divisor + remainder

Hence 10x + y = 2(x + y) + 8 implies 10x + y = 2x + 2y + 8

Or 8x - y = 8

If the digits are interchanged, the new number is 10y + x.

Hence, 10y + x = 8(x + y) + 2 implies 10y + x = 8x + 8y + 2

Or 2y - 7x = 2

Therefore we get a pair of simultaneous equations given by 8x - y = 8 and 2y - 7x = 2.

Solving them we get x = 2 and y = 8.

Hence, the number is 28 and the sum of digits is 10.

The correct answer is A.

 

Difficulty Level: 620


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Posted by kalyani at Jun 11, 2012 8:34:01 PM
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