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When a 2-digit number is divided by the sum of its digits, the quotient is 4. If the digits are reversed, the new number is 6 less than twice the original number. What is the original number(s).
A. 12
B. 21
C. 24
D. 42
E. 62
A. 12
B. 21
C. 24
D. 42
E. 62
14 Jan 2022, 00:54
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When a 2-digit number is divided by the sum of its digits, the quotient is 4:
\(\frac{10x + y }{ x + y}= 4\)
\(10x + y = 4x + 4y\)
\(6x = 3y\)
\(y = 2x\)
If the digits are reversed, the new number is 6 less than twice the original number:
\(10y + x = 2(10x + y) - 6\)
Plugging in \(y = 2x\)
\(20x + x = 2(12x) - 6\)
\(21x = 24x - 6\)
\(3x = 6\)
\(x = 2\)
Plugging that back into \(y = 2x\) will give \(y = 4\)
Therefore the two digit number is 24.
Answer C
\(\frac{10x + y }{ x + y}= 4\)
\(10x + y = 4x + 4y\)
\(6x = 3y\)
\(y = 2x\)
If the digits are reversed, the new number is 6 less than twice the original number:
\(10y + x = 2(10x + y) - 6\)
Plugging in \(y = 2x\)
\(20x + x = 2(12x) - 6\)
\(21x = 24x - 6\)
\(3x = 6\)
\(x = 2\)
Plugging that back into \(y = 2x\) will give \(y = 4\)
Therefore the two digit number is 24.
Answer C
25 Jun 2022, 01:32
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Nidzo
When a 2-digit number is divided by the sum of its digits, the quotient is 4:
\(\frac{10x + y }{ x + y}= 4\)
\(10x + y = 4x + 4y\)
\(6x = 3y\)
\(y = 2x\)
If the digits are reversed, the new number is 6 less than twice the original number:
\(10y + x = 2(10x + y) - 6\)
Plugging in \(y = 2x\)
\(20x + x = 2(12x) - 6\)
\(21x = 24x - 6\)
\(3x = 6\)
\(x = 2\)
Plugging that back into \(y = 2x\) will give \(y = 4\)
Therefore the two digit number is 24.
Answer C
\(\frac{10x + y }{ x + y}= 4\)
\(10x + y = 4x + 4y\)
\(6x = 3y\)
\(y = 2x\)
If the digits are reversed, the new number is 6 less than twice the original number:
\(10y + x = 2(10x + y) - 6\)
Plugging in \(y = 2x\)
\(20x + x = 2(12x) - 6\)
\(21x = 24x - 6\)
\(3x = 6\)
\(x = 2\)
Plugging that back into \(y = 2x\) will give \(y = 4\)
Therefore the two digit number is 24.
Answer C
The question says that the Quotient is 4, But nowhere it mentions that there would be no remainder (R=0). If there was a remainder then the equation presented in the answer would be falsified. Hence this method is not right.
Let me know what you think
