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When a 2-digit number is divided by the sum of its digits, the quotien

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Bunuel
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When a 2-digit number is divided by the sum of its digits, the quotien [#permalink] New post   13 Jan 2022, 07:45
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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
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Nidzo
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Re: When a 2-digit number is divided by the sum of its digits, the quotien [#permalink] New post   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
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parthadlakha
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Re: When a 2-digit number is divided by the sum of its digits, the quotien [#permalink] New post   25 Jun 2022, 01:32
Nidzo wrote:
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


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 :)
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When a 2-digit number is divided by the sum of its digits, the quotien [#permalink] New post   25 Jun 2022, 08:31
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Bunuel wrote:
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


Why on earth would we do anything on this question other than Plugging In The Answers (PITA)? Might be a 700-level question if you do the real math, but a 3rd-grader can get it right with PITA.

A. 12/3 = 4? Yep. 21 = 24-6? Nope. Eliminate.
B. 21/3 = 4? Nope. Eliminate.
C. 24/6 = 4? Yep. 42 = 48-6? Yep.

Answer choice C.

Edited to add: Holy smokes, I just noticed that only 81% of people are getting this right so far! If you do the algebra on a question like this and don't take the extra 10 seconds to confirm that your solution actually works by plugging it back in, it's time to reevaluate your approach! Feel compelled to do the algebra? Go for it. Have a great time. But please please please at least confirm that you didn't make a silly mistake along the way...or just do PITA... ;)


ThatDudeKnowsPITA
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When a 2-digit number is divided by the sum of its digits, the quotien [#permalink]
25 Jun 2022, 08:31
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