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When a two digit number is divided by the sum of its digits, the quot

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Bunuel
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When a two digit number is divided by the sum of its digits, the quot [#permalink] New post   14 Jun 2021, 08:15
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When a two 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.
The number is

(A) 12
(B) 21
(C) 24
(D) 42
(E) Both (C) and (D)
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chetan2u
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Re: When a two digit number is divided by the sum of its digits, the quot [#permalink] New post   14 Jun 2021, 11:18
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Bunuel wrote:
When a two 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.
The number is

(A) 12
(B) 21
(C) 24
(D) 42
(E) Both (C) and (D)



Using the options, we can find the answer relatively fast.

When a two digit number is divided by the sum of its digits, the quotient is 4.
12 divided by 1+2 gives quotient 4.
24 divided by 2+4 gives quotient 4.

If the digits are reversed, the new number is 6 less than twice the original number.
21=2*12-6......No
42=2*24-6......Yes

C
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Re: When a two digit number is divided by the sum of its digits, the quot [#permalink] New post   14 Jun 2021, 12:44
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C. 24

When a two 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.
The number is

(A) 12
(B) 21
(C) 24
(D) 42
(E) Both (C) and (D)

We can move by assuming that each option is the desired number

for A) 12/3 = 4 but 12*2 = 24 is 3 greater than 21
for B) 21/3 = 7 which is not = 4
for C) 24/6 = 4 and 24*2 = 48 is 6 greater than 42
for D) 42/6 = 7 which is not = 4

Therefore, C) is the correct answer
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Re: When a two digit number is divided by the sum of its digits, the quot [#permalink] New post   14 Jun 2021, 22:50
Bunuel wrote:
When a two 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.
The number is

(A) 12
(B) 21
(C) 24
(D) 42
(E) Both (C) and (D)


If anyone wants to solve this algebraically:

Let the digits of two-digit number be x and y respectively.
So, the number is 10x + y.
Sum of digits = x + y.
Given:
\(\frac{10x + y}{x + y} = 4\)
\(10x + y = 4x + 4y\)
\(2x = y\) - eq(1)

If we reverse the digits, number formed = 10y + x
Given: 10y + x = 2(10x + y) - 6
\(8y = 19x - 6\)
Putting y = 2x from eq(1):
\(16x = 19x - 6\)
\(x = 2\), y = 4

So, the number is 24. IMO, (C)!
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Re: When a two digit number is divided by the sum of its digits, the quot [#permalink] New post   15 Jun 2021, 00:44
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Since the quotient of the division is 4, we can say that the two-digit number is divisible by 4.
Answer options B and D can be eliminated along with answer option E.

Consider option A: If the digits of 12 are reversed, the new number is 21 which is actually more than the original number.
Eliminate answer option A.

The correct answer option is D.

In many many Quant questions, getting to the answer is not the same as solving the question fully. We did not have to solve the question mathematically at all. The elimination strategy is a super-potent weapon that any GMAT aspirant should have in his/her armoury.

Hope that helps!
Aravind B T
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Re: When a two digit number is divided by the sum of its digits, the quot [#permalink] New post   15 Jun 2021, 01:31
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Two-digit number = PQ or 10P + Q

Divided by the sum of its digits, the quotient is 4: \(\frac{(10P + Q)}{ P + Q }= 4 \)

=> 10P + Q = 4P + 4Q

=> 6P - 3Q = 0

=> 2P = Q

If the digits are reversed= 10Q + P

The new number is 6 less than twice the original number = 10 Q + P + 6 = 2 (10P + Q)

=> 10 Q + P + 6 = 20 P + 2 Q

=> 20P + P + 6 = 20P + 4 P

=> 21P + 6 = 24 P

=> 6 = 3P

=> P = 2 and hence, Q = 4

Number is 24

Answer C
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Re: When a two digit number is divided by the sum of its digits, the quot [#permalink]
15 Jun 2021, 01:31
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