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Today Rebecca, who is 34 years old, and her daughter, who is 8 years

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Today Rebecca, who is 34 years old, and her daughter, who is 8 years old, celebrate their birthdays. How many years will pass before Rebecca’s age is twice her daughter’s age?

(A) 10
(B) 14
(C) 18
(D) 22
(E) 26

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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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New post 15 Oct 2015, 00:48
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Ans is c,

Present age is 34 & 8

Add x yrs to both their present ages and form the equation which satisfies the other condition, i.e rebecca's age is twice of her daughters.

( 34 + x ) = 2 ( 8 + x )

X = 18.

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.



Today Rebecca, who is 34 years old, and her daughter, who is 8 years old, celebrate their birthdays. How many years will pass before Rebecca’s age is twice her daughter’s age?

(A) 10
(B) 14
(C) 18
(D) 22
(E) 26



After x years passes Rebecca’s age will be (34+x) years old, and her daughter’s age will be (8+x) years old. Since the Rebecca’s age is twice her daughter’s age (34+x)= 2 * (8+x) ---> 34+x=16+2x ---> x= 18.

The answer is (C).
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Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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For this precise problem of age-doubling, I follow a simple reasoning.

Rebecca is 34 years old and her daughter is 8. Thus they’re 26 years apart from each other. While the daughter is younger than 26, her mom’s age will always more than double hers, whereas when she’s older than 26, the mom’s age will less than double hers. It is precisely at 26 that the daughter’s age will be doubled by her mom.

Why?
Let \(a =\)number of years Rebecca had lived before the daughter was born
Let \(b =\)number of years Rebecca has lived after her daughter’s birth
Let \(c =\)number of years the daughter has lived (after being born)

We are looking for:
(1) \(b - 8\), which will be the solution of the problem.

What the stem tells us is:
(2) \(a + b = 2c\)
(3) \(a = 26\)

What logic tells us is
(4) \(b = c\)

Thus:
(5) \(26 + b = 2b\) -> \(b = 26\)

From (1), we get the solution to the problem: \(26-8 = 18\)
Hope this helps!
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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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New post 21 May 2016, 15:24
I think that the easiest way to solve this problem is to pick numbers. Start with C. 34+18=52 18+8=26 26*2=52 Bingo!
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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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New post 28 Aug 2017, 09:30
Bunuel wrote:
Today Rebecca, who is 34 years old, and her daughter, who is 8 years old, celebrate their birthdays. How many years will pass before Rebecca’s age is twice her daughter’s age?

(A) 10
(B) 14
(C) 18
(D) 22
(E) 26

Kudos for a correct solution.


- Now, Rebecca is 38 y.o. and her daughter is 8 y.o.
- How many years from now, the ratio between Rebecca's and Daughter's age will be 2:1?
- Let x = number of years
- Solution = \(\frac{(34+X)}{(8+X)}\) = \(\frac{2}{1}\) -> we can cross multiply : \(34+X=16+2X\) --> \(-X=-18\), thus \(X=18\).

C.
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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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New post 28 Aug 2017, 10:28
Let the number of years be X
So according to question we have X+34=2*(8+X)
X=18

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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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New post 13 Sep 2017, 21:57
Trail and Error
start with middle
34+18 = 2(8+18)
52 = 2(26)
Correct Answer is C
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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years [#permalink]

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New post 19 Sep 2017, 15:46
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Bunuel wrote:
Today Rebecca, who is 34 years old, and her daughter, who is 8 years old, celebrate their birthdays. How many years will pass before Rebecca’s age is twice her daughter’s age?

(A) 10
(B) 14
(C) 18
(D) 22
(E) 26


We are given that Rebecca is 34 and her daughter is 8. We can let n = the number of years before Rebecca is twice as old as her daughter. At that time, Rebecca will be (34 + n) years old and her daughter will be (8 + n) years old, and Rebecca will be twice her daughter’s age:

34 + n = 2(8 + n)

34 + n = 16 + 2n

18 = n

Answer: C
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Re: Today Rebecca, who is 34 years old, and her daughter, who is 8 years   [#permalink] 19 Sep 2017, 15:46
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