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If the ratio of the present age of Anna and Paula is 1 : 2, what co

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If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 25 Apr 2017, 00:09
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Q. If the ratio of the present age of Anna and Paula is 1 : 2, what could be the ratio of their respective ages 8 years ago??

    a. 3 : 8
    b. 4 : 7
    c. 3 : 5
    d. 2 : 3
    e. 4 : 5


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Re: If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 25 Apr 2017, 00:16
5
IMO answer is A

Since a/b is less than 1 and we are subtracting the same constant from num and deno then resulting ratio should less than a/b

which only option A.

Waiting for OA and Kudos too :P
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If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post Updated on: 30 Apr 2017, 01:29
The official solution has been posted. Looking forward to a healthy discussion..:)
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Originally posted by EgmatQuantExpert on 25 Apr 2017, 00:10.
Last edited by EgmatQuantExpert on 30 Apr 2017, 01:29, edited 1 time in total.
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If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post Updated on: 27 Apr 2017, 10:45
The ratio of anna's age:paula's age is 1:2.
Plugging in numbers,
let anna's age is 20
paula's age is 40

8 years before
Anna was 12 and paula was 32
These are in the ratio 3:8(Option A)
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Originally posted by pushpitkc on 25 Apr 2017, 00:24.
Last edited by pushpitkc on 27 Apr 2017, 10:45, edited 1 time in total.
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If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 27 Apr 2017, 10:39
EgmatQuantExpert wrote:
Q. If the ratio of the present age of Anna and Paula is 1 : 2, what could be the ratio of their respective ages 8 years ago??

    a. 3 : 8
    b. 4 : 7
    c. 3 : 5
    d. 2 : 3
    e. 4 : 5
pushpitkc wrote:
The ratio of anna's age:paula's age is 1:2.
Plugging in numbers,
let anna's age is 20
paula's age is 40

8 years before
Anna was 12 and paula was 32
These are in the ratio 3:8(Option A)


pushpitkc, would you explain, please, what method you used to pick your numbers?

I usually have a decent sense of which numbers to pick. Here, I am lost. I picked two different sets of numbers, got different ratios nowhere near answer choices, and abandoned the method. (I fooled around with original ratio, total x:2x = 3x, considered -8, etc., but didn't see a clear path.)

(E.g., A = 10, P = 20, such that ratio eight years ago is 1:6. And A = 30, P = 60, such that ratio eight years ago is 11:26).

I can't figure out where I'm going wrong. Please explain your approach to choice of numbers to plug in? Or Saquib? Thanks in advance.
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Re: If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 27 Apr 2017, 10:58
1
genxer123 wrote:
EgmatQuantExpert wrote:
Q. If the ratio of the present age of Anna and Paula is 1 : 2, what could be the ratio of their respective ages 8 years ago??

    a. 3 : 8
    b. 4 : 7
    c. 3 : 5
    d. 2 : 3
    e. 4 : 5
pushpitkc wrote:
The ratio of anna's age:paula's age is 1:2.
Plugging in numbers,
let anna's age is 20
paula's age is 40

8 years before
Anna was 12 and paula was 32
These are in the ratio 3:8(Option A)


pushpitkc, would you explain, please, what method you used to pick your numbers?

I usually have a decent sense of which numbers to pick. Here, I am lost. I picked two different sets of numbers, got different ratios nowhere near answer choices, and abandoned the method. (I fooled around with original ratio, total x:2x = 3x, considered -8, etc., but didn't see a clear path.)

(E.g., A = 10, P = 20, such that ratio eight years ago is 1:6. And A = 30, P = 60, such that ratio eight years ago is 11:26).

I can't figure out where I'm going wrong. Please explain your approach to choice of numbers to plug in? Or Saquib? Thanks in advance.



I didn't use any specific method to plug in the numbers. Pure trial and error
But generally try smaller numbers like 10 or 20 if the ratios are not too far apart.
On the contrary if the numbers in the ratios are far apart, use bigger numbers like 100.
In this example since the ratios were 3:8,4:7,4:5
I thought of numbers in this ratio and back tracked to get the answer
But, in problems such as time and work, i use the LCM of the numbers.
This generally helps in most of GMAT type questions
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Re: If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 30 Apr 2017, 00:20

Solution



Let me discuss two ways to solve this question.

Method 1:

    • The ratio of the present age of Anna and Paula has been given as 1: 2
    • Let us assume the age of Anna and Paula to be x and 2x respectively.
    • 8 years ago, the ratio of ages would have been

      o \(\frac{Anna}{Paula} = \frac{(x-8)}{(2x-8)}\)…………….(i)

    • Now the correct answer has to be one among the 5 options, let us equate equation (i) with all the options one by one.

      A. \(\frac{(x-8)}{(2x-8)} = \frac{3}{8}\)
      \(8x - 64 = 6x - 24\)
      \(2x = 40\)
      \(x = 20\)

      Since x is positive, this can be our answer, as the ages cannot be negative

      B. \(\frac{(x-8)}{(2x-8)} = \frac{4}{7}\)
      \(7x -56 = 8x - 32\)
      x = negative

      Since x is negative, this cannot be our answer, as the ages cannot be negative.

      C. \(\frac{(x-8)}{(2x-8)} = \frac{3}{5}\)
      \(5x - 40 = 6x - 24\)
      x = negative

      Since x is negative, this cannot be our answer, as the ages cannot be negative.

      D. \(\frac{(x-8)}{(2x-8)} = \frac{2}{3}\)
      \(3x - 24 = 4x - 16\)
      x = negative

      Since x is negative, this cannnot be our answer, as the ages cannot be negative.

      E. \(\frac{(x-8)}{(2x-8)} = \frac{4}{5}\)
      \(5x - 40 = 8x - 32\)
      x = negative

      Since x is negative, this cannnot be our answer, as the ages cannot be negative..

    • As we can see, in only one case, we are getting x as positive, hence the correct answer is Option A.


Thanks,
Saquib
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Re: If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 30 Apr 2017, 00:52
1

Method 2:



    • Now, the first method is a bit cumbersome and time-consuming too.
    • And the purpose of the question was to teach you a simple concept of ratios/fractions

      o Suppose we have a fraction say \(\frac{N}{D}\), where \(\frac{N}{D}\) is a proper fraction (D>N), for example, \(\frac{1}{2},\frac{2}{3}\) etc, and if we subtract the same number (say A) from the numerator and denominator, will the new ratio be greater than \(\frac{N}{D}\) or less than?
      o For example, if we have \(\frac{2}{3} = 0.666\)

      o Now say we subtract 1 from both the numerator and denominator, then the new ratio would be

         \(\frac{(2-1)}{(3-1)} = \frac{1}{2} = 0.5\)
         And we can see clearly that \(\frac{1}{2} < \frac{2}{3}\)
         Hence \(\frac{(N-a)}{(D-a)} < \frac{N}{D}\), when the fraction is a proper fraction.

    • With this knowledge let us now solve the question.
    • Ratio of age of Anna and Paula = 1 : 2 or \(\frac{1}{2} = 0.5\)
    • We have been asked the age ratio 8 years ago

      o Now notice we are subtracting 8 from both the numerator and denominator.
      o Anna: Paula =\(\frac{(x - 8)}{(2x - 8)}\)
      o Thus, we should immediately conclude that the new ratio(fraction) must be less than 0.5.

    • Thus, we just need to look at the options quickly and find a ratio which is less than 0.5

      A. \(3: 8 = \frac{1}{2} = 0.375\)
      B. \(4: 7 = \frac{3}{8} = 0.57\)
      C. \(3:5 = \frac{3}{5} = 0.6\)
      D. \(2: 3 = \frac{2}{3} = 0.66\)
      E. \(4: 5 = \frac{4}{5} = 0.8\)
      (Hence Option A is the correct answer)


Thanks,
Saquib
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Re: If the ratio of the present age of Anna and Paula is 1 : 2, what co  [#permalink]

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New post 01 Jul 2018, 20:41
A really great question.

There are a few ways we can use, but I think the most time-efficient method here would be this.

Current ratio of age (A/P) is 1/2.
By looking back in time, this ratio will dip below 1/2 towards 0 (e.g. If present A/P ratio is 9:18, then the 8 years ago ratio would be 1:10)
By looking ahead of time, this ratio till rise above 1/2 towards 1 (e.g. 90 years later, the ratio would be 99/108)

Looking at the answer choices, only answer A is below 1/2 (since we are looking back in time). Hence A is the answer.
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Re: If the ratio of the present age of Anna and Paula is 1 : 2, what co &nbs [#permalink] 01 Jul 2018, 20:41
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