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

Question

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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Saquib
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Official Answer

A

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varundixitmro2512 · Accepted Answer

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.

EgmatQuantExpert · Answer

Method 2:

bit cumbersome and time-consuming

a simple concept of ratios/fractions

the fraction is a proper fraction

must be less than 0.5

Option A

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Saquib
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EgmatQuantExpert · Answer

The official solution has been posted. Looking forward to a healthy discussion..

pushpitkc · Answer

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)

generis · Answer

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.

pushpitkc · Answer

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

EgmatQuantExpert · Answer

Solution

Let me discuss two ways to solve this question.

Method 1:

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

one among the 5 options

this can be our answer, as the ages cannot be negative

this cannot be our answer, as the ages cannot be negative.

this cannot be our answer, as the ages cannot be negative

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

Option A

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Saquib
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e-GMAT

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Wongderful · Answer

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.

ScottTargetTestPrep · Answer

Some possible ratios of ages are:

A/P = 8/16, 9/18, 10/20, 11/22, 12/24, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 20/40

So 8 years ago, these ratios would be:

A/P = 0/8, 1/10, 2/12, 3/14, 4/16, 5/18, 6/20, 7/22, 8/24, 9/26, 10/28, 11/30, 12/32.

We see that if Anna is 20 and Paula is 40, the ratio of their ages 8 years ago is 12/32 = 3/8.

Alternate Solution:

Let x = Ann’s present age. Since the ratio of Ann’s present age to Paula’s present age is 1:2, Paula’s present age must be 2x.

8 years ago, Ann’s age was (x - 8), and Paula’s age was (2x - 8); therefore, the ratio of their ages was (x - 8)/(2x - 8). Let’s set this expression equal to each answer choice and see which one gives a positive integer value for x:

A) 3:8

(x - 8)/(2x - 8) = 3/8

8x - 64 = 6x -24

2x = 40

x = 20

We see that answer choice A gives us a positive integer value for x, so it must be the correct answer choice. Indeed, the ratio of Ann’s present age to Paula’s present age is 20/40, and the ratio of Ann’s age 8 years ago to Paula’s age 8 years ago is 12/32 = 3/8.

Answer: A

rmk69 · Answer

Anna/Paula=(x−8)/(2x−8)

2x-8 is always going to be even so A is the right option.

ullamdicta · Answer

This isn't the right way. If I plug 10 in the place of 20 the answer will never match

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

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