If the ratio of the present age of Anna and Paula is 3 : 4, what could

Question

If the ratio of the present age of Anna and Paula is 3 : 4, what could be the ratio of their respective ages after 8 years??

A. 1 : 2
B. 3 : 8
C. 3 : 5
D. 2 : 3
E. 4 : 5

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Official Answer

E

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EgmatQuantExpert · Accepted Answer

Method 2:

bit cumbersome and time-consuming

a simple concept of ratios/fractions

the fraction is a proper fraction

must be more than 0.75

Option E

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pushpitkc · Answer

The ratio of anna's age:paula's age is 3:4
Plugging in numbers, 
let anna's age is 24
paula's age is 32

8 years later
Anna will be 32 and paula will be 40 Ratio 4:5(Option E)

EgmatQuantExpert · Answer

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

skothaka · Answer

ratio of ages after 8 years will be 3x+8:4x+8
put x= 1,2,3,4,5....
you will get 
11:12
increase 11 by 3 and 12 by 4 and continue the process.
14:16
17:20
20:24
23:28
26:32
29:36
32:40 = 4:5

hence answer is E

EgmatQuantExpert · Answer

Solution

Let me discuss two ways to solve this question.

Method 1:

o \(\frac{Anna}{Paula} = \frac{(3x+8)}{(4x+8)}\)…………….(i)

one among the 5 options

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.

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

Option E

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BrentGMATPrepNow · Answer

Here's a nice property of fractions:    If a, b and k are positive, then (a + k)/(b + k) approaches 1 as k gets bigger.    
For example, the fraction (2+11)/(3+11) is closer to 1 than 2/3 is.
Likewise, the fraction (1+7)/(2+7) is closer to 1 than 1/2 is.

Let A = Anna's present age
Let P = Paula's present age
So,  A/P = 3/4

In EIGHT YEARS, we can conclude that: 
Let A + 8= Anna's future age
Let P + 8 = Paula's future age
So, in EIGHT YEARS, the ratio of their ages = (A + 8)/(P + 8)

By the above   rule  , we know that (A + 8)/(P + 8) is closer to 1 than is  A/P  is.
In other words, (A + 8)/(P + 8) is closer to 1 than  3/4  is.

Check the answer choices.....
Only answer choice E (aka 4/5) is closer to 1 than  3/4  is.

Answer: E

RELATED VIDEO FROM OUR COURSE
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Temurkhon · Answer

let us use fractions properties. When we add the same number to numerator and denominator the fraction increases.
In our case we do so.
So, we have 3/4 and look answer choices. Only E, in which 4/5>3/4 can be correct

E

ScottTargetTestPrep · Answer

Some possible ratios of their current ages are:

A/P = 3/4, 6/8, 9/12, 12/15, 15/20, 18/24, 21/28, 24/32…

So after 8 years, these ratios, would be:

11/12, 14/16 = 7/8, 17/20, 20/23, 23/28, 26/32 = 13/16, 29/36, 32/40 = 4/5, …
We see that if Anna is 24 and Paula is 32, the ratio of their ages 8 years later is 32/40 = 4/5, or 4 : 5.

Answer: E

YB101 · Answer

Hi Scott,

Just wanted to clarify - you've picked an example here of Anna being 24 and Paula being 32. I.e. 24/32 = 3/4 so these numbers fit the initial ratio. When I did this question, I picked a different set of numbers (Anna is 12, Paula is 16) and then went 12+8/16+8 = 20/24 = 5/6. Why did my numbers not work? Alternatively, why did you pick the numbers 24 and 32? 12/16 still reduces down to 3/4 after all...

Thanks

ScottTargetTestPrep · Answer

First of all, your numbers work too; you determined that the ratio of ages could be 5/6. It’s just that 5/6 is not among the answer choices.

About your second question on why the numbers 24 and 32; what I’ve done is actually listing all numbers with a ratio of 3:4 or at least, I’ve started listing such numbers (there are infinitely many of them). In the next step, I added 8 to the numerator and the denominator to get the possible values for the ratio after 8 years. I’ve continued this process until I got one of the values among the answer choices and that’s why I ended the list when I reached 24 and 32.

edlc313 · Answer

Simple, elegant, excellent.

Although I knew such property existed, I got the question wrong. I assumed (terribly) that because an odd + even must equal odd, then the new ratio of their ages would also be odd:odd. Of course, I had the foresight in forgetting that their ages could be  \frac{3(even)+8}{4(even)+8}  which would collapse my whole theory.

Andrewcoleman · Answer

This video was totally what I needed to apply properties of fractions. I got this answer right the long hard way this video brought me back to the basics and is exactly what this question is trying to test.

GmatPoint · Answer

Let the current age of Anna and Paula be 3x and 4x, respectively.
After 8 years, the ratio will become (3x + 8):(4x + 8)

The only option in this form is E, i.e., when x = 8.

When x = 8, the ration will become (3*8 + 8)/(4*8 + 8) = 32/40 = 4/5

Thus, the correct option is E.

frokly · Answer

Let A be the age of Anna and P the age of Paula. A/P = 3/4 therefore P 3/4 — correct option! For nerds i made more formal proof of this idea (why fractions work so) The main property of a fraction says that (P*k)/(A*k)=P/A (k > 0 in this case). Let k be s.t. P+8 is equal to P*k (e.g if P = 16, P+8 = 24, k = 24/16 =3/2) therefore A+8 will be greater than A*k as we increase a lower number by the same factor k (e.g. P=16 => A=12, A*k = 12*3/2 = 18, the increase of A is 6 which is less than 8) therefore A/P = (A*k)/(P*k) < (A+8)/(P+8)

If the ratio of the present age of Anna and Paula is 3 : 4, what could

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If the ratio of the present age of Anna and Paula is 3 : 4, what could

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