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# 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  [#permalink]

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Updated on: 25 Apr 2017, 00:06
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Q. 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

Thanks,
Saquib
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Originally posted by EgmatQuantExpert on 25 Apr 2017, 00:04.
Last edited by EgmatQuantExpert on 25 Apr 2017, 00:06, edited 1 time in total.
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If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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30 Apr 2017, 00:10
4
2

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 add the same number (say A) to 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 add 1 to both the numerator and denominator, then the new ratio would be

 $$\frac{(2+1)}{(3+1)} = \frac{3}{4} = 0.75$$
 And we can see clearly that $$\frac{3}{4} > \frac{2}{3}$$
 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 = 3 : 4 or $$\frac{3}{4} = 0.75$$
• We have been asked the age after 8 years

o Now notice we are adding 8 to both the numerator and denominator.
o Anna: Paula =$$\frac{(3x + 8)}{(4x + 8)}$$
o Thus, we should immediately conclude that the new ratio(fraction) must be more than 0.75.

• Thus, we just need to look at the options quickly and find a ratio which is more than 0.75

A. $$1: 2 = \frac{1}{2} = 0.5$$
B. $$3: 8 = \frac{3}{8} = 0.375$$
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 E is the answer)

Thanks,
Saquib
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##### General Discussion
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If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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Updated on: 30 Apr 2017, 00:01

Originally posted by EgmatQuantExpert on 25 Apr 2017, 00:04.
Last edited by EgmatQuantExpert on 30 Apr 2017, 00:01, edited 1 time in total.
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If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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25 Apr 2017, 00:30
1
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)
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Re: If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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25 Apr 2017, 00:42
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

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

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30 Apr 2017, 00:00

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 3: 4
• Let us assume the age of Anna and Paula to be 3x and 4x respectively.
• After 8 years, the ratio of ages would be

o $$\frac{Anna}{Paula} = \frac{(3x+8)}{(4x+8)}$$…………….(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. $$\frac{(3x+8)}{(4x+8)} = \frac{1}{2}$$
$$6x + 16 = 4x + 8$$
$$2x = - 8$$
Since x is negative, this cannot be our answer, as the ages cannot be negative.

B. $$\frac{(3x+8)}{(4x+8)} = \frac{3}{8}$$
$$24x + 64 = 12x + 24$$
x = negative
Since x is negative, this cannot be our answer, as the ages cannot be negative.

C. $$\frac{(3x+8)}{(4x+8)} = \frac{3}{5}$$
$$15x + 40 = 12x + 24$$
x = negative
Since x is negative, this cannot be our answer, as the ages cannot be negative.

D. $$\frac{(3x+8)}{(4x+8)} = \frac{2}{3}$$
$$9x + 24 = 8x + 16$$
x = negative
Since x is negative, this cannnot be our answer, as the ages cannot be negative.

E. $$\frac{(3x+8)}{(4x+8)} = \frac{4}{5}$$
$$15x + 40 = 16x + 32$$
$$x = 8$$
Since x is positive, this can 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 E.

Thanks,
Saquib
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Re: If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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16 Sep 2018, 09:21
Top Contributor
EgmatQuantExpert wrote:
Q. 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

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.

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

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

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07 Oct 2018, 21:27
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
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Re: If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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10 Apr 2019, 17:55
EgmatQuantExpert wrote:
Q. 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

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.

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Re: If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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19 Apr 2019, 09:00
ScottTargetTestPrep wrote:
EgmatQuantExpert wrote:
Q. 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

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.

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
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Re: If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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23 Apr 2019, 16:06
YB101 wrote:
ScottTargetTestPrep wrote:
EgmatQuantExpert wrote:
Q. 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

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.

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

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.
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If the ratio of the present age of Anna and Paula is 3 : 4, what could  [#permalink]

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25 Apr 2019, 17:27
EgmatQuantExpert wrote:

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 add the same number (say A) to 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 add 1 to both the numerator and denominator, then the new ratio would be

 $$\frac{(2+1)}{(3+1)} = \frac{3}{4} = 0.75$$
 And we can see clearly that $$\frac{3}{4} > \frac{2}{3}$$
 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 = 3 : 4 or $$\frac{3}{4} = 0.75$$
• We have been asked the age after 8 years

o Now notice we are adding 8 to both the numerator and denominator.
o Anna: Paula =$$\frac{(3x + 8)}{(4x + 8)}$$
o Thus, we should immediately conclude that the new ratio(fraction) must be more than 0.75.

• Thus, we just need to look at the options quickly and find a ratio which is more than 0.75

A. $$1: 2 = \frac{1}{2} = 0.5$$
B. $$3: 8 = \frac{3}{8} = 0.375$$
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 E is the answer)

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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.
If the ratio of the present age of Anna and Paula is 3 : 4, what could   [#permalink] 25 Apr 2019, 17:27
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