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# The ratio of the ages of A and B is 7 : 11. Which of the following can

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Math Expert
Joined: 02 Sep 2009
Posts: 51214
The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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30 Jun 2017, 02:21
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The ratio of the ages of A and B is 7 : 11. Which of the following can be the ratio of their ages after 5 years?

(A) 1 : 3
(B) 9 : 20
(C) 4 : 15
(D) 3 : 5
(E) 2 : 3

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Joined: 02 Aug 2009
Posts: 7106
Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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30 Jun 2017, 07:43
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Bunuel wrote:
The ratio of the ages of A and B is 7 : 11. Which of the following cannot be the ratio of their ages after 5 years?

(A) 1 : 3
(B) 9 : 20
(C) 4 : 15
(D) 3 : 5
(E) 2 : 3

hi Bunuel,

seems there is a typo. i think it should be can and not cannot..

if the Q says can be, the logic to get the answer immediately without any trial is..
Ratio is $$\frac{7}{11}$$ or the numbers are $$\frac{7x}{11x}$$, so if you are adding SAME amount to both denominator and numerator, the value of RATIO will INCREASE

A,B,C are LESS than 7/11 in first look ..
D. 3/5 .. it is close so check 3/5 , 7/11.....$$\frac{3*11 , 7*5}{55}$$...
35>33 so 7/11>3/5

when x is 5..$$\frac{7x}{11x} = \frac{35}{55}$$..
add 5 to both ages $$\frac{35+5}{55+5}=\frac{40}{60}=\frac{2}{3}$$

E
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Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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30 Jun 2017, 08:08
2
Bunuel wrote:
The ratio of the ages of A and B is 7 : 11. Which of the following cannot be the ratio of their ages after 5 years?

(A) 1 : 3
(B) 9 : 20
(C) 4 : 15
(D) 3 : 5
(E) 2 : 3

With chetan2u
Attachment:

Capture.PNG [ 7.23 KiB | Viewed 1717 times ]

IMHO with (E)
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Joined: 01 May 2017
Posts: 30
Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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30 Jun 2017, 08:12
2
1
Adding the same number to the numerator and denominator of a ratio causes the resultant ratio to move closer to "1".

Eg: Consider 1/2 (0.5) which is lesser than 1. Suppose we add 2 to both numerator and denominator. Final ration = 3/4 (0.75) -> closer to 1.
Now consider 3/2 (1.5) which is greater than one 1. Suppose we add 2 to both numerator and denominator. Final ration = 5/4 (1.25) -> closer to 1.

Using the same logic for solving the above question,
7/11 = 0.6363

after 5 years,
[(7x + 5)/ (11x + 5)] >0.6363 (adding 5 to both numerator and denominator should cause the final value to move closer to 1)

I agree with Chetan2u - there is a typo probably - should be "can" and not "cannot"

(A) 1 : 3 = 0.33
(B) 9 : 20 = 0.45
(C) 4 : 15 = 0.26
(D) 3 : 5 = 0.60
(E) 2 : 3 = 0.66 => Ans
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Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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30 Jun 2017, 08:30
4
After 5 years the ratio of their ages MUST be higher than what it is now (since same value is being added to both numerator and denominator). Therefore only valid option is Option (E).
Math Expert
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Posts: 51214
Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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01 Jul 2017, 05:36
Bunuel wrote:
The ratio of the ages of A and B is 7 : 11. Which of the following can be the ratio of their ages after 5 years?

(A) 1 : 3
(B) 9 : 20
(C) 4 : 15
(D) 3 : 5
(E) 2 : 3

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Edited. Thank you all.
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Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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04 Jul 2017, 07:14
2
1
Bunuel wrote:
The ratio of the ages of A and B is 7 : 11. Which of the following can be the ratio of their ages after 5 years?

(A) 1 : 3
(B) 9 : 20
(C) 4 : 15
(D) 3 : 5
(E) 2 : 3

We may recall the rule that if any ratio a/b, in which a is less than b, and a positive constant is added to both the numerator and denominator of the fraction, then the resulting fraction is greater than the original one.

We see that 7/11 is around 0.63, and since 2/3 = 0.667, we see that 2/3 is the only ratio that is larger than 0.63.

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Re: The ratio of the ages of A and B is 7 : 11. Which of the following can  [#permalink]

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16 Aug 2018, 12:07
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Re: The ratio of the ages of A and B is 7 : 11. Which of the following can &nbs [#permalink] 16 Aug 2018, 12:07
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