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While discussing their ages, Anthony tells Kaira, 'My age is 6 times

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While discussing their ages, Anthony tells Kaira, 'My age is 6 times  [#permalink]

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New post 15 Jan 2017, 05:25
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A
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D
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Difficulty:

  55% (hard)

Question Stats:

58% (01:45) correct 42% (01:51) wrong based on 31 sessions

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While discussing their ages, Anthony tells Kaira, 'My age is 6 times what your age was when I was your age'. The sum of their current ages is 57. Find Kaira's current age.

A. Cannot be determined
B. 19
C. 20
D. 21
E. 22

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Re: While discussing their ages, Anthony tells Kaira, 'My age is 6 times  [#permalink]

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New post 15 Jan 2017, 06:45
2
winionhi wrote:
While discussing their ages, Anthony tells Kaira, 'My age is 6 times what your age was when I was your age'. The sum of their current ages is 57. Find Kaira's current age.

A. Cannot be determined
B. 19
C. 20
D. 21
E. 22



Anthony's age = X

Kaira's age = Y

X = 6(Y - (X - Y))

X = 12Y - 6X

X = 12/7Y

X + Y = 57

12/7Y + Y = 57

19/7Y = 57

19Y = 399

Y = 21

Answer D
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Re: While discussing their ages, Anthony tells Kaira, 'My age is 6 times  [#permalink]

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New post 12 Feb 2017, 19:00
How did you get the highlighted equation ?

[/quote]
Anthony's age = X

Kaira's age = Y

X = 6(Y - (X - Y))

X = 12Y - 6X

X = 12/7Y

X + Y = 57

12/7Y + Y = 57

19/7Y = 57

19Y = 399

Y = 21

Answer D[/quote]
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Re: While discussing their ages, Anthony tells Kaira, 'My age is 6 times  [#permalink]

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New post 12 Feb 2017, 20:37
winionhi wrote:
While discussing their ages, Anthony tells Kaira, 'My age is 6 times what your age was when I was your age'. The sum of their current ages is 57. Find Kaira's current age.

A. Cannot be determined
B. 19
C. 20
D. 21
E. 22




Let Anthuony's age be A and Kaira's age be K...

A was equal to K, A-K years back...
So at that time K would be equal to K-(A-K)=2K-A...
Given that A=6(2K-A)=12K-6A...
7A=12K.... But A+K=57...
So 7(57-K)=12K.......7*57=12K+7K....
K=7*57/19=7*3=21
D
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Re: While discussing their ages, Anthony tells Kaira, 'My age is 6 times  [#permalink]

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New post 12 Feb 2017, 20:48
1
Hi winionhi,

This question can be solved by TESTing THE ANSWERS.

We're given a couple of facts to work with:
1) Anthony's current age IS 6 times what Kaira's age WAS when Anthony was Kaira's (current) age.
2) The sum of their CURRENT ages is 57.

We're asked for Kaira's current age.

Let's TEST Answer B: 19

IF....
Kaira is 19
Anthony is 57 - 19 = 38
38 is "6 times" 6 1/3, which would be a strange way to refer to an age (so this is likely NOT the correct answer).
Eliminate Answer B.

Let's TEST Answer D: 21
IF....
Kaira is 21
Anthony is 57 - 21 = 36
36 is "6 times" 6
Anthony was 21 fifteen years ago; at that time, Kaira was 21 - 15 = 6
This is an exact match for what we were told, so this MUST be the answer.

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Re: While discussing their ages, Anthony tells Kaira, 'My age is 6 times  [#permalink]

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New post 12 Feb 2017, 20:49
Great Question.
Here is what i did in this question -->

Let Anthony's age be x and Kaira's age be y.
We are asked the value of y.

Lets make the equation.

x+y=57.

The second part is a bit trickier.
When Anthony was Kaira's age --> That would be x-y years ago.
Hence x-y years ago Kaira's age would be y-(x-y) => y-x+y=2y-x

As per question => x=6(2y-x)
Hence x=12y-6x=> 7x=12y

Solving the two equations -->
x+y=57
7x=12y
7x+7y=57*7
19y=57*7
Hence y=21

So Kaira's present age is 21.

Hence D.

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Re: While discussing their ages, Anthony tells Kaira, 'My age is 6 times &nbs [#permalink] 12 Feb 2017, 20:49
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