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

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

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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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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