If Sara's age is exactly twice Bill's age, what is Sara's ag

If Sara's age is exactly twice Bill's age, what is Sara's age?

Given: S = 2B.

(1) Four years ago, Sara's age was exactly 3 times Bill's age --> S - 4 = 3(B-4). We have two distinct linear equations (S - 4 = 3(B-4) and S = 2B) with two unknowns, thus we can solve for both. Sufficient.

(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age --> S + 8 =1.5(B + 8). The same here: we have two distinct linear equations with two unknowns, thus we can solve for both. Sufficient.

Answer: D.
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I solved this correctly via solving simultaneous equations ... but I could not understand the other approach the OG mentioned in the answer explanation : " another way to conclude that we can determine the value of s is to note that the pair of equations represents 2 non - parallel lines in the coordinate plane"

What they try to say is that the equations can be considered linear functions with different slopes. Therefore they will intersect at a certain point leading to one solution.

We're given the equation S = 2B


1) S - 4 = 3(B - 4), we now have two equations and two unknowns, that's enough. Sufficient
2) S + 8 = 1.5(B + 8), again two equations and two unknowns, sufficient.

So, D.

I thought the answer would be A because

2) S=2B
and S+8 = 1.5(B+8); solve this we have B=4/3.5 => B is not an integer => insufficient

Should B and S be integers because they are years of age?
Could someone help to explain when integers should be considered and when not?

When you solve S + 8 =1.5(B + 8) and S = 2B you get B = 8 and S = 16.

Also, why should a statement be insufficient if the result is not an integer?

And finally, I haven't seen a single official question where age is not an integer.

Check other Age Problems in our Speial Questions Directory.

Hope it helps
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we have 1 equation as per given data

Statement 1 : gives another equation along with Given data , can be solved , sufficient
Statement 2 : gives another equation along with Given data , can be solved , sufficient

hence D

Target question: What is Sara's age?

Given: Sara's age is exactly twice Bill's age
Let x = Bill's PRESENT age
So, 2x = Sara's PRESENT age

Statement 1: Four years ago, Sara's age was exactly 3 times Bill's age.
x - 4 = Bill's age FOUR YEARS AGO
2x - 4 = Sara's age FOUR YEARS AGO

We're told that: (Sarah's age 4 years ago) = 3(Bill's age 4 years ago)
We can write: 2x - 4 = 3(x - 4)
Expand: 2x - 4 = 3x - 12
Solve: x = 8
This means Bill's PRESENT age is 8 years old.
So, Sara's PRESENT age is 16
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Eight years from now, Sara's age will be exactly 1.5 times Bill's age.
x + 8 = Bill's age EIGHT YEARS FROM NOW
2x + 8 = Sara's age EIGHT YEARS FROM NOW

We're told that: (Sarah's age 8 years from now) = 1.5(Bill's age 8 years from now)
We can write: 2x + 8 = 1.5(x + 8)
Expand: 2x + 8 = 1.5x + 12
Rearrange to get: 0.5x = 4
Solve: x = 8
This means Bill's PRESENT age is 8 years old.
So, Sara's PRESENT age is 16
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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