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

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

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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