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# In four years, Andy will be twice as old as Betsy. How old is Betsy?

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In four years, Andy will be twice as old as Betsy. How old is Betsy?  [#permalink]

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27 Jul 2017, 00:42
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Difficulty:

75% (hard)

Question Stats:

53% (01:37) correct 47% (01:09) wrong based on 108 sessions

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In four years, Andy will be twice as old as Betsy. How old is Betsy?

(2) Four years ago, Andy was twice as old as Betsy is now.

(2) Four years ago, Andy was four times as old as Betsy.

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Re: In four years, Andy will be twice as old as Betsy. How old is Betsy?  [#permalink]

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27 Jul 2017, 01:37
Bunuel wrote:
In four years, Andy will be twice as old as Betsy. How old is Betsy?

(1) Four years ago, Andy was twice as old as Betsy is now.

(2) Four years ago, Andy was four times as old as Betsy.

It should be B

Let A and B be respective ages of Andy and Betsy today. Question provides us this statement.

$$A + 4 = 2 (B + 4)$$

Statement 1: Insufficient

$$A - 4 = 2*B$$

This is basically the same equation as equation 1 with just 8 subtracted from both sides.

Statement 2: Sufficient

$$A - 4 = 4 (B - 4)$$

$$A - 4 = 4B - 16$$
$$A + 4 = 2B + 8$$ - subtracting original equation from equation of statement 2.
$$-8 = 2B - 24$$
$$2B = 16$$
$$B = 8$$
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Re: In four years, Andy will be twice as old as Betsy. How old is Betsy?  [#permalink]

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27 Jul 2017, 03:22
Bunuel wrote:
In four years, Andy will be twice as old as Betsy. How old is Betsy?

(2) Four years ago, Andy was twice as old as Betsy is now.

(2) Four years ago, Andy was four times as old as Betsy.

a+4 = 2 (b+4)
a+4 = 2b+8
a-2b = 4
b=?

(1) a-4 = 2 b
a-2b = 4
Nothing new
Not Sufficient

(2) a-4 = 4 (b-4)
a-4 = 4b - 16
a-4b = -12

we already know a-2b = 4
two unique equations two variables
we can solve for a and b to be 20 and 8 respectively

B
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Re: In four years, Andy will be twice as old as Betsy. How old is Betsy?  [#permalink]

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27 Jul 2017, 04:43
Bunuel wrote:
In four years, Andy will be twice as old as Betsy. How old is Betsy?

(2) Four years ago, Andy was twice as old as Betsy is now.

(2) Four years ago, Andy was four times as old as Betsy.

Looks like we have 2 variables (A - Andy's present age and B - Betsy's present age)
The question stem gives an equation: 4 + A = 2 (B + 4)
A = 2B + 4
We see that we will get another equation from each statement. So you might feel that since it is a DS question and you don't really need to solve to get the answer, you should mark D and move on. But this is a DS pitfall. You have to ensure that the two equations are distinct for you to get a unique solution.

(1) Four years ago, Andy was twice as old as Betsy is now.
A - 4 = 2B
Note that this is same as A = 2B + 4
Hence, we do not have 2 distinct equations and hence we will not be able to solve for A and B.

(2) Four years ago, Andy was four times as old as Betsy.
A - 4 = 4*(B - 4)
A = 4B - 12
This does give us a different equation and hence we will be able to solve for A and B.

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In four years, Andy will be twice as old as Betsy. How old is Betsy?  [#permalink]

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28 Nov 2017, 07:09
Top Contributor
1
Bunuel wrote:
In four years, Andy will be twice as old as Betsy. How old is Betsy?

(2) Four years ago, Andy was twice as old as Betsy is now.

(2) Four years ago, Andy was four times as old as Betsy.

Given: In four years, Andy will be twice as old as Betsy.
Let A = Andy's PRESENT age
Let B = Betsy's PRESENT age
So, A+4 = Andy's age IN 4 YEARS
And so, B+4 = Betsy's age IN 4 YEARS
If Andy will be twice as old as Betsy IN 4 YEARS, we can write: A+4 = 2(B+4)
Expand: A + 4 = 2B + 8
Rearrange to get: A - 2B = 4

Target question: How old is Betsy (i.e., what is the value of B)?

Statement 1: Four years ago, Andy was twice as old as Betsy is now.
A-4 = Andy's age 4 YEARS AGO
B is Betsy's PRESENT age
We can write: A - 4 = 2B
Rearrange to get: A - 2B = 4
IMPORTANT: This equation is the SAME as the equation we derived from the given information (A - 2B = 4)
So, statement 1 does NOT provide any new information.
As such, this information is not sufficient to answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: Four years ago, Andy was four times as old as Betsy.
A-4 = Andy's age 4 YEARS AGO
B-4 = Betsy's age 4 YEARS AGO
We can write: A - 4 = 4(B - 4)
Expand: A - 4 = 4B - 16
Rearrange to get: A - 4B = -12
We also know that A - 2B = 4
Since we have two DIFFERENT linear equations with 2 variables, we can DEFINITELY solve this system for A and B (but we won't actually do so, since that would be a waste of time)
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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In four years, Andy will be twice as old as Betsy. How old is Betsy? &nbs [#permalink] 28 Nov 2017, 07:09
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