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.
OA B
Source: Veritas Prep
In four years, Andy will be twice as old as Betsy. How old
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Say Andy's age is A and Betsy's age is B.BTGmoderatorDC 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.
OA B
Source: Veritas Prep
Thus, from the information, in four years, Andy will be twice as old as Betsy, we have
A + 4 = 2(B + 4) ---(1)
We have to get the value of B.
Let's take each statement one by one.
(1) Four years ago, Andy was twice as old as Betsy is now.
A - 4 = 2B ---(2)
From (1) and (2), we can't get the value of B. Insufficient.
(2) Four years ago, Andy was four times as old as Betsy.
A - 4 = 4(B - 4) ---(3)
From (1) and (3), we B = 8. Sufficient.
The correct answer: B
Hope this helps!
-Jay
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- Brent@GMATPrepNow
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Given: In four years, Andy will be twice as old as Betsy.BTGmoderatorDC 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.
OA B
Source: Veritas Prep
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 is equations 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
Answer: B
Cheers,
Brent
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In four years, Andy will be twice as old as Betsy.BTGmoderatorDC 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.
Since Andy's age in 4 years is twice Betsy's age in 4 years, we get:
A+4 = 2(B+4)
A+4 = 2B+8
A-2B = 4.
Statement 1:
Since Andy's age 4 years ago is twice Betsy's current age, we get:
A-4 = 2B
A-2B = 4.
Same equation as given in the prompt.
Thus, Statement 1 offers no new information.
INSUFFICIENT.
Statement 2:
Since Andy's age 4 years ago is 4 times Betsy's age 4 years ago, we get:
A-4 = 4(B-4)
A-4 = 4B-16
A-4B= -12.
Since we have two variables (A and B) and two distinct linear equations (A-2B=4 and A-4B=-12), we can solve for the two variables.
Thus, Betty's current age can be determined.
SUFFICIENT.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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