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.
The OA is B .
How can I conlcude that statement (1) is not sufficient and statement (2) is sufficient? Experts, may you help me?
In four years, Andy will be twice as old as Betsy. How . . .
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The prompt should clarify the intended meaning, as follows:Vincen 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.
In four years, Andy will be twice as old as Betsy will be in four years.
Translated into math:
A + 4 = 2(B + 4)
A + 4 = 2B + 8
A = 2B + 4
Statement 1: Four years ago, Andy was twice as old as Betsy is now.
A - 4 = 2B
A = 2B + 4.
Same equation as in the prompt.
INSUFFICIENT.
Statement 2 should clarify the intended meaning, as follows:
Four years ago, Andy was four times as old as Betsy was four years ago.
Translated into math:
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, the value of B can be determined.
SUFFICIENT.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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
Student Review #2
Student Review #3
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
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Given: In four years, Andy will be twice as old as Betsy.Vincen 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.
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