• Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Manhattan GMAT 700+ Problem - July 17, 2006

This topic has 2 member replies
Kevin Community Manager Default Avatar
Joined
05 Jun 2006
Posted:
47 messages
Thanked:
7 times

Manhattan GMAT 700+ Problem - July 17, 2006

Post Mon Jul 17, 2006 9:16 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Most Manhattan GMAT students are trying to break the 700 barrier. As a result, we've developed our own math problems written at the 700+ level; these are the types of questions you'll WANT to see, when you are working at that level. Try to solve this 700+ level problem (I'll post the solution next Monday).

    Now and Then:
    Bobby and his younger brother Johnny have the same birthday. Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now. What is Bobby's age now?

    (1) Bobby is currently four times as old as he was when Johnny was born.
    (2) Bobby was six years old when Johnny was born.

    (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
    (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
    (C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
    (D) EACH statement ALONE is sufficient to answer the question.
    (E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

    _________________
    Kevin Fitzgerald
    Director of Marketing and Student Relations
    Manhattan GMAT
    800-576-4626

    Contributor to Beat The GMAT!

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    mba4ms Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    28 Apr 2006
    Posted:
    7 messages
    Thanked:
    1 times
    Post Tue Jul 18, 2006 6:07 am
    I think the answer is (B)

    Here is my solution -

    Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now means
    J = B/2 + (B-J)

    J = Johnny's present age
    B/2 = Johnny's age when he was half the age of Bobby's present age
    B/2 + (J-B) = Bobby's age was when Johnny was half as old as Bobby's present age

    Solves to 4J=3B

    Using statement (1), Bobby is currently four times as old as he was when Johnny was born.
    B = 4*(B-J) => 4J = 3B. Hence not sufficient.

    Using statement (2), Bobby was six years old when Johnny was born.
    B-J=6. Which is sufficient to answer the ques about Bobby's present age.

    Although we dont need to calcuate but still ... Bobby's present age is 24 and Johnny's present age is 18.

    Kevin, I would say tough one! Really enjoyed doing it.

    _________________
    ms

    Thanked by: Anaira Mitch
    Kevin Community Manager Default Avatar
    Joined
    05 Jun 2006
    Posted:
    47 messages
    Thanked:
    7 times
    Post Wed Jul 26, 2006 11:47 am
    Answer

    In questions like this, it helps to record the given information in a table. Upon initial reading, the second sentence is probably very confusing but what is clear is that it discusses the ages of the two boys at two different points in time: let's refer to them as "now", and "then". So, let's construct a table such as the one below. Let x and y denote the boys' ages "now":

    Johnny's age Bobby's age
    now x y
    then


    Now, re-read the first few words of the second sentence: "Johnny's age now is the same as Bobby's age . . . 'then'". We can fill in one more entry of the table as shown:

    Johnny's age Bobby's age
    now x y
    then x



    Finally, the rest of the second sentence tells us that "then" was the time when Johnny's age was half Bobby's current age; i.e., Johnny's age "then" was (1/2)y. We can complete the table as follows:

    Johnny's age Bobby's age
    now x y
    then (1/2)y x



    One way to solve this problem is to realize that, as two people age, the ratio of their ages changes but the difference in their ages remains constant. In particular, the difference in the boys ages "now'" must be the same as the difference in their ages "then". This leads to the equation: y - x = x - (1/2)y, which reduces to x = (3/4)y; Johnny is currently three-fourths as old as Bobby.

    Without another equation, however, we can't solve for the values of either x or y. (Alternatively, we could compute the elapsed time between "then" and "now" for each boy and set the two equal; this leads to the same equation as above.)

    (1) INSUFFICIENT: Bobby's age at the time of Johnny's birth is the same as the difference between their ages, y - x. So statement (1) tells us that y = 4(y - x), which reduces to x = (3/4)y. This adds no more information to what we already knew! Statement (1) is insufficient.

    (2) SUFFICIENT: This tells us that Bobby is 6 years older than Johnny; i.e., y = x + 6. This gives us a second equations in the two unknowns so, except in some rare cases, we should be able to solve for both x and y -- statement (2) is sufficient. Just to verify, substitute x = (3/4)y into the second equation to obtain y = (3/4)y + 6 , which implies y = 24. Bobby is currently 24 and Johnny is currently 18.

    The correct answer is B, Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.

    _________________
    Kevin Fitzgerald
    Director of Marketing and Student Relations
    Manhattan GMAT
    800-576-4626

    Contributor to Beat The GMAT!

    Thanked by: Sriram18

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 65 topics
    3 Roland2rule 49 topics
    4 ardz24 44 topics
    5 LUANDATO 23 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    147 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    103 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    102 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    94 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts