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# Bobby and his younger brother Johnny have the same birthday. Johnny's

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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03 Nov 2014, 08:31
1
16
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:37) correct 57% (02:48) wrong based on 186 sessions

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Tough and Tricky questions: Word Problems.

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.

Kudos for a correct solution.

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Posts: 7035
Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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08 Mar 2016, 20:42
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2
RITU700 wrote:
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.

Hi,
A real GOOD Q worth the TAG 700 level..

To do this Q, you have to UNDERSTAND what it means...

Let the ages be..
Bobby Now= B
Bobby then=b
Johnny Now=J and
Johnny then=j..
1) Johnny's age now is the same as Bobby's age was when Johnny was half as old as Bobby is now
When johnny was half as old as bobby nwo... j=B/2..
what was bobby then b, so J=b..
now the difference in Johnny's age then and now, and bobby's age then and now should be SAME, as same years have passed for both..
therefore J-j=B-b

Solution--

1) J-j=B-b
2) J=b, and
3) j=B/2
lets get all terms in values of B or b..
so
b-B/2=B-b..
2b=3B/2..

since we have ratios of all through above ratio, we require a NUMERIC value to find answer..

Lets see the statements
(1) Bobby is currently four times as old as he was when Johnny was born.
Just gives another ratio ... no NUMERIC value
Insuff

(2) Bobby was six years old when Johnny was born.
this gives us the difference in age of two J-B=j-b=6..
now j=B/2 so j-b=B/2-b=6..
or b=B/2 + 6..
Substitute this in our Equation 2b=3B/2..
so 2(B/2 + 6)=3B/2..
B+12=3B/2
or 2B+12*2=3B..
B=24..
Suff

B..

Ofcourse, we can do a bit of intelligent guessing,
the Q gives us a ratio..
STatement 1 gives us another Ratio
so 1 can not be suff on its own.. eliminate A and D..
Statement 2 gives you a numeric value..
Now you have a numeric value and a ratio..
in likelihood we should get an answer, eliminate E....
betweenB and C, fo rthe above mentioned reason you should be inclined towards B..
atleast you have got your probability of answering correctly to 1/2 from 1/5..

+1 kudos for good Q to you and to manhattan mgmat
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Joined: 12 Jul 2017
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Schools: Boston U '20
Re: Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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14 Jul 2017, 10:03
5
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.
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 50619
Re: Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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04 Nov 2014, 09:28
Bunuel wrote:

Tough and Tricky questions: Word Problems.

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.

Kudos for a correct solution.

Check other Age Problems HERE.
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Re: Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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04 Nov 2014, 10:10
1
3
Bunuel wrote:

Tough and Tricky questions: Word Problems.

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.

Kudos for a correct solution.

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

J=B-(J-B/2)
4J=3B

Stmt 1:
Bobby is currently four times as old as he was when Johnny was born.
B = 4(b-j) , b and j being ages when johnny was born. J being zero. NO information given. can not be solved.

Stmt 2:
B-J=6, question stem can be solved.

Ans B
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Joined: 17 Dec 2015
Posts: 41
Re: Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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10 Feb 2016, 21:31
Let J, B be the current ages of Johnny and Bobby respectively.
D be the difference when Johnny was half as old as Bobby is now.
So, J-D=B/2 and J=B-D which gives B=4/3J
from statement 1 : no information about either B or J : insuff
from statement 2 : B=J+6
which gives us values for B and J : suff
hit kudos if you like the solution
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Joined: 04 Aug 2010
Posts: 306
Schools: Dartmouth College
Bobby and his younger brother Johnny have the same birthday. Johnny's  [#permalink]

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20 Jul 2018, 02:56
Bunuel wrote:

Tough and Tricky questions: Word Problems.

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.

I received a PM requesting that I comment.

Let Bobby's current age = B and Johnny's current age = J.
Let Bobby's earlier age = B-x and Johnny's earlier age = J-x.
Here, x = the number of years between the CURRENT year and the year WHEN JOHNNY WAS HALF AS OLD AS BOBBY IS NOW.

Johnny was half as old as Bobby is now.
Since Johnny's EARLIER age is equal to half Bobby's CURRENT age, we get:
J - x = B/2
J - B/2 = x

Johnny's age now is the same as Bobby's age was.
Since Johnny's CURRENT age is equal to Bobby's EARLIER age, we get:
J = B - x
x = B - J.

The expressions in blue are both equal to $$x$$ and thus are equal to EACH OTHER:
B - J = J - B/2
2B - 2J = 2J - B
3B = 4J
B = (4/3)J

Statement 1: Bobby is currently four times as old as he was when Johnny was born
Case 1: J=3, implying that B = (4/3)(3) = 4
Since J=3, Johnny was born 3 years ago.
Since B=4, at Johnny's birth 3 years ago Bobby must have been 1 year old, satisfying the condition that Bobby is currently four times as old as he was when Johnny was born.

Case 2: J=6, implying that B = (4/3)(6) = 8
Since J=6, Johnny was born 6 years ago.
Since B=8, at Johnny's birth 6 years ago Bobby must have been 2 years old, satisfying the condition that Bobby is currently four times as old as he was when Johnny was born.

Since B can be different values, INSUFFICIENT.

Statement 2: Bobby was six years old when Johnny was born
In other words, Bobby is 6 years older than Johnny:
B = J+6
Since we have two distinct linear equations (the green equations above) and two variables (B and J), we can solve for the two variables.
Thus, the value of B can be determined.
SUFFICIENT.

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Bobby and his younger brother Johnny have the same birthday. Johnny's &nbs [#permalink] 20 Jul 2018, 02:56
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