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Five years ago Jim was three times as old as Raoul was and Monica was

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Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III
[Reveal] Spoiler: OA

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Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 29 Mar 2017, 09:55
Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III


Case 1:-
Let present age of raoul =6yrs
then 5 yrs back his age =1 yrs
then jim =3*Roaul= 3 yrs...
but monica's age was then =1+6=7 yrs

Case 2:-
Let present age of raoul =25yrs
then 5 yrs back his age =20 yrs
then jim =3*Roaul= 60yrs...
but monica's age was then =20+6=26yrs

(1) From case1 --> monica is older than jim
From case2-----> monica is younger than jim
Not true

(2)true for both cases

(3) true for case 2
False for case 1
not true

Ans B

Last edited by rohit8865 on 30 Mar 2017, 09:36, edited 1 time in total.
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Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 29 Mar 2017, 10:12
Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III


Let the present ages of Jim, Raoul and Monica be J, R and M respectively.

5 years ago, we will have the following equations as per the question:
(J-5)=3(R-5) which can be simplified to => J=3R-10 ....................[A]
and, M=R+6 ...................................................................................

As per [A] ,the minimum value of R should be minimum 4 for J to be alive.
Case 1: When R=4, J=2 and M=10
Case 2: When R=20, J=40 and M=26

Therefore, the answer should be II ---> B
[b]
Hi Bunuel, please correct me if I am wrong in my assumption regarding the question.

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Re: Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 29 Mar 2017, 10:25
gmatexam439 wrote:
Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III


Let the present ages of Jim, Raoul and Monica be J, R and M respectively.

5 years ago, we will have the following equations as per the question:
(J-5)=3(R-5) which can be simplified to => J=3R-10 ....................[A]
and, M=R+6 ...................................................................................

As per [A] ,the minimum value of R should be minimum 4for J to be alive.
Case 1: When R=4, J=2 and M=10
Case 2: When R=20, J=40 and M=26

Therefore, the answer should be II ---> B
[b]
Hi Bunuel, please correct me if I am wrong in my assumption regarding the question.


Hope bunuel too respond....

but for now the highlighted part is not correct....
R should be minimum of 5 Yrs ...
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Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 29 Mar 2017, 10:37
rohit8865 wrote:
gmatexam439 wrote:
Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III


Let the present ages of Jim, Raoul and Monica be J, R and M respectively.

5 years ago, we will have the following equations as per the question:
(J-5)=3(R-5) which can be simplified to => J=3R-10 ....................[A]
and, M=R+6 ...................................................................................

As per [A] ,the minimum value of R should be minimum 4for J to be alive.
Case 1: When R=4, J=2 and M=10
Case 2: When R=20, J=40 and M=26

Therefore, the answer should be II ---> B
[b]
Hi Bunuel, please correct me if I am wrong in my assumption regarding the question.


Hope bunuel too respond....

but for now the highlighted part is not correct....
R should be minimum of 5 Yrs ...



I am sorry my silly mistake ... but I think it should 6 and not 5 because if R=5, J will be 0 five years ago which is not as per our assumption .... therefore if R>=6, then
case1: When R=6, J=8 and M=12
case2: as per above post;

Therefore answer should be E and not C.
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Re: Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 29 Mar 2017, 18:44
Assume ages of Joe,Roula and monica five years back = J ,R,M respectivily

given that J = 3R and M=R+6 (this is 5 years back)
so 5 years from now the ages will be (we need to add 10 to each age)
J = 3R+10
M= R+16
and R = R+10

I. Monica is older than Jim.
Not true. because R should be at least 10 years old then J >M

II. Raoul is six years younger than Monica
True. From the equation R-M = 16-10 =6

III. The combined ages of Jim and Raoul are more than Monica's age.
True. J+M = 4R+20
M = R+16
therefore J+M > M

Hence answer is E



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Re: Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 30 Mar 2017, 12:44
Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III


Let CURRENT ages of Jim=j, Raoul=r, and Monica=m

Five Years ago: Jim=j-5, Raoul=r-5, and Monica=m-5

Set up equations:
j-5=3(r-5)...........j+10=3r
m-5=r-5+6........m=r+6

Because we have only 2 equations in 3 variables, there is open cases. So we need to be careful to choose numbers that cover multiple cases.

Plug in numbers:
case 1: r=7, j=11, m=13, After 5 Yeas: r=12, j=16, m=18

case 2: r=10, j=20, m=16, After 5 Years: r=15, j=25, m=21

Checking Numeral I as it is most frequent.

From case 1: m>j

From case 2: m<j

Not always true...........Eliminate A,C & D

To save time, check Numeral III not II. Because if you do II and get correct then you will move to III. But we do III first, you will eliminate one choice in one step.

From case 1: r+j>m

From case 2: r+j>m

Therefore, Eliminate choice B

Answer: E
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Re: Five years ago Jim was three times as old as Raoul was and Monica was [#permalink]

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New post 04 Apr 2017, 15:04
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Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?

I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.

A. I only
B. II only
C. I and II
D. I and III
E. II and III



We can let Jim’s age today = J, Raoul’s age today = R, and Monica’s age today = M.

Let’s set up their ages 5 years ago: Jim was (J - 5), Rauol was (R - 5), and Monica was (M - 5).

Since five years ago Jim was three times as old as Raoul was:

(J - 5) = 3(R - 5)

J - 5 = 3R - 15

J = 3R - 10

Since five years ago Monica was six years older than Raoul was:

(M - 5) = (R - 5) + 6

M - 5 = R + 1

M = R + 6

Notice that Raoul is the youngest of the three people, and Raoul must be more than 5 years old since only then can we talk about their ages 5 years ago.

Let’s now test each Roman numeral:

I. Monica is older than Jim.

We can represent Monica's age in 5 years as M + 5, or R + 6 + 5 = R + 11.

We can represent Jim’s age in 5 years as J + 5, or 3R - 10 + 5 = 3R - 5.

Is M + 5 > J + 5 ?

Is R + 11 > 3R - 5 ?

Is 16 > 2R ?

Is 8 > R ?

Is R < 8?

We know that R > 5, however, we can’t determine whether R < 8. Thus, we cannot determine whether Monica is older than Jim.

II. Raoul is six years younger than Monica

Since M = R + 6, in 5 years Raoul will still be 6 years younger than Monica. Roman numeral II is true.

III. The combined ages of Jim and Raoul are more than Monica's age.

We already see that in 5 years, Monica’s age will be R + 11, Jim’s age will be 3R - 5, and Raoul’s age will be R + 5. We can create the following inequality:

Is 3R - 5 + R + 5 > R + 11 ?

Is 4R > R + 11 ?

Is 3R > 11 ?

Is R > 11/3 ?

We know that R > 5, so R > 11/3. Thus Roman numeral III is true.

Answer: E
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Re: Five years ago Jim was three times as old as Raoul was and Monica was   [#permalink] 04 Apr 2017, 15:04
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