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# If Bob's age is three times Tony's age, what is Bob's age?

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If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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Updated on: 20 Aug 2019, 09:53
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If Bob's age is three times David's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

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Originally posted by Bunuel on 19 Aug 2019, 07:33.
Last edited by Bunuel on 20 Aug 2019, 09:53, edited 2 times in total.
TYPO EDITED.
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 07:39
2
The problem gives us one condition and the question

Condition of problem: (1): B = 3T
Question: B?

(2): B - 2 = 5(D - 2) NOT SUFFICIENT because combining (1) and (2) gives 2 equations and 3 variables

(3): B+12 = 1.5(D + 12) NOT SUFFICIENT because combining (1) and (3) gives 2 equations and 3 variables

(2) and (3) together gives us two variables and two equations, so we can calculate the value of B

OPTION C
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If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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Updated on: 20 Aug 2019, 11:22
From the question stem we know that Bob’s age (x) is three times David’s age (y). We are to find Bob’s age.

x = 3y .....(1)

Statement 1 says that Bob’s age was five times David’s age two years ago. This translates into the following equation:
x-2=5(y-2)
x-5y=-8 .......(2)
We have two equations and two variables. So we can solve (1) and (2) to get x=12 and y=4. Hence we know that David is 12 years old. Statement 1 alone is therefore sufficient.

Statement 2 says that in twelve years time Bob’s age will be 50% more than the age of David.
x+12 = 1.5*(y+12)
2x-3y = 12 ......(3)
We have two equations once again with two variables which we are able to solve to get x=12 and y=4. We can therefore say answer that David is 12 years old. Statement 2 alone is also sufficient.
Clearly statement 2 is also insufficient on its own.

Answer is therefore D.

Originally posted by eakabuah on 19 Aug 2019, 08:12.
Last edited by eakabuah on 20 Aug 2019, 11:22, edited 1 time in total.
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 08:20
Let the present age of Bob = B and
present age of Tony = T
Given: B = 3*T

Few things I noticed is B should be a multiple of 3. We need to find a unique value for Bob's age.

Statement 1: Two years ago, Bob age was exactly 5 times David's age.

Let David's present age = D
2 years ago, Bob was B-2 and David was D-2,

B-2 = 5*(D-2)
B-2 = 5D-10
B = 5D-8

Not enough information to find Bob's age. Hence, statement 1 is INSUFFICIENT

Statement 2: Twelve years from now, Bob's age will be exactly 50% greater than David's age.
After 12 years, Bob's age will be B+12 and David's age will be D+12

B+12 = 1.5*(D+12)
B+12 = 1.5D+18
B = 1.5D+6

Again there is not enough information to find Bob's age. Hence, statement 2 is INSUFFICIENT

(1)+(2)

Combining both the equations from statement 1 and 2,

B = 5D-8
B = 1.5D+6

5D-8 = 1.5D+6
3.5D = 14
D = 4

Substituting D in B,

=> B = 5*(4)-8 = 12

Therefore the answer is C
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 08:21
Assume present ages of Bob, Tony and David be A, B and D respectively

Question stem says $$B = 3T$$ . What is B?

Statement 1
$$B-2=5(D-2)$$Just one equation in B and D, We can't find B with this. Moreover, we cant use the equation in question stem either, as it involves B and T not B and D. Strike off A and D

Statement 2
$$B+ 12 =1.5* (D+12)$$. For similar reasons as statement 1, Statement 2 alone is NOT SUFFICIENT Strike off B as well

St 1 + St 2 We now have 2 different equations in B and D. Hence we will get the value of both B and D from this.

Hence, IMO C
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 08:22
Given: B=3T
To find: B=?

(1) Two years ago, Bob age was exactly 5 times David's age.
(B-2)=5(D-2)
B-2= 5D-10
B= 5D-8 and B=3T........two unknowns INSUFFICIENT

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.
B+12=1.5(D+12)
B+12=1.5D+18
B=1.5D+6 and B=3T........two unknowns INSUFFICIENT

(1)+(2) => B= 5D-8 (eq1) and B=1.5D+6(eq.2).....SUFFICIENT (2 variables)....but still let's solve

substituting eq1 in eq2
5D-8=1.5D+6
D=4

B= 5D-8=5(4)-8 = 12
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 08:29
Given: Bob's age is three times Tony's age

Asked: What is Bob's age?

Let Bob's age be b
and let Tony's age be t

b = 3t. (1)

(1) Two years ago, Bob age was exactly 5 times David's age.
b-2 = 5(d-2) = 5d -10.
b = 5d -8 = 3t (2)
If d =4 b = 20-8 = 12 = 3*4
If d =19; b=87 = 3*29
NOT SUFFICIENT

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.
b+12 = 1.5 (d+12)
b + 12 = 1.5d + 18
b = 1.5d + 6 = 3t (3)
If d=2; b=9 = 3*3
If d=4; b=12 =3*4
NOT SUFFICIENT

Combining (1) & (2)
(1) Two years ago, Bob age was exactly 5 times David's age.
b-2 = 5(d-2) = 5d -10.
b = 5d -8 (2)
(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.
b = 1.5d + 6. (3)
b = 5d -8 = 1.5d + 6
3.5d = 14
d = 4
b = 20 -8 = 12
Bob's age is 12
SUFFICIENT

IMO C
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 09:11
Let Bob’s age now = B and Tony’s age now = T
We are told B = 3T and asked to find B

St 1: Let David’s age now = D
B-2 = 5(D-2) ==> B = 5D-8 ==> not sufficient since it tells us nothing about Tony

St 2: B+12 = (D+12) (1+5/100) ==> B = 1.5D + 6 ==> not sufficient since it tells us nothing about Tony

Combine Sts 1 and 2:

5D – 8 = 1.5D +6 ==> D = 14/3.5 = 4
Therefore B = 5(4) – 8 = 12
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 09:20
If Bob's age is three times Tony's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

given B= 3D b=?

statement 1 gives b-2 = 5 (d-2) USING GIVEN AND THIS , we can solve for b hence sufficient

statement 2 gives b +12 = 3/2 (d+12) using given and this, we can solve for b . hence sufficient

ans is D
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 10:10
If Bob's age is three times Tony's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

given B=3t
#1 Two years ago, Bob age was exactly 5 times David's age.
b-2= 5*(d-5)
insufficient we get an eqn ; b=5d-25
#2
Twelve years from now, Bob'b age will be exactly 50% greater than David's age.
b+12 = (d+12)+1.5d
again insufficient
from 1 & 2
we can find b
IMO C
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 10:12
1
If Bob's age is three times Tony's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

Let Bob’s age = B and Tony’s age = T. So B = 3T from questions. B = ?
Statement 1) B – 2 = 5(T - 2)
At this point we can see that we can solve or B since we have two equations and thus need not to solve further. However we can solve as follows:
 3T – 2 = 5T – 10
 2T = 8
 T = 4
 B = 3x4 = 12
SUFFICIENT.

Statement 2) B + 12 = 1.5(T + 12)
Similar to statement 1 we can see at this point that we can solve for B. Solving for B as follows:
 3T + 12 = 1.5T + 18
 1.5T = 6
 T = 4
 B = 3x4 = 12
SUFFICIENT.
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 10:54
IMO correct answer is C

St I - Two years ago, Bob age was exactly 5 times David's age.

Let X yrs be Bob's Current Age & Y yrs be David's Current age.
Accordingly,
X-2=5(Y-2) ---------(1)

St 2 Twelve years from now, Bob'b age will be exactly 50% greater than David's age.
accordingly,
X+12=3/2(Y+12)---------(2)

2 equations & 2 Variables - Solvable
Correct answer is C
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 10:56
Age of bob = B ; Age of Tony = T

B=3T

To find B?

(1) David age = D

B - 2 =5(D-2)
=> 5D - B = 8 ; This statement alone is insufficient.

(2) B + 12 = 1.5(D+12)
=> B - 1.5D = 6 ; Insufficient

(1) + (2) 3.5D = 14 => d = 4 ; B = 22 ; Sufficient. (C)
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 13:02
Quote:
If Bob's age is three times Tony's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.
(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

given: if b=3t, then b=?
(1) b-2=5(d-2); insuf.
(2) b+12=3/2(d+12); insuf.
(1&2) b=5(d-2)+2 and b=3/2(d+12)-12, equate d to find b; sufic.

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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 21:41
Let be
-----Bob's age=b
-----Tom's age =t

--> b=?

Statement1: Two years ago, Bob age was exactly 5 times David's age.

Let be David's age =d

(b-2)=5(d-2)
b-2=5d-10
b=5d-8
No info about Tom's age and David's age
Insufficient

Statement2: Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

(b+12)=(d+2)+($$\frac{50}{100}$$)*(d+2)=$$\frac{3}{2}$$*(d+2)
(b+12)=$$\frac{3}{2}$$*(d+12)
2b+24=3d+36
2b=3d+12

No info about Tom's age and David's age
Insufficient

Taken together 1 and 2,
b=5d-8
2b=3d+12
--> 2(5d-8)=3d+12
10d-16=3d+12
7d=28
d=4
--> b=5d-8=20-8=12
b=12

Sufficient
The answer is C.
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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19 Aug 2019, 22:18
If Bob's age is three times Tony's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

GIVEN: B = 3T, B = ?

1. (B - 2) = 5(D-2) ...
So what? This itself do not give further info. Hence A is out, automatically making D out as well.

2. B +12 = 1.5(D+12)
Again, this info ALONE do not give further info. Hence B is out.

Combine info 1 & 2, we can solve to find David is 4 years old.

<<< How to find David's Age >>>

From the 1st equation ...

B-2 = 5D-10

B = 5D-8 ---- a)

Now substitute a) into the second equation

5D-8+12=1.5(D+12)

5D+4 = 1.5D + 18
3.5D = 14
D = 4
----------------------------

Since now we know David's age, we plug D's age into any of the equation 1 or 2 to find B's age, which both yield 12 as Bob's age.

Hence C is and should be the answer.

GG to dummy info about Tony ( ͡° ͜ʖ ͡°)
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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20 Aug 2019, 16:52
Bunuel The original question had Bob and Tony in the question stem, so I guess that is why option D is the correct answer, otherwise the answer would have been C.
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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20 Aug 2019, 19:58
lnm87 wrote:
If Bob's age is three times Tony's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.

(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

Let Bob’s age = B and Tony’s age = T. So B = 3T from questions. B = ?
Statement 1) B – 2 = 5(T - 2)
At this point we can see that we can solve or B since we have two equations and thus need not to solve further. However we can solve as follows:
 3T – 2 = 5T – 10
 2T = 8
 T = 4
 B = 3x4 = 12
SUFFICIENT.

Statement 2) B + 12 = 1.5(T + 12)
Similar to statement 1 we can see at this point that we can solve for B. Solving for B as follows:
 3T + 12 = 1.5T + 18
 1.5T = 6
 T = 4
 B = 3x4 = 12
SUFFICIENT.

Got it wrong in the worst possible manner. I must have carried another question's picture to solve this one.
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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20 Aug 2019, 20:01
lnm87 Don't beat yourself up. There was an error in the original question. If you look closely, you will find that the original question had Bob and Tony, not Bob and David. That little mistake sent many of us in the wrong direction (answer choice C).
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Re: If Bob's age is three times Tony's age, what is Bob's age?  [#permalink]

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20 Aug 2019, 20:10
bebs

Ya... But even after so, I should have been able to solve it(wrong question) correctly. Anyway..
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Re: If Bob's age is three times Tony's age, what is Bob's age?   [#permalink] 20 Aug 2019, 20:10

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