Kenny is three times older than Bob. In P years he will be twice older

Question

Kenny is three times older than Bob. In P years he will be twice older than Bob will be Q years later. Which of the following represents Kenny's age comparing to Bob's? (If X = Kenny's age)

A. X + P = 6X (P+Q).

B. 2(X+P) = 3X + Q.

C. (X+P)/2 = X/3 + P + Q.

D. 3(X+P+Q) = 2X.

E. 3X = 2(P + Q).

GMATinsight · Answer

Kenny's present age = X
Bob's present age = B

Kenny is three times older than Bob, i.e. X = 3B
i.e. B = X/3

P years later, Kenny's age = X+P
Q years later, Bob's Age = B+Q

X+P = 2*(B+Q)
i.e. X+P = 2*(X/3) + 2Q

i.e. (X+P)/2 = X + Q

i.e. X/3 = 2Q-P

C option looks the closest but not the correct one as per option.

Is there any mistake in Options???

hibobotamuss · Answer

What am I doing wrong?

Ken's age: X
Bob's: X/3

In P years, Ken's age: X+P
In Q Years, Bob's age: X/3 + Q

Equation,
(X+P) = 2 (X/3 + Q)
X+P = 2( x+3Q / 3)
3 (X+P) = 2x + 6Q
3(X+P-2Q) = 2x

I can't get this to match anything...

giupitex · Answer

I think it's:

X=3B
X+P=2(B+P+Q)

This one lead to C

energetics · Answer

Plugging in easy numbers: 
Plug in 10 for Bob, so Kenny is now 30.
Plug in 10 for P since (30+10) is twice (10+10).
Since Kenny is already twice as old as Bob, plug in 0 for Q (this could be an unworkable number if there was division or multiplication)

Check C first:
(30+10)/2 = 30/3 + 10
20 = 20, works.

If you scan the other choices, you can see that in A), D) and E) are out immediately since we're essentially comparing multiples of 30 to something smaller..

B) 2(30+10) = 90 + 0
80 ≠ 90

ScottTargetTestPrep · Answer

We can create the equations:

X = 3B

X/3 = B

and

X + P = 2(B + P + Q)

Substituting, we have:

X + P = 2(X/3 + P + Q)

Dividing both sides by 2, we have:

(X + P)/2 = X/3 + P + Q

Answer: C

TheNightKing · Answer

ScottTargetTestPrep 
Hello, Can you please explain me the highlighted part in Red.

Thank you!

KarishmaB · Answer

The question is written poorly. 'than Bob will be Q years later' implies 'Bob's current age + Q years' but what it wants to say is 'Bob's current age + P + Q years'. This needs to be re-written. Something like: 'After P years pass, Kenny will be twice the age that Bob will be after another Q years'
Also, what is the meaning of 'Which of the following represents Kenny's age comparing to Bob's?' We already know that Kenny is three times older than Bob.

Solving the question as per its intent:

Kenny is three times older than Bob.

Since Kenny's age is X, Bob's age is X/3.

In P years he will be twice older than Bob will be Q years later.

In P years, Kenny will be (X + P). In another Q years, Bob will be (X/3 + P + Q).
Then (X + P) = 2 * (X/3 + P + Q)

Which of the following represents Kenny's age comparing to Bob's?  
If I am to choose an option which shows the equation above,

A. X + P = 6X (P+Q).

Our equations says, (X + P) = 2 * (X/3 + P + Q). 
The LHS is the same but not the RHS.

B. 2(X+P) = 3X + Q.

As per our equation, 2(X + P) = 4 * (X/3 + P + Q)
The LHS is the same but not the RHS.

C. (X+P)/2 = X/3 + P + Q.

As per our equation, (X + P)/2 = (X/3 + P + Q)
Both same.

Answer (C)

bumpbot · Answer

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Kenny is three times older than Bob. In P years he will be twice older

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Kenny is three times older than Bob. In P years he will be twice older

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