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Math Expert V
Joined: 02 Sep 2009
Posts: 59730
Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 61% (02:41) correct 39% (03:20) wrong based on 70 sessions

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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).

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Re: Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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Bunuel wrote:
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).

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???
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Manager  B
Joined: 28 Jun 2018
Posts: 73
Re: Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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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...
Intern  B
Joined: 16 Oct 2018
Posts: 1
Re: Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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I think it's:

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

Senior Manager  P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 444
Re: Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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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
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Re: Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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Bunuel wrote:
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).

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

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Re: Kenny is three times older than Bob. In P years he will be twice older  [#permalink]

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Quote:
We can create the equations:

X = 3B

X/3 = B

and

X + P = 2(B + P + Q) - I assume you got this equation from "In P years he will be twice older than Bob will be Q years later".
Substituting, we have:

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

Dividing both sides by 2, we have:

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

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

Thank you!
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You are missing on great learning if you don't know what this is: Project SC Butler Re: Kenny is three times older than Bob. In P years he will be twice older   [#permalink] 23 Nov 2019, 10:29
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