Problem Solving

Hi boomgoesthegmat,

To start, there's a typo in your transcription - it's supposed to read "...and 1/2 as many as Paula...."

We can answer this question by TESTing VALUES or by doing algebra...

IF...
Jeff = 2 books
David = 6 books = D books
Paula = 12 books

The total number of books = 2+6+12 = 20

So we're looking for an answer that equals 20 when D=6. There's only one answer that matches...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

boomgoesthegmat wrote:David has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d ?

A) (5/6)d
B) (7/3)d
C) (10/3)d
D) (7/2)d
E) (9/2)d

OA: C

Rich has demonstrated the INPUT-OUTPUT approach. Here's an algebraic approach.

d = # of books that David has

David has 3 times as many books as Jeff
So, d/3 = # of books that Jeff has

David has 1/2 as many books as Paula
So, 2d = # of books that Paula has

How many books do the three of them have altogether, in terms of d ?
TOTAL # of books = d + d/3 + 2d
= 3d/3 + d/3 + 6d/3
= [spoiler]10d/3[/spoiler]
= C

---------------------------------

Rich and I have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Here are some more questions to practice with:
- https://www.beatthegmat.com/what-mistak ... 76293.html
- https://www.beatthegmat.com/car-dealer- ... 74136.html
- https://www.beatthegmat.com/ps-rate-times-t276107.html
- https://www.beatthegmat.com/to-find-the ... 73338.html
- https://www.beatthegmat.com/y-dollars-f ... 73031.html
- https://www.beatthegmat.com/meters-in-x ... 73854.html
- https://www.beatthegmat.com/a-better-ex ... 79396.html


Cheers,
Brent

boomgoesthegmat wrote:David has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d ?

A) (5/6)d
B) (7/3)d
C) (10/3)d
D) (7/2)d
E) (9/2)d

We can let the number of books David has = d, the number of books Jeff has = j, and the number of books Paula has = p

We are given that David has 3 times as many books as Jeff. We can now express this in an equation.

d = 3j

d/3 = j

We are also given that David has 1/2 as many books as Paula. We can also express this in an equation.

d = (1/2)p

2d = p

We need to determine, in terms of d, the sum of the number of books for David, Jeff, and Paula. Thus, we have:

d + d/3 + 2d

3d/3 + d/3 + 6d/3 = 10d/3 = (10/3)d

Answer: C