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Source: Official Guide for the GMAT 13th Ed. Problem Solving; #131 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #131

1

David has d books, which is 3

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?

2 Explanations

1

SONIKA VASANTH

David had 3 times as many as Jeff
How did we get 1/3rds for Jeff
and Paula can have 1d when David have half of it
I am bit confused. Please guide

Thanks in advance:)

Dec 8, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Sonika :)

Good questions! We're describing the number of books for the three in terms of the number of books that David has, d.

Let's say that Jeff has j number of books. Since David has three times as many books as Jeff,

3j = d

Now, let's solve for j to describe the number of books Jeff has in terms of d:

3j = d
j = (1/3)d

We can check this is correct using actual values. Let's say that David has 12 books, which means that Jeff has 4 books:

j = (1/3)d
j = (1/3)*12
j = 4 <-- this matches what we said above!

On the other hand, David has half of the number of books as Paula. Another way of saying this is that Paula has double the number of books as David:

p = 2d

Again, let's say that David has 4 books. That would mean that Paula has 8 books (4/8 = 1/2):

p = 2*4 = 8 <-- again this matches what we said just above.

Since we want to solve for the number of books in terms of d (the number of books David has), we must solve for the number of books that Jeff and Paula have, j and p respectively, in terms of d. And that's the process I've shown above!

Hope this clears up your doubts :)

Dec 9, 2016 • Reply

1

Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

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