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Manager  Joined: 02 Dec 2012
Posts: 173
David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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Question Stats: 89% (01:18) correct 11% (01:50) wrong based on 1444 sessions

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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) $$\frac{5}{6}*d$$

(B) $$\frac{7}{3}*d$$

(C) $$\frac{10}{3}*d$$

(D) $$\frac{7}{2}*d$$

(E) $$\frac{9}{2}*d$$
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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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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

David has d books;
Jeff has d/3 books;
Paula has 2d books;

Total = d+d/3+2d=10d/3.

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Manager  Joined: 12 Jan 2013
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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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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 are given: [(d/3) = J] and [(d/2) = P], and we also have Davids own books = d

Just add all three together and express them in common denominator of 3: (3/3)*d + (d/3) + (6/3)*d = (10/3)*d
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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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It's also possible to solve with smart numbers
David has 120
Jeff 120/3 = 40
Paula 120*2 = 240
Total 400 Books --> 400/120 = 10/3
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Manager  Joined: 07 Apr 2014
Posts: 100
Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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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

David = d ; jeff=f ; paula = p

d=3j ; d=p(1/2)

d+j+p = d+ d/3 + 2d = 10d /3
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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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David ................ Jeff ................... Paula

d ........................ $$\frac{d}{3}$$ ....................... 2d

$$Total = 3d + \frac{d}{3} = \frac{10d}{3}$$

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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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Attached is a visual that should help.
Attachments Screen Shot 2016-05-25 at 9.42.32 PM.png [ 110.22 KiB | Viewed 18265 times ]

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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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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

Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.

number of books David has = d

number of books Jeff has = j

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 ½ as many books as Paula. We can also express this in an equation.

d = (1/2)p

2d = p

Notice that we immediately solved for j in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. 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

Getting a common denominator of 3, we have:

3d/3 + d/3 + 6d/3 = 10d/3 = 10/3*d

The answer is C.
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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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Hello Moderators,

Do you think the answers choices should be made math friendly? It will be helpful when solving.
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Posts: 58442
Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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susheelh wrote:
Hello Moderators,

Do you think the answers choices should be made math friendly? It will be helpful when solving.

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Edited. Thank you.
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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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JeffTargetTestPrep 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

Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.

number of books David has = d

number of books Jeff has = j

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 ½ as many books as Paula. We can also express this in an equation.

d = (1/2)p

2d = p

Notice that we immediately solved for j in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. 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

Getting a common denominator of 3, we have:

3d/3 + d/3 + 6d/3 = 10d/3 = 10/3*d

The answer is C.

Hi. Can you please explain what does "j in terms of d and p in terms of d " mean ? I cant somehow digest the meaning of " in terms of " Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 58442
Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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dave13 wrote:
JeffTargetTestPrep 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

Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, let’s start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.

number of books David has = d

number of books Jeff has = j

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 ½ as many books as Paula. We can also express this in an equation.

d = (1/2)p

2d = p

Notice that we immediately solved for j in terms of d and p in terms of d. Getting j and p in terms of d is useful when setting up our final expression. 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

Getting a common denominator of 3, we have:

3d/3 + d/3 + 6d/3 = 10d/3 = 10/3*d

The answer is C.

Hi. Can you please explain what does "j in terms of d and p in terms of d " mean ? I cant somehow digest the meaning of " in terms of " Thanks!

Express x in terms of y means to write x = some equation with y. For example, in x = 12y^2 - 3, x is expressed in terms of y.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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Hi All,

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...

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Re: David has d books, which is 3 times as many as Jeff and 1/2  [#permalink]

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_________________ Re: David has d books, which is 3 times as many as Jeff and 1/2   [#permalink] 10 Feb 2019, 13:15
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