David has d books, which is 3 times as many as Jeff and 1/2

Question

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

Bunuel · Accepted Answer

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

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

Answer: C.

aeglorre · Answer

We are given:   and  , 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

BrainLab · Answer

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

luckyme17187 · Answer

David = d ; jeff=f ; paula = p

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

d+j+p = d+ d/3 + 2d = 10d /3

PareshGmat · Answer

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

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

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

Answer = C

mcelroytutoring · Answer

Attached is a visual that should help.

JeffTargetTestPrep · Answer

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.

susheelh · Answer

Hello Moderators,

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

Bunuel · Answer

_________________
Edited. Thank you.

dave13 · Answer

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!

Bunuel · Answer

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.

EMPOWERgmatRichC · Answer

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...

Final Answer:  C

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

TheUltimateWinner · Answer

dave13 
''In terms of d'' means--> You must keep the alphabet ''d'' in the answer options. You're NOT allowed to put the value of ''d'' in the answer option.

TheUltimateWinner · Answer

Total books has to be more than  d  books. But, choice A carries less than  d  books because of proper fraction. So, we can cross choice A. 
--AA

keshavmishra · Answer

given that 
david = d books
jeff = d/3 books
paula = 2d

total books = d+(d/3)+2d
LCM --> 10d/3
Answer C

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=5er3q8XF_n4

YuktiMaheshwari · Answer

David = d books
Jeff = d/3 books
Paula = 2d

total books = d+(d/3)+2d = 10d/3 (C)

Posted from my mobile device

DanTheGMATMan · Answer

No sweat. Just express everything in terms of d:

https://www.youtube.com/watch?v=AYVXEOJ7TBQ

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=C0-ziBsq92M Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

David has d books, which is 3 times as many as Jeff and 1/2

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David has d books, which is 3 times as many as Jeff and 1/2

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