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Presents Bill received [Word Translation - Kaplan Premier]?

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Presents Bill received [Word Translation - Kaplan Premier]?

by JGoode » Mon Jun 28, 2010 8:48 am
This question is taken from Kaplan Premier 2010-2011 on page 514 of the Word Problems chapter. Unfortunately, and rather annoyingly, as the question is used as an example to highlight how one should approach a word problem, the book does not provide neither answer choices or the actual answer. Thus, I don't know whether the answer should be algebraic or an actual whole number? The book does provide some kind of break down as to the equations used for each person, therefore I will post this below in the spoiler section - although I think there is a typo in Kaplan's working out which I would be grateful if someone could clarify.

"Bill received three fewer presents for his birthday than did John, who received half the number of presents as Betty and Sue averaged. If Sue received as many as John and Betty put together, and Bill and John together received one more than did Betty, then how many presents did Bill receive?"

[spoiler]Kaplan states:
"Bill received three fewer presents for his birthday than did John" therefore: Bill= J - 3
"John received half the number of presents as Betty and Sue averaged" therefore: J= (Betty + S)/2 (<<<Surely this is a typo as it only calculates the average of Betty and Sue, rather than 0.5 of their average?)
"Sue received as many as John and Betty put together" therefore: S= J + Betty
"Bill and John together received one more than did Betty" therefore: Bill + J= Betty + 1[/spoiler]

Any help would be great! Thanks.
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by albatross86 » Mon Jun 28, 2010 9:15 am
You are indeed correct. Half of the average would be (B + S) / 4

Well spotted!

W = J - 3 ...1
J = (B + S) / 4 ...2
S = J + B ...3
W + J = B + 1 ...4

W = ?

From 2 and 3:

S = (B+S)/4 + B

=> 4S = B + S + 4B

=> S = 5/3*B ....5

Substituting this in eqn. 2

=> J = (B + 5/3*B) / 4

=> J = 2/3*B ...6

Substituting this in eqn. 1

=> W = 2/3*B - 3 ...7

Substituting 6 an 7 in eqn 4

=> 2/3*B - 3 + 2/3*B = B + 1

=> 4/3*B - B = 1 + 3

=> B = 12 ...8

Substituting in 7

=> W = 2/3*12 - 3

=> W = 5 ...Ans


Phew.
Last edited by albatross86 on Mon Jun 28, 2010 9:40 am, edited 1 time in total.
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by amising6 » Mon Jun 28, 2010 9:29 am
JGoode wrote:This question is taken from Kaplan Premier 2010-2011 on page 514 of the Word Problems chapter. Unfortunately, and rather annoyingly, as the question is used as an example to highlight how one should approach a word problem, the book does not provide neither answer choices or the actual answer. Thus, I don't know whether the answer should be algebraic or an actual whole number? The book does provide some kind of break down as to the equations used for each person, therefore I will post this below in the spoiler section - although I think there is a typo in Kaplan's working out which I would be grateful if someone could clarify.

"Bill received three fewer presents for his birthday than did John, who received half the number of presents as Betty and Sue averaged. If Sue received as many as John and Betty put together, and Bill and John together received one more than did Betty, then how many presents did Bill receive?"

[spoiler]Kaplan states:
"Bill received three fewer presents for his birthday than did John" therefore: Bill= J - 3
"John received half the number of presents as Betty and Sue averaged" therefore: J= (Betty + S)/2 (<<<Surely this is a typo as it only calculates the average of Betty and Sue, rather than 0.5 of their average?)
"Sue received as many as John and Betty put together" therefore: S= J + Betty
"Bill and John together received one more than did Betty" therefore: Bill + J= Betty + 1[/spoiler]

Any help would be great! Thanks.

if bill received x then
john had=x+3 ........ eq1
(betty+sue)/2=2(x+3)
(betty+sue)=4(x+3) ------ eq 2
sue=john+betty
sue=x+3+betty substituting this in eq2
x+3+betty+betty=4(x+3)
2betty=3(x+3)
betty=3(x+3)/2
bill+john=x+john
x+john=1+(3(x+3)/2) (given Bill and John together received one more than did Betty)
john=((11+x)/2) .......eq3
now from eq1 we know john had x+3
so equating eq1 and eq3
x+3 =((11+x)/2
2x+6=11+x
x=5
hence
answer 5
off two many calculation but go step by step
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by Stuart@KaplanGMAT » Mon Jun 28, 2010 9:47 am
JGoode wrote:This question is taken from Kaplan Premier 2010-2011 on page 514 of the Word Problems chapter. Unfortunately, and rather annoyingly, as the question is used as an example to highlight how one should approach a word problem, the book does not provide neither answer choices or the actual answer. Thus, I don't know whether the answer should be algebraic or an actual whole number? The book does provide some kind of break down as to the equations used for each person, therefore I will post this below in the spoiler section - although I think there is a typo in Kaplan's working out which I would be grateful if someone could clarify.

"Bill received three fewer presents for his birthday than did John, who received half the number of presents as Betty and Sue averaged. If Sue received as many as John and Betty put together, and Bill and John together received one more than did Betty, then how many presents did Bill receive?"

[spoiler]Kaplan states:
"Bill received three fewer presents for his birthday than did John" therefore: Bill= J - 3
"John received half the number of presents as Betty and Sue averaged" therefore: J= (Betty + S)/2 (<<<Surely this is a typo as it only calculates the average of Betty and Sue, rather than 0.5 of their average?)
"Sue received as many as John and Betty put together" therefore: S= J + Betty
"Bill and John together received one more than did Betty" therefore: Bill + J= Betty + 1[/spoiler]

Any help would be great! Thanks.
Thanks for spotting that! I'll pass it on to our development team.
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by JGoode » Mon Jun 28, 2010 4:39 pm
Fantastic explanations Abhay and Amising, I'm very grateful! Wow that is quite an intense amount of working out to do. If that appeared on the GMAT, clearly you have to be very confident as there are so many areas you can slip up. And thanks also for clarifying Kaplan's typo.
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by KapTeacherEli » Mon Jun 28, 2010 10:09 pm
Stuart Kovinsky wrote: Thanks for spotting that! I'll pass it on to our development team.
Beat you to it!

But JGoode, let me repeat Stuart's thanks. Be reassured that we've already caught the typo and it's on the block for a fix in the next printing.
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Cambridge, MA
www.kaptest.com/gmat

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by fitzgerald23 » Wed Jun 30, 2010 8:04 pm
Here is how I would set this up.

Choose Bill = X

John received 3 more than Bill, so John = X + 3

Betty = 1 Less than Bill and John = X + X + 3 -1 = 2x +2

Sue= As much as John and Betty= X + 3 + 2x + 2 = 3X + 5

To solve it use the info that John is half the average of Betty and Sue

X + 3 = (3X + 5 + 2X + 2)/4
4X + 12 = 5X + 7
5=X

So Bill received 5 gifts.
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