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Two teams are distributing information booklets. Team A dist

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Two teams are distributing information booklets. Team A dist [#permalink] New post 05 Jun 2013, 12:52
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Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900
[Reveal] Spoiler: OA
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 05 Jun 2013, 20:44
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Let x be the no of booklets in each box that team B distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team B. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team B=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy

As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.

Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 05 Jun 2013, 20:58
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Lets assume that the no of boxes distributed by team B =10x
Lets assume that the no of booklet/box for team B =10y

Thus the no of boxes distributed by team A =16x
Thus the no of booklet/box for team A =4y

Total booklets distributed by Team B = 100xy
Total booklets distributed by Team A = 64xy
Total booklets distributed = 164xy = 4.41.xy

So the total no of books distributed must be a multiple of 41, a prime no.
Only option C fulfills this criteria.

Answer C
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 06 Jun 2013, 00:01
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josemarioamaya wrote:
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900


{boxes by A} = {boxes by B}*1.6;
{booklets in box for A} = {booklets in box for B}*0.4;

Total booklets =
= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for B}*0.4*{boxes by B}*1.6 + {booklets in box for B}*{boxes by B} =
= {booklets in box for B}*{boxes by B}(0.64+1) =
= {booklets in box for B}*{boxes by B}*1.64 =
= {booklets in box for B}*{boxes by B}*41/25.

So, we have that the total number of booklets must be a multiple of 41. Only C is a multiple of 41.

Answer: C.

Hope it's clear.
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 11 Nov 2013, 02:04
can you explain how

= {booklets in box for A}*{boxes by A}*1.64 =
= {booklets in box for A}*{boxes by A}*41/25.

1.64 --> 41/25

Since the decimal is a 1.xx, you had to get it to 100. So did you have 164 / 100 and then simplify to 41/25. How do we know that a 41 in the numerator means that the answer choice must have 41 as a factor??
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 11 Nov 2013, 02:15
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laserglare wrote:
can you explain how

= {booklets in box for A}*{boxes by A}*1.64 =
= {booklets in box for A}*{boxes by A}*41/25.

1.64 --> 41/25

Since the decimal is a 1.xx, you had to get it to 100. So did you have 164 / 100 and then simplify to 41/25. How do we know that a 41 in the numerator means that the answer choice must have 41 as a factor??


1.64=1\frac{64}{100}=1\frac{16}{25}=\frac{25+16}{25}=\frac{41}{25} (notice that 41/25 is reduced to its lowest term).

So, we have that:

{Total booklets} = {booklets in box for B}*{boxes by B}*41/25 = ({booklets in box for B}*{boxes by B}/25)*41 = {integer}*41 = {a multiple of 41}.

Hope it's clear.
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 17 Dec 2013, 13:00
Bunuel wrote:
josemarioamaya wrote:
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900


{boxes by B} = {boxes by A}*1.6;
{booklets in box for B} = {booklets in box for A}*0.4;



Doesn't the equation above mean that Team B distributes more boxes than Team A and that Team B has less booklets per box than Team A? I thought the question says that Team A distributes more boxes than Team B and that Team A has fewer booklets per box than Team B. Am I missing something?
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 17 Dec 2013, 22:29
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josemarioamaya wrote:
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900


Team A boxes:team B boxes = 160:100 = 8:5
Hence, Team A distributes 8a boxes while team B distributes 5a boxes.

Team A booklets per box: Team B booklets per box = 40:100 = 2:5 (since 60% fewer means 40%)
Team A's boxes have 2b booklets each while team B's have 5b each.

Total number of booklets = 16ab + 25ab = 41ab

a and b must be integers so the correct answer must be divisible by 41. Answer (C)
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 18 May 2014, 14:58
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Bunuel wrote:
josemarioamaya wrote:
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900


{boxes by B} = {boxes by A}*1.6;
{booklets in box for B} = {booklets in box for A}*0.4;

Total booklets =
= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} +{booklets in box for A}*0.4*{boxes by A}*1.6 =
= {booklets in box for A}*{boxes by A}(1+0.64) =
= {booklets in box for A}*{boxes by A}*1.64 =
= {booklets in box for A}*{boxes by A}*41/25.

So, we have that the total number of booklets must be a multiple of 41. Only C is a multiple of 41.

Answer: C.

Hope it's clear.


Hi Bunuel,

I'm having a hard time following this transition:

= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} + {booklets in box for A}*0.4*{boxes by A}*1.6 =


My original relationship was:

Booklets in A = 1.6 (Booklets in B)
Boxes in A = .4(Boxes in B)

Therefore, shouldn't Booklets in B = Booklets in A/1.6? and the same theory for Boxes in B?

Thanks!
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 19 May 2014, 01:02
Expert's post
russ9 wrote:
Bunuel wrote:
josemarioamaya wrote:
Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team B, but each box of Team A’s has 60% fewer booklets than each box of Team B’s. Which of the following could be the total number of booklets distributed by the two groups?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900


{boxes by B} = {boxes by A}*1.6;
{booklets in box for B} = {booklets in box for A}*0.4;

Total booklets =
= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} +{booklets in box for A}*0.4*{boxes by A}*1.6 =
= {booklets in box for A}*{boxes by A}(1+0.64) =
= {booklets in box for A}*{boxes by A}*1.64 =
= {booklets in box for A}*{boxes by A}*41/25.

So, we have that the total number of booklets must be a multiple of 41. Only C is a multiple of 41.

Answer: C.

Hope it's clear.


Hi Bunuel,

I'm having a hard time following this transition:

= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} + {booklets in box for A}*0.4*{boxes by A}*1.6 =


My original relationship was:

Booklets in A = 1.6 (Booklets in B)
Boxes in A = .4(Boxes in B)

Therefore, shouldn't Booklets in B = Booklets in A/1.6? and the same theory for Boxes in B?

Thanks!


Yes, there was a typo mixing A and B. Edited. It should read:

{boxes by A} = {boxes by B}*1.6;
{booklets in box for A} = {booklets in box for B}*0.4.

Thank you.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 19 May 2014, 17:40
Bunuel wrote:
russ9 wrote:
Bunuel wrote:

{boxes by B} = {boxes by A}*1.6;
{booklets in box for B} = {booklets in box for A}*0.4;

Total booklets =
= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} +{booklets in box for A}*0.4*{boxes by A}*1.6 =
= {booklets in box for A}*{boxes by A}(1+0.64) =
= {booklets in box for A}*{boxes by A}*1.64 =
= {booklets in box for A}*{boxes by A}*41/25.

So, we have that the total number of booklets must be a multiple of 41. Only C is a multiple of 41.

Answer: C.

Hope it's clear.


Hi Bunuel,

I'm having a hard time following this transition:

= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} + {booklets in box for A}*0.4*{boxes by A}*1.6 =


My original relationship was:

Booklets in A = 1.6 (Booklets in B)
Boxes in A = .4(Boxes in B)

Therefore, shouldn't Booklets in B = Booklets in A/1.6? and the same theory for Boxes in B?

Thanks!


Yes, there was a typo mixing A and B. Edited. It should read:

{boxes by A} = {boxes by B}*1.6;
{booklets in box for A} = {booklets in box for B}*0.4.

Thank you.


Great. Thanks for clarifying.

Lastly, I see how you derived the 41/20 and how that leads to 4100. Why/How can we completely ignore the 20 in trying to find a suitable number?

P.S: I think the highlighted part is still a typo but I get the point. Thanks again for your help.
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 19 May 2014, 20:40
Let us take No of boxes distributed by A is a and by B is b.
Also take number of booklets in the boxes distributed by A is x and by B is y.
Since Team A distributes 60% more boxes of booklets than Team B
A = 1.6B
Again ,each box of Team A’s has 60% fewer booklets than each box of Team B’s
x = 0.4y
Number of booklets = Number of boxes X number of booklets in each box
Total Booklets distributed by A = Ax
Total Booklets distributed by B = By
Total booklets distributed = Ax + By
=1.6B*0.4y + By = 1.64By

Since number of boxes, booklets in each box and total booklets distributed are integers, we have to find those values which after equating to 1.64By gives integer value of By. In other words, we have to find that value which when divided by 1.64 gives an integer value. Only option C gives an integer value when divided by 1.64.

Hence C is the answer
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Re: Two teams are distributing information booklets. Team A dist [#permalink] New post 19 May 2014, 23:55
Expert's post
russ9 wrote:
Bunuel wrote:
russ9 wrote:

Hi Bunuel,

I'm having a hard time following this transition:

= {booklets in box for A}*{boxes by A} + {booklets in box for B}*{boxes by B} =
= {booklets in box for A}*{boxes by A} + {booklets in box for A}*0.4*{boxes by A}*1.6 =


My original relationship was:

Booklets in A = 1.6 (Booklets in B)
Boxes in A = .4(Boxes in B)

Therefore, shouldn't Booklets in B = Booklets in A/1.6? and the same theory for Boxes in B?

Thanks!


Yes, there was a typo mixing A and B. Edited. It should read:

{boxes by A} = {boxes by B}*1.6;
{booklets in box for A} = {booklets in box for B}*0.4.

Thank you.


Great. Thanks for clarifying.

Lastly, I see how you derived the 41/20 and how that leads to 4100. Why/How can we completely ignore the 20 in trying to find a suitable number?

P.S: I think the highlighted part is still a typo but I get the point. Thanks again for your help.


Why is there a typo?

As for your question, I think it's addressed here: two-teams-are-distributing-information-booklets-team-a-dist-153853.html#p1290913
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Two teams are distributing information booklets. Team A dist   [#permalink] 19 May 2014, 23:55
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