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Two teams are distributing information booklets. Team A dist [#permalink]

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05 Jun 2013, 13:52

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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?

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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05 Jun 2013, 21:44

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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.

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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06 Jun 2013, 01:01

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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.

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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11 Nov 2013, 03:04

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??

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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11 Nov 2013, 03:15

Expert's post

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}.

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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17 Dec 2013, 14:00

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?

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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17 Dec 2013, 23:29

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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) _________________

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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18 May 2014, 15:58

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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?

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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19 May 2014, 02:02

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.

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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19 May 2014, 18:40

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.

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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19 May 2014, 21:40

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.

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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20 May 2014, 00:55

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.

Two teams are distributing information booklets. Team A dist [#permalink]

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05 Dec 2014, 20:56

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

Answer:

Box A: x Box B: x/1.6

Booklet A: 0.4n BookletB: n

Total number of booklets = T = x*0.4n + x/1.6*n = xn * 41/40 => xn = (T * 40)/41. xn MUST be an integer => T must be divisible by 41 => C

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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06 Dec 2014, 07:42

VeritasPrepKarishma 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

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)

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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07 Dec 2014, 20:50

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Expert's post

haihai89 wrote:

VeritasPrepKarishma 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

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)

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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08 Dec 2014, 12:58

Bunuel can you plz help me out here, I also followed the same approach that most people had, but with some difference in the end: I multiplied the total number of boxes and total booklets in each box

Team B=x boxes, so team A = 1.6 x boxes (1.6x+x=2.6x boxes) Team B = y booklets/box, so team A=0.4 Y (1.4y booklets/box)

I multiplied 2.6x into 1.4y and got answer 3.64xy which simplifies into 91/25. I cant figure out why cant this give me the correct answer. Thanks in advance !

Re: Two teams are distributing information booklets. Team A dist [#permalink]

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09 Dec 2014, 08:40

Expert's post

sunaimshadmani wrote:

Bunuel can you plz help me out here, I also followed the same approach that most people had, but with some difference in the end: I multiplied the total number of boxes and total booklets in each box

Team B=x boxes, so team A = 1.6 x boxes (1.6x+x=2.6x boxes) Team B = y booklets/box, so team A=0.4 Y (1.4y booklets/box)

I multiplied 2.6x into 1.4y and got answer 3.64xy which simplifies into 91/25. I cant figure out why cant this give me the correct answer. Thanks in advance !

Say you have 2 red and 3 blue boxes. The number of booklets in each red box is 1 and the number of booklets in each blue box is 2. What is the total number of booklets? Is it 2*1 + 3*2 = 8 or (2 + 3)(1 + 2) = 10? _________________

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