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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]

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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?

A. 2,000
B. 3,200
C. 4,100
D. 4,800
E. 4,900
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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)
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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.
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Re: Two teams are distributing information booklets. Team A dist  [#permalink]

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05 Jun 2013, 21:58
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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.

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

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06 Jun 2013, 01:01
11
5
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.

Hope it's clear.
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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??
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Re: Two teams are distributing information booklets. Team A dist  [#permalink]

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11 Nov 2013, 03:15
1
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]

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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)

Dear VeritasPrepKarishma and other experts,

I nearly follow Karishma's way of solving this math.
Please correct me if I'm wrong. Thank you!!

Below is my solution:

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

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07 Dec 2014, 20:50
1
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)

Dear VeritasPrepKarishma and other experts,

I nearly follow Karishma's way of solving this math.
Please correct me if I'm wrong. Thank you!!

Below is my solution:

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

Yes, this is correct. You can note here itself:
T = xn * 41/40

T is a multiple of 41 (since xn is an integer) so answer must be (C)
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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.
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Re: Two teams are distributing information booklets. Team A dist  [#permalink]

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09 Dec 2014, 08:40
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.

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

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10 Dec 2014, 21:29
1
.......................... Team A ......................... Team B

Boxes .................. $$\frac{160x}{100}$$ .......................... x (Say "x" boxes are distributed by Team B)

Books ..................... $$\frac{40y}{100}$$ ........................... y (Say "y" books are per box of Team B)

$$Total books = xy + xy \frac{160}{100} * \frac{40}{100} = \frac{164}{100} xy = \frac{41}{25} xy$$

On comparing with OA, only 4100 is divisible by 41

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

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10 Apr 2015, 09:58
1
Hi Bunnel,

I solved it like this please let me know if this is correct.

The number of boxes for team A = 160
The number of boxes for team B = 100

Each box of A contains = 40 Booklets
Each box of B contains = 100 Booklets

Total Booklets = 160*40 + 100*100 = 6400 + 10000 = 16400

Since 16400 is a multiple of 4100 so I chose answer C

Let me know what you think.

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

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10 Apr 2015, 10:37
1
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

B distributes y boxes with each box having 100 magazines.

A will distribute 1.6y boxes with each box having 40 magazines.

1.6y *40 + y*100 =164y =41*4*y

Looking at answer choices . C looks to fit perfectly When y=25.
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Re: Two teams are distributing information booklets. Team A dist  [#permalink]

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19 Apr 2016, 11:20
Can anyone explain why it's not a if there is a 2 to 3 ratio (or am i reading this wrong?)

Because 2000 with 800 vs 1200 is a 40 percent to 60 percent ratio... or am i reading this wrong?
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Re: Two teams are distributing information booklets. Team A dist  [#permalink]

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19 Apr 2016, 22:35
Can anyone explain why it's not a if there is a 2 to 3 ratio (or am i reading this wrong?)

Because 2000 with 800 vs 1200 is a 40 percent to 60 percent ratio... or am i reading this wrong?

It isn't a simple ratio of 2:3.

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 gives 60% extra so 3/5th extra. If B gives 5 boxes, A gives 3/5th more i.e. 3 more so total 8 boxes.
So the ratio is 8:5 boxes.

But no of books in boxes is different.
Team A boxes have 60% fewer books so 3/5th fewer books. So if team B has 5 books per box, team A has 3 fewer i.e. only 2 books per box.

So in every 8 boxes team A gives, it gives 8*2 = 16 books.
For every 5 boxes team B gives, it gives 5*5 = 25 books.

So ratio is actually 16:25.
Total will be a multiple of 16+25 = 41.

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

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03 Jun 2017, 03:07
From the stem we know:
# of boxes: A=1.6B, now to make the calculations easier translate the decimal into a ratio: A=8/5B-->or 5A=8B.
# of booklets: A=0.4B again make the simplification: A=2/5B--> 5A = 2B.
Now find first the least possible combinations: for the # of boxes that would be 8 for A and 5 for B and for the # of booklets 2 for A and 5 for B.
As we want to find the total # of booklets multiply first the number of boxes and booklets of Team A together (8*2)=16 and then from Team B (5*5)=25.
Adding the two least possible combinations of each team we get 16+25=41. Now we know that the total sum must be a multiple of 41, so C is the answer.
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Re: Two teams are distributing information booklets. Team A dist  [#permalink]

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05 Feb 2018, 08:43
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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

This REAL WORLD question requires us to find values that are positive INTEGERS.
So, for example, we can't have 1.3 boxes or 12.44 boxes.

Team A distributes 60% more boxes of booklets than Team B
Since we must have positive integers for these values, the SMALLEST possible numbers are as follows:
Team A: 8 boxes
Team B: 5 boxes

Team A has 60% fewer booklets per box than Team B
Since we must have positive integers for these values, the SMALLEST possible numbers are as follows:
Team A: 2 booklets per box
Team B: 5 booklets per box

In this case, the TOTAL number of booklets distributed by EACH TEAM is as follows:
Team A: (8)(2) = 16
Team B: (5)(5) = 25

So, the TOTAL = 16 + 25 = 41

Check the answer choices....nope, 41 is not an option.

Now recognize that multiples of 41 will also work.
For example, if each team sold TWICE as many boxes than they did in our first scenario, then the total would equal 82.
If each team sold 10 times as many boxes than they did in our first scenario, then the total would equal 410.
And so on.

When we scan the answer choices, we see that C (4100) is a multiple of 41.

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

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06 Feb 2018, 18:33
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

We can let the number of boxes of booklets distributed by Team B = b and thus the number of booklets distributed by Team A = 1.6b.

We can let the number of booklets per box for Team B = n and thus the number of booklets per box for Team A = 0.4n.

So the total number of booklets distributed is:

(1.6b)(0.4n) + bn = 0.64bn + bn = 1.64bn

Since b and n are integers, so is bn. Thus, we see we need to find an answer choice that results in an integer when divided by 1.64.

Since 4100 produces an integer when divided by 1.64, 4100 could be the number of booklets distributed by the two groups.

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

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16 Feb 2018, 18:55
Hi All,

This question can be solved by TESTing VALUES (and involves a Number Property):

We're told that Team A distributes 60% MORE boxes of booklets than Team B, BUT each of Team A's boxes has 60% FEWER booklets than each of Team B's boxes...

If...
Team B = 100 boxes
Team A = 160 boxes

And if....
Team B = 100 pamphlets/box
Team A = 40 pamphlets/box

Under these circumstances...
Team A = 40(160) = 6400 pamphlets
Team B = 100(100) = 10,000 pamphlets
Total = 16,400 pamphlets

Now, this answer (16,400) is NOT among the choices, but notice how it's exactly 4 times Answer C???

If you keep the number of boxes as is and change the number of pamphlets by dividing each number by 4....
Team B = 25 pamphlets/box
Team A = 10 pamphlets/box

Then...
Team A = 10(160) = 1600 pamphlets
Team B = 25(100) = 2500 pamphlets
Total = 4100 pamphlets

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Re: Two teams are distributing information booklets. Team A dist   [#permalink] 16 Feb 2018, 18:55

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