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Boxes weigh 5, 7 or 11 pounds.
We will need either the numbers or ratios of all the three boxes to solve this:
Statement 1: No. of boxes with 5 pounds = 2 ones with 11 pounds. Doesn't give any relation for the 7 pound boxes.
Insufficient.

Statement 2:
The 5,7 and 11 pounds boxes are in the ratio 4:2:2

= ((5*4x) + (7*2x) + (11*2x))/(4x+2x+2x)
Remove the x by cancelling out and this gives average as: 7..
Sufficient.

Hence answer is B.
Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Each box in a shipment weighs 5, 7, or 11 pounds. We have to find the mean weight of boxes.
Let the number of 5, 7, 11 pound boxes be k, l, m respectively.

Evaluating answer choices
A) This says that there is double the number of 5pound boxes as 11 pound boxes.
k = 2m
we do not have any idea of l. Hence we cannot find mean. This statement is insufficient

B) k : l : m = 4 : 2 : 2
Let the constant of proportionality be c
Mean = (5*4c + 7*2c + 11*2c) / (4c + 2c + 2c)
= (20 + 14 + 22) / 8
= 56 / 8
= 7
This statement is sufficient
Hence answer is B
Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Let x = 5 lbs boxes, y = 7lbs boxes and z = 11 lbs boxes

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds. Hence given that x=2z but no information about y is provided. Hence insufficient.


(2) x:y:z = 4:4:2

Let x = 4k , y=4k and z =2k

So average weight will be
(5*4k+7*4k+11*2k)/(4k+2k+2k)= 7 lbs

Hence Statement 2 alone is sufficient .

Hence, answer B
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Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Given each box weighs 5p, 7p, 11p

to find avg of all boxes.

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.
No idea abt 7 pound boxes. Insufficient. AD/BCE

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.
5p, 7p, 11p
number: 4x, 2x, 2x

Average = (5*4x + 7*2x + 11*2x)/(4x+2x+2x)

obviously we'll get a real number. Sufficient
AD/BCE


Correct Answer: B
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Statement 1 5 pounds=A, 7 pounds=B, 11 Pounds=C
A= 2C, AM= (5A+7B+11C)/(A+B+C)= 21C+7B/3C+B=7
Statement 1 is sufficient

Statement 2
A:B:C::4:2:2 or A:B:C::2:1:1
or else A=2C again same as statement 1
AM=7. Statement 2 is sufficient
Answer is D.
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Avg weight (A) = 5x+7y+11z/x+y+z

St1: x=2z

5(2z)+7y+11z/2z+z+y = 21z+7y/3z+y = 7(3z+y)/3z+y = 7. Sufficient.

St2: x:y:z = 4:2:2 => x=4k, y=2k, z=2k

So, 5(4k)+7(2k)+11(2k)/8k = 56k/8k = 7. Sufficient.

Option D

Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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1)

5 pound boxes = 2x
11 pound boxes = x
7 pound boxes = y

Average = 10x + 11x + 7y / 3x + y

21x+7y / 3x + y

7(3x+y)/(3x+y)

= 7


Sufficient.

2) 5 pound : 7 pound : 11 pound ::4:2:2
= 2: 1: 1

This is the information as statement 1.

Hence, sufficent.

Option D
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Let's assume a = number of 5 pound boxes, b = 7lb boxes & c = 11lb boxes

Given: 3 types of boxes are there - 5lbs, 7lbs & 11lbs

Question: To find average weight.

Need: Either need the values of a, b & c or the ratio of a, b & c.

1) a = 2c

No info about b, hence can't make any conclusion

so D & A out.

2) a:b:c = 4:2:2

Boom we got what we wanted & we can find the average weight using this.

Answer: B

No need to solve, but doing it here just for the clarity:

=> \frac{4(5) + 2(7) + 2(11)}{4+2+2}
=> \frac{56}{8}
=> 7
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Let say, number of boxes of 5 pounds, 7 pounds and 11 pounds are a,b,c respectively.

Average weight per box = (5a+7b+11c)/(a+b+c)

Statement I a=2c. Nothing mentioned about b. Not sufficient to answer.
Statement II a:b:c = 4:2:2
a=4k, b=2k, c=2k
Average weight/box = (5*4k + 7*2k + 11*2k)/(4k+2k+2k) = 56/8 = 7pounds. (Sufficient)
Correct Answer B
Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Let's assess each statement 1 by 1 :

1. Let the number of 11ln boxes be x => Number of 5lb boxes = 2x, Number of 7lb boxes = y(unknown) => average = (5(2x)+7y+11x)/(2x+y+x) = 21x+7y/3x+y
Depends on y so not sufficient.
2. ratio of 5+7+11 = 4:2:2
Average = (5*4+7*2+11*2)/(4+2+2) = 56/8 = 7
Sufficient.

Hence statement 2 alone is sufficient => B
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Each of the boxes in a shipment weighs either 5 pounds (a), 7 pounds (b) , or 11 pounds (c). What is the average (arithmetic mean) weight per box = (5a+7b+11c)/(a+b+c)

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.
a=2c
Put in the above equation
Average = (5(2c)+7b+11c)/(2c+b+c) = (21c+7b)/(3c+b) = 7(3c+b)/(3c+b) = 7
It is Sufficient

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.
a:b:c = 4:2:2
Put in above equation
Average = (5(4x)+7(2x)+11(2x))/(4x+2x+2x) = 56x/8x = 7
It is sufficient

D
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(1)
5 pounds: 2x
7 pounds: y
11 pounds: x

5*2x+7*y+11*x = 10x+7y+11x=21x+7y

(21x+7y)/(3x+y) = 7 * (3x+y)/(3x+y) = 7

Sufficient

(2)
5 pounds: 4a
7 pounds: 2a
11 pounds: 2a

5*4a+7*2a+11*2a = 56a

56a/8a = 7

Sufficient

IMO D
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Weights can be [5, 7, 11] pounds

Average mean of the boxes on shipment
Let 5-pound boxes be a
Let 7-pound boxes be b
Let 11-pound boxes be c

=> Average mean = (5a + 7b + 11c)/(a + b + c) ---- (1)

1. a = 2c
=> Average mean = (5(2c) + 7b + 11c)/(2c + b + c)
= (10c + 7b + 11c)(3c + b)
= (21c + 7b)/(3c + b)
= 7(3c + b)/(3c + b)
=> Average mean = 7
Sufficient

2. a:b:c = 4:2:2
By using values like a = 4x, b = 2x and c = 2x it would be sufficient to reduce eq(1) to a valid number
Sufficient

Option D

Bunuel
Each of the boxes in a shipment weigh either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Since, both the statements on the whole doesn't provide us with the single answer as both are pointing to the data that 5 pound boxes are twice in number compared to 11 pound boxes.. We still don't know the number of 7-pound boxes.. So, the correct answer is choice:E
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average = (5*a + 7*b + 11*c)/(a+b+c)

(1)
(5*2c + 7*b + 11*c)/(2c+b+c) = (21c + 7b)/(3c+b) = 7

Condition sufficient

(2)
4:2:2 is the same as 2:1:1
(5*2c + 7*c + 11*c)/(2c+c+c) = 28c/4c = 7

Condition sufficient

Answer D
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From what we know,
Each box weights 5,7 or 11 pounds and we need to find average weight per box
Let the number of 5,7 and 11 pound boxes be x,y and z

=> Average weight = (5x+7y+11z) / x+y+z
Lets check each given statement 1 by 1

Statement (1),
The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

=> x = 2z
We dont know anything about the 7 pound boxes.

Statement 1 is insufficient

Statement(2),
The ratio of the number of boxes weighing 5 pounds, 7 pounds and 11 pounds is 4 to 2 to 2

=> Let,
x = 4a
y = 2a
z = 2a

Average = (5x + 7y + 11z) / x+y+z = (5(4a) + 7(2a) + 11(2a)) / 4a+2a+2a = 56a / 8a = 7

Statement(2) alone is sufficient

B. Statement (2) alone is sufficient, but statement(1) alone is not
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Bunuel
Each of the boxes in a shipment weighs either 5 pounds, 7 pounds, or 11 pounds. What is the average (arithmetic mean) weight per box in the shipment?

(1) The number of boxes that weigh 5 pounds is twice as many as the number that weigh 11 pounds.

(2) The ratio of the number of boxes weighing 5 pounds, 7 pounds, and 11 pounds is 4 to 2 to 2.

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Lets consider the number of boxes x, y and z weighing 5 , 7 and 11 pounds respectively..

To find = 5x+7y +11z /(x+y+z)

AD --> x= 2y ---> Avg = 27x + 7y /(3x+z ) --Insufficient

B ---> x:y:z = 4:2:2 ---> Avg = 20k+14k+22k/(8k) = 56/8 = 7 - Sufficient Answer B
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