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Some milk was added to each of the 5 cans. If standard deviation of the quantity of milk in the 5 cans at the beginning was 3.5 liters, what was the standard deviation of the quantity of milk in the 5 cans at the end?
(1)  In each can, 20% of existing amount of milk was added.
(2)  The average volume of milk in the cans at the end was 25 liters.
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
  • c)
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
  • d)
    EACH statement ALONE is sufficient. 
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Some milk was added to each of the 5 cans. If standard deviation of th...
Step 1 & 2 – Understand the question and draw inferences from the question statement.
To Find:  We have to find the standard deviation of the volume of milk in 5 cans after some was added to each of the cans.
Given: Standard Deviation of the 5 cans of milk in the beginning is 3.5 liters.
Let the quantity of milk in 5 cans be a, b, c, d and e.
Finding standard deviation of {a, b, c, d, e}
Step 1
Mean of {a,b,c, d, e} = {a + b + c + d + e}/5 = M
Step 2
Distances of each point from the mean:
  • a-M
  • b-M
  • c-M
  • d-M
  • e-M
Step 3
Squared Distance from Mean
  • = (a -M)2 + (b-M)2 + (c -M)2 + (d -M)2 + (e -M)2
Step 4
Average = {(a -M)2 + (b-M)2 + (c -M)2 + (d -M)2 + (e -M)2}  /5
Step 5
  • Standard Deviation = √ [{(a -M)2 + (b-M)2 + (c -M)2 + (d -M)2 + (e -M)2}  / 5] = 3.5
Step 3 – Analyze Statement 1 Independently
Statement 1 – In each can, 20% of the existing quantity of milk was added
The amount of milk be a+20%a, b+20%b, c+20%c, d+20%d, e+20%e
Remember:  If all the elements of a set are increased by the x%, the standard deviation of the set also increases by the x%.
So the standard deviation of this set will increase by 20%
New S = 3.5 + 20% *3.5 = Unique number
Alternatively you can calculate the standard deviation of this set as shown below by following same step by step method.
 Set = { a+20%a, b+20%b, c+20%c, d+20%d, e+20%e }
Step 1
  • Sum of {a+20%a, b+20%b, c+20%c, d+20%d, e+20%e}
    • = (1.2)(a + b + c + d + e)
    • Mean of {a+20%a, b+20%b, c+20%c, d+20%d, e+20%e}
      • = (1.2)(a + b + c + d + e)/5 = 1.2 M
Step 2
Distances of each point from the mean:
  • 1.2 (a –M)
  • 1.2 (b-M)
  • 1.2(c-M)
  • 1.2(d-M)
  • 1.2(e-M)
Step 3
Squared Distance from Mean
  • = 1.22 [(a -M)2 + (b-M)2 + (c -M)2 + (d -M)2 + (e -M)2 ]
Step 4
  • Average = 1.22{(a -M)2 + (b-M)2 + (c -M)2 + (d -M)2 + (e -M)2}  /5
Step 5
  • Standard Deviation = 1.2 √ [{(a -M)2 + (b-M)2 + (c -M)2 + (d -M)2 + (e -M)2}  / 5]
    • = 1.2 *3.5 = 3.5 + 20% *3.5
    • = Unique value
Statement (1) is independently sufficient to arrive at a unique answer.
Step 4 – Analyze Statement 2 Independently
Statement 2 -The average quantity of milk in the cans at the end was 25 liters
We do not know how the quantity changed in each of the cans.
Thus, the information given in statement (2) is not sufficient to arrive at a unique solution.
Step 5 – Analyze Both Statements Together
We get a unique value in Step 3.
Statement (1) independently is sufficient to arrive at a unique answer
Answer:  Option (A)
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Most Upvoted Answer
Some milk was added to each of the 5 cans. If standard deviation of th...
Concept: To find the standard deviation of the quantity of milk in the 5 cans at the end, we need to know the change in the quantity of milk in each can and the initial standard deviation of the quantity of milk in the 5 cans.

Statement 1: In each can, 20% of the existing amount of milk was added.

  • We know the percentage increase in the quantity of milk in each can.

  • However, we don't know the initial quantity of milk in each can or the initial standard deviation of the quantity of milk in the 5 cans.

  • Therefore, statement 1 alone is not sufficient.



Statement 2: The average volume of milk in the cans at the end was 25 liters.

  • We know the average quantity of milk in the 5 cans at the end.

  • However, we don't know the change in the quantity of milk in each can or the initial standard deviation of the quantity of milk in the 5 cans.

  • Therefore, statement 2 alone is not sufficient.



Statements 1 and 2:

  • We know the percentage increase in the quantity of milk in each can and the average quantity of milk in the 5 cans at the end.

  • However, we don't know the initial quantity of milk in each can or the initial standard deviation of the quantity of milk in the 5 cans.

  • Therefore, statements 1 and 2 together are not sufficient.



Therefore, the answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Some milk was added to each of the 5 cans. If standard deviation of the quantity of milk in the 5 cans at the beginning was 3.5 liters, what was the standard deviation of the quantity of milk in the 5 cans at the end?(1) In each can, 20% of existing amount of milk was added.(2) The average volume of milk in the cans at the end was 25 liters.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?
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Some milk was added to each of the 5 cans. If standard deviation of the quantity of milk in the 5 cans at the beginning was 3.5 liters, what was the standard deviation of the quantity of milk in the 5 cans at the end?(1) In each can, 20% of existing amount of milk was added.(2) The average volume of milk in the cans at the end was 25 liters.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Some milk was added to each of the 5 cans. If standard deviation of the quantity of milk in the 5 cans at the beginning was 3.5 liters, what was the standard deviation of the quantity of milk in the 5 cans at the end?(1) In each can, 20% of existing amount of milk was added.(2) The average volume of milk in the cans at the end was 25 liters.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Some milk was added to each of the 5 cans. If standard deviation of the quantity of milk in the 5 cans at the beginning was 3.5 liters, what was the standard deviation of the quantity of milk in the 5 cans at the end?(1) In each can, 20% of existing amount of milk was added.(2) The average volume of milk in the cans at the end was 25 liters.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?.
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