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04 Feb 2026, 22:25
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Difficulty:
25%
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Question Stats:
70% (01:03) correct
30%
(01:33)
wrong
based on 83
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Some Nitrogen was added into each of the 5 Nitrogen cylinders in a lab. If the standard deviation of the volume of Nitrogen in the 5 cylinders before the addition was 10 gallons, what was the standard deviation of the same after the addition?
(1) 7 gallons of Nitrogen was added into each of the cylinders.
(2) The average volume of Nitrogen in the 5 cylinders was 30 gallons before the addition and 37 gallons after the addition.
(1) 7 gallons of Nitrogen was added into each of the cylinders.
(2) The average volume of Nitrogen in the 5 cylinders was 30 gallons before the addition and 37 gallons after the addition.
nemoexplicabo
05 Feb 2026, 06:48
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This is a statistics problem testing your understanding of standard deviation properties - a concept that's crucial for GMAT Focus Data Insights questions. When I was preparing for my 725 score, standard deviation questions used to confuse me until I mastered the fundamental rules.
The question states that nitrogen was added to each of the 5 cylinders in a lab. Originally, the standard deviation of the nitrogen volume was 10 gallons. We need to find the new standard deviation after the addition.
The Critical Concept:
Standard deviation measures the spread or variability of data around the mean. Here's the key property that makes this question straightforward: when you add (or subtract) the same constant to every value in a dataset, the standard deviation remains UNCHANGED.
Why? Because standard deviation measures how spread out the values are from their average. If you shift all values by the same amount, they remain equally spread out - you've just moved the entire distribution, not changed its shape.
Analyzing Statement 1: 7 gallons of Nitrogen was added into each of the cylinders
This directly tells us that the same amount (7 gallons) was added to each cylinder. Since we're adding a constant value to all data points, the standard deviation stays at 10 gallons.
Statement 1 is SUFFICIENT.
Analyzing Statement 2: The average volume was 30 gallons before and 37 gallons after
Let's think about what this tells us. If the average increased from 30 to 37 gallons, that's a difference of 7 gallons. For the average of 5 cylinders to increase by exactly 7 gallons, each cylinder must have received the same amount: 7 gallons.
Why? Total volume before = 5 × 30 = 150 gallons. Total volume after = 5 × 37 = 185 gallons. Total added = 185 - 150 = 35 gallons across 5 cylinders = 7 gallons per cylinder.
Since the same amount was added to each cylinder, the standard deviation remains 10 gallons.
Statement 2 is SUFFICIENT.
Answer: D (Each statement alone is sufficient)
Common Mistake Alert:
Many students instinctively think that adding nitrogen would increase the standard deviation because the volumes got bigger. This confuses absolute values with spread. Remember:
- Adding/subtracting a constant: SD stays the same
- Multiplying/dividing by a constant: SD changes proportionally
Real-World Example:
Imagine five people's ages: 20, 25, 30, 35, 40 (SD = 7.07 years). If everyone ages 5 years: 25, 30, 35, 40, 45. The SD is still 7.07 years because they're still spread out by the same amount - they just all got older together.
Key Takeaway for Data Insights:
Standard deviation questions frequently test whether you understand transformation properties. Before doing calculations, ask yourself: "Am I adding/subtracting the same value to all points (SD unchanged) or multiplying/dividing (SD changes)?" This saves time and prevents careless errors.
The question states that nitrogen was added to each of the 5 cylinders in a lab. Originally, the standard deviation of the nitrogen volume was 10 gallons. We need to find the new standard deviation after the addition.
The Critical Concept:
Standard deviation measures the spread or variability of data around the mean. Here's the key property that makes this question straightforward: when you add (or subtract) the same constant to every value in a dataset, the standard deviation remains UNCHANGED.
Why? Because standard deviation measures how spread out the values are from their average. If you shift all values by the same amount, they remain equally spread out - you've just moved the entire distribution, not changed its shape.
Analyzing Statement 1: 7 gallons of Nitrogen was added into each of the cylinders
This directly tells us that the same amount (7 gallons) was added to each cylinder. Since we're adding a constant value to all data points, the standard deviation stays at 10 gallons.
Statement 1 is SUFFICIENT.
Analyzing Statement 2: The average volume was 30 gallons before and 37 gallons after
Let's think about what this tells us. If the average increased from 30 to 37 gallons, that's a difference of 7 gallons. For the average of 5 cylinders to increase by exactly 7 gallons, each cylinder must have received the same amount: 7 gallons.
Why? Total volume before = 5 × 30 = 150 gallons. Total volume after = 5 × 37 = 185 gallons. Total added = 185 - 150 = 35 gallons across 5 cylinders = 7 gallons per cylinder.
Since the same amount was added to each cylinder, the standard deviation remains 10 gallons.
Statement 2 is SUFFICIENT.
Answer: D (Each statement alone is sufficient)
Common Mistake Alert:
Many students instinctively think that adding nitrogen would increase the standard deviation because the volumes got bigger. This confuses absolute values with spread. Remember:
- Adding/subtracting a constant: SD stays the same
- Multiplying/dividing by a constant: SD changes proportionally
Real-World Example:
Imagine five people's ages: 20, 25, 30, 35, 40 (SD = 7.07 years). If everyone ages 5 years: 25, 30, 35, 40, 45. The SD is still 7.07 years because they're still spread out by the same amount - they just all got older together.
Key Takeaway for Data Insights:
Standard deviation questions frequently test whether you understand transformation properties. Before doing calculations, ask yourself: "Am I adding/subtracting the same value to all points (SD unchanged) or multiplying/dividing (SD changes)?" This saves time and prevents careless errors.
05 Feb 2026, 10:33
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ExpertsGlobal5
Statement 1: each cylinder (data set) is added a constant (7gallon) - SD doesnot change when a constant is added to data set. Thus SD will remain same. It is SUFFICIENT.
Statement 2: Interpret it like -> Total gas was 150 gallons in 5 cylinders and was increased to 185 gallons in 5 cylinder. But question doesn't state that each cylinder will get same amount of gas, just that each will get some. So 4 may get 1 gallon and 5th one gets 31 gallon. Or any other arrangement. Thus we cannot determine SD. NOT SUFFICIENT.
Soln: A
