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15 Jun 2022, 01:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:00) correct
25%
(02:17)
wrong
based on 223
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A jeweller has a black pouch and a white pouch, and each pouch contains nine gold nuggets. Some of the nuggets weigh 7 grams and the remaining nuggets weigh 5 grams. Does the black pouch contain a greater number of 7 gram nuggets than the white pouch?
1) If one 10 gram gold nugget were added to each pouch, the average (arithmetic mean) weight of a nugget in the white pouch would increase by a greater amount than would the average (arithmetic mean) weight of a nugget in the black pouch.
2) The average (arithmetic mean) weight of a nugget in the black pouch is greater than the average (arithmetic mean) weight of a nugget in the white pouch.
1) If one 10 gram gold nugget were added to each pouch, the average (arithmetic mean) weight of a nugget in the white pouch would increase by a greater amount than would the average (arithmetic mean) weight of a nugget in the black pouch.
2) The average (arithmetic mean) weight of a nugget in the black pouch is greater than the average (arithmetic mean) weight of a nugget in the white pouch.
15 Jun 2022, 02:10
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Statement 1:
The average weight of both the pouches is less than or equal to 7. If a nugget of 10 gm is added to either of the pouches, the average weight will increase. The lesser the average weight of the pouch, the more will be the increase in the average weight after the addition of a 10 gm nugget.
Thus, the white pouch will have a lesser number of 7 gm nuggets.
Statement 2:
If one pouch has more average weight, that means it contains more 7 gm nuggets. Thus, the black pouch will have more number of 7 gm nuggets.
Since both statements alone are sufficient to answer the question, the correct answer is D.
The average weight of both the pouches is less than or equal to 7. If a nugget of 10 gm is added to either of the pouches, the average weight will increase. The lesser the average weight of the pouch, the more will be the increase in the average weight after the addition of a 10 gm nugget.
Thus, the white pouch will have a lesser number of 7 gm nuggets.
Statement 2:
If one pouch has more average weight, that means it contains more 7 gm nuggets. Thus, the black pouch will have more number of 7 gm nuggets.
Since both statements alone are sufficient to answer the question, the correct answer is D.
03 Jul 2026, 12:47
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Each pouch has 9 nuggets, each either 7g or 5g.
Key trick: The more 7g nuggets a pouch has, the higher its average weight will be (since the average sits somewhere between 5g and 7g).
So the real question becomes: "Is the Black pouch's average weight higher than the White pouch's average weight?"
That's all we need to figure out.
Statement (2) directly tells us: Black's average > White's average
That answers it immediately — Black has more 7g nuggets. ✅ Sufficient
Statement (1) — A bit indirect
This one says: if you add one 10g nugget to each pouch, White's average increases by more than Black's average does.
Here's the logic to understand:
Imagine two groups with different averages, and you add a heavy new item (10g) to both. The group that started with the lower average will get pulled up more, because the 10g nugget is farther above its average, so it has a bigger pulling effect.
(Simple analogy: two students have average test scores of 40 and 60. If both take one more test and score 100 on it, the student with the average of 40 will see their overall average jump up more — because 100 is much farther from 40 than it is from 60.)
So: White's average increased more → this means White started with the lower average → which means Black's average was higher.
That's the exact same conclusion as Statement (2)! ✅ Sufficient
Final Answer: D
Key trick: The more 7g nuggets a pouch has, the higher its average weight will be (since the average sits somewhere between 5g and 7g).
So the real question becomes: "Is the Black pouch's average weight higher than the White pouch's average weight?"
That's all we need to figure out.
Statement (2) directly tells us: Black's average > White's average
That answers it immediately — Black has more 7g nuggets. ✅ Sufficient
Statement (1) — A bit indirect
This one says: if you add one 10g nugget to each pouch, White's average increases by more than Black's average does.
Here's the logic to understand:
Imagine two groups with different averages, and you add a heavy new item (10g) to both. The group that started with the lower average will get pulled up more, because the 10g nugget is farther above its average, so it has a bigger pulling effect.
(Simple analogy: two students have average test scores of 40 and 60. If both take one more test and score 100 on it, the student with the average of 40 will see their overall average jump up more — because 100 is much farther from 40 than it is from 60.)
So: White's average increased more → this means White started with the lower average → which means Black's average was higher.
That's the exact same conclusion as Statement (2)! ✅ Sufficient
Final Answer: D
Russ19
