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17 May 2026, 19:00
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A home-goods warehouse inspected a shipment of ceramic mugs for glazing flaws. Of the mugs in the shipment, 70% were blue-glazed, and the rest were not blue-glazed. Of the mugs that were not blue-glazed, 2/5 had a glazing flaw. What percentage of the blue-glazed mugs did not have a glazing flaw?
(1) If one mug is selected at random from the shipment, the probability that it will have a glazing flaw is 0.32.
(2) If one mug with a glazing flaw is selected at random from the shipment, the probability that it will be blue-glazed is 5/8.
(1) If one mug is selected at random from the shipment, the probability that it will have a glazing flaw is 0.32.
(2) If one mug with a glazing flaw is selected at random from the shipment, the probability that it will be blue-glazed is 5/8.
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M47-158
09 Jun 2026, 19:15
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GMAT Club Official Solution:
A home-goods warehouse inspected a shipment of ceramic mugs for glazing flaws. Of the mugs in the shipment, 70% were blue-glazed, and the rest were not blue-glazed. Of the mugs that were not blue-glazed, 2/5 had a glazing flaw. What percentage of the blue-glazed mugs did not have a glazing flaw?
Use 100 mugs as a convenient total. Since 70% of the mugs were blue-glazed:
• Blue-glazed = 70
• Not blue-glazed = 30
Of the mugs that were not blue-glazed, 2/5 had a glazing flaw:
• So 2/5 * 30 = 12 not-blue-glazed mugs had a glazing flaw.
The question asks what percentage of the 70 blue-glazed mugs did not have a glazing flaw.
(1) If one mug is selected at random from the shipment, the probability that it will have a glazing flaw is 0.32.
So 32% of the mugs had a glazing flaw. Since we are using 100 mugs, 32 mugs had a glazing flaw.
Of these 32 flawed mugs, 12 were not blue-glazed, so:
blue-glazed mugs with a flaw = 32 - 12 = 20
Therefore:
blue-glazed mugs without a flaw = 70 - 20 = 50
So the required percentage is:
50/70 = 5/7
Sufficient.
(2) If one mug with a glazing flaw is selected at random from the shipment, the probability that it will be blue-glazed is 5/8.
This means:
blue-glazed mugs with a flaw / all mugs with a flaw = 5/8
We already know that 12 not-blue-glazed mugs had a glazing flaw.
Let B be the number of blue-glazed mugs with a glazing flaw. Then:
B/(B + 12) = 5/8
B = 20
So 20 blue-glazed mugs had a glazing flaw.
Therefore:
blue-glazed mugs without a flaw = 70 - 20 = 50
So the required percentage is:
50/70 = 5/7
Sufficient.
Answer: D.
A home-goods warehouse inspected a shipment of ceramic mugs for glazing flaws. Of the mugs in the shipment, 70% were blue-glazed, and the rest were not blue-glazed. Of the mugs that were not blue-glazed, 2/5 had a glazing flaw. What percentage of the blue-glazed mugs did not have a glazing flaw?
Use 100 mugs as a convenient total. Since 70% of the mugs were blue-glazed:
• Blue-glazed = 70
• Not blue-glazed = 30
Of the mugs that were not blue-glazed, 2/5 had a glazing flaw:
• So 2/5 * 30 = 12 not-blue-glazed mugs had a glazing flaw.
The question asks what percentage of the 70 blue-glazed mugs did not have a glazing flaw.
(1) If one mug is selected at random from the shipment, the probability that it will have a glazing flaw is 0.32.
So 32% of the mugs had a glazing flaw. Since we are using 100 mugs, 32 mugs had a glazing flaw.
Of these 32 flawed mugs, 12 were not blue-glazed, so:
blue-glazed mugs with a flaw = 32 - 12 = 20
Therefore:
blue-glazed mugs without a flaw = 70 - 20 = 50
So the required percentage is:
50/70 = 5/7
Sufficient.
(2) If one mug with a glazing flaw is selected at random from the shipment, the probability that it will be blue-glazed is 5/8.
This means:
blue-glazed mugs with a flaw / all mugs with a flaw = 5/8
We already know that 12 not-blue-glazed mugs had a glazing flaw.
Let B be the number of blue-glazed mugs with a glazing flaw. Then:
B/(B + 12) = 5/8
B = 20
So 20 blue-glazed mugs had a glazing flaw.
Therefore:
blue-glazed mugs without a flaw = 70 - 20 = 50
So the required percentage is:
50/70 = 5/7
Sufficient.
Answer: D.
General Discussion
ankushsambare
Joined: 13 Jun 2022
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17 May 2026, 20:19
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Let total mugs = 100.
Blue-glazed mugs = 70
Non-blue mugs = 30
Of the non-blue mugs, 2/5 had flaws.
So flawed non-blue mugs:
2/5 × 30 = 12
We need to find the percentage of blue-glazed mugs that did NOT have flaws.
Let flawed blue mugs = x.
Then non-flawed blue mugs = 70 − x.
So we only need to find x.
Statement (1)
Probability that a randomly selected mug has a flaw = 0.32.
So total flawed mugs = 32.
Already, flawed non-blue mugs = 12.
Therefore flawed blue mugs:
32 − 12 = 20
So non-flawed blue mugs:
70 − 20 = 50
A unique value is obtained.
Statement (1) is sufficient.
Statement (2)
Given a flawed mug, probability it is blue-glazed = 5/8.
So,
flawed blue / total flawed = 5/8
Let flawed blue mugs = x.
Then total flawed mugs = x + 12.
So,
x / (x + 12) = 5/8
Cross multiply:
8x = 5x + 60
3x = 60
x = 20
Thus flawed blue mugs are uniquely determined.
So the required percentage can be found.
Statement (2) is sufficient.
Each statement alone is sufficient.
Answer: D
Blue-glazed mugs = 70
Non-blue mugs = 30
Of the non-blue mugs, 2/5 had flaws.
So flawed non-blue mugs:
2/5 × 30 = 12
We need to find the percentage of blue-glazed mugs that did NOT have flaws.
Let flawed blue mugs = x.
Then non-flawed blue mugs = 70 − x.
So we only need to find x.
Statement (1)
Probability that a randomly selected mug has a flaw = 0.32.
So total flawed mugs = 32.
Already, flawed non-blue mugs = 12.
Therefore flawed blue mugs:
32 − 12 = 20
So non-flawed blue mugs:
70 − 20 = 50
A unique value is obtained.
Statement (1) is sufficient.
Statement (2)
Given a flawed mug, probability it is blue-glazed = 5/8.
So,
flawed blue / total flawed = 5/8
Let flawed blue mugs = x.
Then total flawed mugs = x + 12.
So,
x / (x + 12) = 5/8
Cross multiply:
8x = 5x + 60
3x = 60
x = 20
Thus flawed blue mugs are uniquely determined.
So the required percentage can be found.
Statement (2) is sufficient.
Each statement alone is sufficient.
Answer: D
