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07 Jul 2025, 09:15
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Condition One:
Only the proportion of fragile boxes, which is 2/3 of the total number of boxes, is known.
No information is available regarding the distribution of electronic products.
It is impossible to determine whether electronic products exceed half of the fragile category.
(1) Insufficient
Condition Two:
The total proportion of boxes containing electronic products is known to be 4/5.
However, the distribution of fragile boxes within this category is unknown.
It is not possible to ascertain how many fragile boxes contain electronic products.
(2) Insufficient
Condition One + Condition Two:
Firstly, let's analyze the distribution.
For example,
It is known that the proportion of electronic products in the total is 12/15.
The proportion of fragile items in the total is 10/15.
In other words, as long as the distribution of electronic products within the fragile category exceeds 5/15,
the condition is satisfied.
Let's consider the extreme distributions:
10/15 electronic products within fragile boxes satisfy the distribution.
2/15 electronic products + 3/15 non-electronic products also satisfy the 1/3 distribution of non-fragile items.
10/15 > 5/15 satisfies the condition.
If the non-fragile category has the maximum distribution of electronic products:
5/15 electronic products are in non-fragile boxes.
The remaining 7/15 are distributed within fragile boxes + 3/15 non-electronic products within fragile boxes, which also satisfies the distribution.
7/15 > 5/15 satisfies the condition.
Conditions are sufficient. Answer: C
Only the proportion of fragile boxes, which is 2/3 of the total number of boxes, is known.
No information is available regarding the distribution of electronic products.
It is impossible to determine whether electronic products exceed half of the fragile category.
(1) Insufficient
Condition Two:
The total proportion of boxes containing electronic products is known to be 4/5.
However, the distribution of fragile boxes within this category is unknown.
It is not possible to ascertain how many fragile boxes contain electronic products.
(2) Insufficient
Condition One + Condition Two:
Firstly, let's analyze the distribution.
For example,
It is known that the proportion of electronic products in the total is 12/15.
The proportion of fragile items in the total is 10/15.
In other words, as long as the distribution of electronic products within the fragile category exceeds 5/15,
the condition is satisfied.
Let's consider the extreme distributions:
10/15 electronic products within fragile boxes satisfy the distribution.
2/15 electronic products + 3/15 non-electronic products also satisfy the 1/3 distribution of non-fragile items.
10/15 > 5/15 satisfies the condition.
If the non-fragile category has the maximum distribution of electronic products:
5/15 electronic products are in non-fragile boxes.
The remaining 7/15 are distributed within fragile boxes + 3/15 non-electronic products within fragile boxes, which also satisfies the distribution.
7/15 > 5/15 satisfies the condition.
Conditions are sufficient. Answer: C
07 Jul 2025, 09:16
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Assume total boxes to be 150.
Statement 1 - 2/3 of the boxes is Fragile. Therefore, 100 boxes is fragile and 50 boxes non-fragile. There is no information on electronics. Hence, insufficient.
Statement 2 - 4/5 of the boxes contain electronics.
Therefore, 4/5*150 = 120 boxes contain electronics.
Again, insufficient since, we don't know anything about fragile boxes from this statement alone.
When you combine the two statements:
Fragile is 100
Even if all the 30 non-electronic are considered to be part of fragile boxes, fragile electronics = 70 which is more than half.
Hence, C.
Statement 1 - 2/3 of the boxes is Fragile. Therefore, 100 boxes is fragile and 50 boxes non-fragile. There is no information on electronics. Hence, insufficient.
Statement 2 - 4/5 of the boxes contain electronics.
Therefore, 4/5*150 = 120 boxes contain electronics.
Again, insufficient since, we don't know anything about fragile boxes from this statement alone.
When you combine the two statements:
Fragile is 100
Even if all the 30 non-electronic are considered to be part of fragile boxes, fragile electronics = 70 which is more than half.
Hence, C.
07 Jul 2025, 09:26
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A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?
Is x > F/2 ?
(1) Two-thirds of the boxes in the shipment are fragile.
Since there is no information about shipments containing electronics.
NOT SUFFICIENT
(2) Four-fifths of the boxes in the shipment contain electronics.
Since there is no information about shipments that are fragile.
NOT SUFFICIENT
(1) + (2)
(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.
x>=0
4/5 - x >= 0; x<=4/5
x - 7/15>=0 ; x>=7/15
2/3-x>=0; x<=2/3
Combing all above,
0<7/15 <= x <= 2/3 < 4/5
F/2 = 1/3
x > 7/15 > 5/15 = 1/3
SUFFICIENT
IMO C
| Fragile | Not fragile | Total | |
| Electronics | x | ||
| Not electronics | |||
| Total | F |
Is x > F/2 ?
(1) Two-thirds of the boxes in the shipment are fragile.
| Fragile | Not fragile | Total | |
| Electronics | x | ||
| Not electronics | |||
| Total | 2/3 | 1/3 | 1 |
Since there is no information about shipments containing electronics.
NOT SUFFICIENT
(2) Four-fifths of the boxes in the shipment contain electronics.
| Fragile | Not fragile | Total | |
| Electronics | x | 4/5 | |
| Not electronics | 1/5 | ||
| Total | 1 |
Since there is no information about shipments that are fragile.
NOT SUFFICIENT
(1) + (2)
(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.
| Fragile | Not fragile | Total | |
| Electronics | x | 1/3 + 7/15 - x = 4/5 - x | 4/5 |
| Not electronics | 2/3-x | 1/5+x-2/3 = x - 7/15 | 1/5 |
| Total | 2/3 | 1/3 | 1 |
x>=0
4/5 - x >= 0; x<=4/5
x - 7/15>=0 ; x>=7/15
2/3-x>=0; x<=2/3
Combing all above,
0<7/15 <= x <= 2/3 < 4/5
F/2 = 1/3
x > 7/15 > 5/15 = 1/3
SUFFICIENT
IMO C
