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Rahul_Sharma23
GMAT Focus 1: 695 Q87 V83 DI83 
Posts: 114
08 Jul 2025, 02:45
Kudos
Bookmarks
Statement 1 not giving any information about electronics items
Statement 2 not giving any information about number of fragile and non fragile boxes
combining both we know
fragile boxes = 2/3 ; non-fragile boxes = 1/3
boxes containing electronics item 4/5
let's suppose we have 15 boxes in total
f = 10 ; nf = 5
boxes containing electronic items = 12
now if all 5 non fragile boxes contains electronic items, 7 out of 10 fragile boxes will have electronics items
therefore, at least 7 fragile boxes will have electronic items
sufficient
Statement 2 not giving any information about number of fragile and non fragile boxes
combining both we know
fragile boxes = 2/3 ; non-fragile boxes = 1/3
boxes containing electronics item 4/5
let's suppose we have 15 boxes in total
f = 10 ; nf = 5
boxes containing electronic items = 12
now if all 5 non fragile boxes contains electronic items, 7 out of 10 fragile boxes will have electronics items
therefore, at least 7 fragile boxes will have electronic items
sufficient
Bunuel
08 Jul 2025, 03:33
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Bunuel
Two types of Boxes given - fragile and non-fragile. We need to determine whether half of the fragile boxes contain electronics.
-> we don't know the proportion of fragile and non-fragile boxes --> and contents of fragile or non-fragile boxes.
1. we still don't know what proportion of fragile or non-fragile has electronics and other items. - Insufficient.
2. we still don't know the proportion of fragile and non- fragile boxes. - Insufficient.
Combining both lets say total boxes = x,
Number of boxes fragile = 2x/3 and non-fragile =x/3.
Number boxes with Electronics = 4x/5...
Lets consider x=60 for better visualization
boxes fragile = 40 and non-fragile = 20
Number boxes with Electronics = 48...
If all non-fragile box contain electronics =20
% of fragile = 28/40 >50% ----> Since, when less number of non-fragile boxes containing electronics will only decrease -> Hence, fragile boxes will always have electronics in more than half of the boxes.
08 Jul 2025, 03:52
Kudos
Bookmarks
Option C is the correct answer.
Lets understand the information and what we need to find in order to answer the question.
So the question starts by telling us that a department store received a shipment in which their are two types of boxes: Fragile and Non-Fragile, and from the question we came to know that there are two categories of product in these boxes: Electronic and Non-Electronic. And in the end it asks us whether more than half of the Fragile boxes contains Electronics product or not.
Now lets see the statements and check whether we can answer the question using those statements or not.
Statement 1: "Two-thirds of the boxes in the shipment are fragile". This statement tells us that 2/3rd of the boxes in the shipment are Fragile which would mean that if their are 3 boxes in the shipment 2 out of those will be Fragile, similarly if the shipment contains 6 boxes then 4 of them will be Fragile and so on. But it does not give us any information regarding the boxes that contains Electronic products which means that it can be 1/5, 2/3, 1/4 and so on. So this statement on its own is Not Sufficient to answer the question.
Statement 2: "Four-fifths of the boxes in the shipment contain electronics". This statement tells us that 4/5th of the boxes in the shipment contains Electronic product which would mean that if their are 5 boxes in the shipment 4 out of those will contain Electronic products, similarly if the shipment contains 10 boxes then 8 of them will contain Electronic product and so on. But it does not give us any information regarding the boxes that contains Fragile products which means that it can be 1/5, 2/3, 1/4 and so on. So this statement on its own is Not Sufficient to answer the question.
As we have checked that both the statements on their own are Not Sufficient to answer the question. So now lets try by combining both the statements.
After combining both the statements we we now know that 2/3rd boxes contain Fragile items and 4/5th of the boxes contains Electronic products. Now lets assume the total number of boxes to be 15 which will give us our answer in integer form and it will make the calculation much more easier.
So as per our assumption Total Boxes = 15
Fragile boxes = 15*(2/3) = 10
Non-Fragile Boxes = 15-10 = 5
Boxes with Electronic products = 15*(4/5) = 12
Boxes without Electronic products = 15-12 = 3
From here to see the minimum number of boxes that will be both Fragile and Electronic category we need to fit maximum boxes into Non-Fragile category which will be '5' that will leave '7' boxes for Fragile which will be more than half. But lets check for few other numbers to confirm our answer.
Example:
So lets assumption Total Boxes = 30
Fragile boxes = 30*(2/3) = 20
Non-Fragile Boxes = 30-20 = 10
Boxes with Electronic products = 30*(4/5) = 24
Boxes without Electronic products = 30-24 = 6
Now lets assumption Total Boxes = 45
Fragile boxes = 45*(2/3) = 30
Non-Fragile Boxes = 45-30 = 15
Boxes with Electronic products = 45*(4/5) = 36
Boxes without Electronic products = 45-36 = 9
Now lets assumption one last value of Total Boxes = 450
Fragile boxes = 450*(2/3) = 300
Non-Fragile Boxes = 450-300 = 150
Boxes with Electronic products = 450*(4/5) = 360
Boxes without Electronic products = 450-360 = 90
From all these cases we can easily conclude that more than more than half of the fragile boxes contain electronics. So Option C is our answer.
Lets understand the information and what we need to find in order to answer the question.
So the question starts by telling us that a department store received a shipment in which their are two types of boxes: Fragile and Non-Fragile, and from the question we came to know that there are two categories of product in these boxes: Electronic and Non-Electronic. And in the end it asks us whether more than half of the Fragile boxes contains Electronics product or not.
Now lets see the statements and check whether we can answer the question using those statements or not.
Statement 1: "Two-thirds of the boxes in the shipment are fragile". This statement tells us that 2/3rd of the boxes in the shipment are Fragile which would mean that if their are 3 boxes in the shipment 2 out of those will be Fragile, similarly if the shipment contains 6 boxes then 4 of them will be Fragile and so on. But it does not give us any information regarding the boxes that contains Electronic products which means that it can be 1/5, 2/3, 1/4 and so on. So this statement on its own is Not Sufficient to answer the question.
Statement 2: "Four-fifths of the boxes in the shipment contain electronics". This statement tells us that 4/5th of the boxes in the shipment contains Electronic product which would mean that if their are 5 boxes in the shipment 4 out of those will contain Electronic products, similarly if the shipment contains 10 boxes then 8 of them will contain Electronic product and so on. But it does not give us any information regarding the boxes that contains Fragile products which means that it can be 1/5, 2/3, 1/4 and so on. So this statement on its own is Not Sufficient to answer the question.
As we have checked that both the statements on their own are Not Sufficient to answer the question. So now lets try by combining both the statements.
After combining both the statements we we now know that 2/3rd boxes contain Fragile items and 4/5th of the boxes contains Electronic products. Now lets assume the total number of boxes to be 15 which will give us our answer in integer form and it will make the calculation much more easier.
So as per our assumption Total Boxes = 15
Fragile boxes = 15*(2/3) = 10
Non-Fragile Boxes = 15-10 = 5
Boxes with Electronic products = 15*(4/5) = 12
Boxes without Electronic products = 15-12 = 3
From here to see the minimum number of boxes that will be both Fragile and Electronic category we need to fit maximum boxes into Non-Fragile category which will be '5' that will leave '7' boxes for Fragile which will be more than half. But lets check for few other numbers to confirm our answer.
Example:
So lets assumption Total Boxes = 30
Fragile boxes = 30*(2/3) = 20
Non-Fragile Boxes = 30-20 = 10
Boxes with Electronic products = 30*(4/5) = 24
Boxes without Electronic products = 30-24 = 6
Now lets assumption Total Boxes = 45
Fragile boxes = 45*(2/3) = 30
Non-Fragile Boxes = 45-30 = 15
Boxes with Electronic products = 45*(4/5) = 36
Boxes without Electronic products = 45-36 = 9
Now lets assumption one last value of Total Boxes = 450
Fragile boxes = 450*(2/3) = 300
Non-Fragile Boxes = 450-300 = 150
Boxes with Electronic products = 450*(4/5) = 360
Boxes without Electronic products = 450-360 = 90
From all these cases we can easily conclude that more than more than half of the fragile boxes contain electronics. So Option C is our answer.
Bunuel
