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Q:If GB (x) > 5, Total x = ?

St1: If N=6
  • Magnets per bag: 24/6 = 4
  • Postcards per bag: 36/6 = 6
  • Bookmarks per bag: 48/6 = 8
  • Keychains per bag: 60/6 = 10
If N = 12
  • Magnets per bag: 24/12 = 2
  • Postcards per bag: 36/12 = 3
  • Bookmarks per bag: 48/12 = 4
  • Keychains per bag: 60/12 = 5

Both values of N are possible, hence, Not sufficient.

St2: This means that for some positive integer x, each bag contains 2x magnets, 3x postcards, 4x bookmarks, and 5x keychains.

No info on x. Not sufficient.

Combing St1 and St2:

From 1, when N=6

The ratio of items per bag: 4:6:8:10

Dividing the ratio by 2, we get 2:3:4:5

when n= 12, also the ratio becomes 2:3:4:5

Since both the values of N are still valid and no unique value can be determined,

Option E

Bunuel
A museum gift shop packed a number of souvenir items: magnets, postcards, bookmarks, and keychains into identical gift bags for visitors. If more than 5 gift bags were packed, how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.


 


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The correct answer is (A)

Statement 1 gives us information about how many of each item were packed into similar combinations with identical amounts of each item in it. Since the question also mentions greater than 5, we know that we have to find a common factor among all these item counts - 12. So 12 bags were made.

Statement 2 on its own does not tell us about counts, however the ratios nicely reinforce the breakdown of every item count into 12 bags. Still, statement 1 was sufficient enough for an answer without needing statement 2.
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Key words: identical gift cards means equal capacity. So whatever number is packed must be uniform across the different gifts
S1 Gives us the total gifts which must be distributed in even proportions to the available bags so we find the GCD which is 12. Meaning the number of bags required was 12 which is greater than 5 and can accommodate all the gifts evenly hence sufficient
S1 Does not tell us about the total gifts packed so they could be any number requiring any number of bags hence insufficient
ANS A
Bunuel
A museum gift shop packed a number of souvenir items: magnets, postcards, bookmarks, and keychains into identical gift bags for visitors. If more than 5 gift bags were packed, how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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But its mentioned identical bags doesnt that reflect identical as no. of items distributed in them are identical making them identical?
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GMAT Club Official Explanation:



A museum gift shop packed a number of souvenir items: magnets, postcards, bookmarks, and keychains into identical gift bags for visitors. If more than 5 gift bags were packed, how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

Clearly insufficient. We know the total, but nothing about how items were distributed.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

Clearly insufficient. Without knowing total quantities, we cannot determine how many bags were packed.

(1)+(2) Combining the statements, we can check how many gift bags could have been packed by matching the total quantities to the given ratio. The following combinations are possible:

  • 6 gift bags: 4 magnets, 6 postcards, 8 bookmarks, 10 keychains per bag
  • 12 gift bags: 2 magnets, 3 postcards, 4 bookmarks, 5 keychains per bag

Since more than one value satisfies the conditions, we still cannot determine the exact number. Not sufficient.

Answer: E.
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eshika23
But its mentioned identical bags doesnt that reflect identical as no. of items distributed in them are identical making them identical?
Bunuel
­

GMAT Club Official Explanation:



A museum gift shop packed a number of souvenir items: magnets, postcards, bookmarks, and keychains into identical gift bags for visitors. If more than 5 gift bags were packed, how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

Clearly insufficient. We know the total, but nothing about how items were distributed.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

Clearly insufficient. Without knowing total quantities, we cannot determine how many bags were packed.

(1)+(2) Combining the statements, we can check how many gift bags could have been packed by matching the total quantities to the given ratio. The following combinations are possible:

  • 6 gift bags: 4 magnets, 6 postcards, 8 bookmarks, 10 keychains per bag
  • 12 gift bags: 2 magnets, 3 postcards, 4 bookmarks, 5 keychains per bag

Since more than one value satisfies the conditions, we still cannot determine the exact number. Not sufficient.

Answer: E.

Your doubt is a bit unclear. Identical bags mean that each bag has the same set of items in the same ratio. When combining the two statements, we can have, for example:

  • 6 identical bags, each containing 4 magnets, 6 postcards, 8 bookmarks, 10 keychains

or

  • 12 identical bags, each containing 2 magnets, 3 postcards, 4 bookmarks, 5 keychains.

Both work, so we can’t get a unique answer.
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Does this mean if sum of ratio would have been a prime number then we could have certainly said that these are the number of bags or all factors would have been less than 5, but since the HCF is 12 and it also has 6 and 12 so we cannot really say that the exact number of bags it could be 6 or 12, correct?
Bunuel
eshika23
But its mentioned identical bags doesnt that reflect identical as no. of items distributed in them are identical making them identical?
Bunuel
­

GMAT Club Official Explanation:



A museum gift shop packed a number of souvenir items: magnets, postcards, bookmarks, and keychains into identical gift bags for visitors. If more than 5 gift bags were packed, how many gift bags were packed?

(1) A total of 24 magnets, 36 postcards, 48 bookmarks, and 60 keychains were packed.

Clearly insufficient. We know the total, but nothing about how items were distributed.

(2) Each gift bag contained magnets, postcards, bookmarks, and keychains in the ratio 2:3:4:5, respectively.

Clearly insufficient. Without knowing total quantities, we cannot determine how many bags were packed.

(1)+(2) Combining the statements, we can check how many gift bags could have been packed by matching the total quantities to the given ratio. The following combinations are possible:

  • 6 gift bags: 4 magnets, 6 postcards, 8 bookmarks, 10 keychains per bag
  • 12 gift bags: 2 magnets, 3 postcards, 4 bookmarks, 5 keychains per bag

Since more than one value satisfies the conditions, we still cannot determine the exact number. Not sufficient.

Answer: E.

Your doubt is a bit unclear. Identical bags mean that each bag has the same set of items in the same ratio. When combining the two statements, we can have, for example:

  • 6 identical bags, each containing 4 magnets, 6 postcards, 8 bookmarks, 10 keychains

or

  • 12 identical bags, each containing 2 magnets, 3 postcards, 4 bookmarks, 5 keychains.

Both work, so we can’t get a unique answer.
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eshika23
Does this mean if sum of ratio would have been a prime number then we could have certainly said that these are the number of bags or all factors would have been less than 5, but since the HCF is 12 and it also has 6 and 12 so we cannot really say that the exact number of bags it could be 6 or 12, correct?

Not sure what you mean by "sum of ratio."

Answer is E because we can have 6 identical bags or 12 identical bags, so no unique answer.
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