At a community center, Nora and five other volunteers packed snack bag

Question

At a community center, Nora and five other volunteers packed snack bags for an event. If altogether they packed 43 snack bags, and no two volunteers packed the same number of snack bags, did Nora pack more than 6 snack bags?

(1) Each volunteer packed at least 4 snack bags, and the greatest number of snack bags packed by a volunteer was greater than 12.
(2) Nora packed fewer snack bags than the median number of snack bags packed by the six volunteers.

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a community center, Nora and five other volunteers packed snack bags for an event. If altogether they packed 43 snack bags, and no two volunteers packed the same number of snack bags, did Nora pack more than 6 snack bags?

(1) Each volunteer packed at least 4 snack bags, and the greatest number of snack bags packed by a volunteer was greater than 12.

The smallest possible total of 6 distinct integers, each at least 4, is:

4 + 5 + 6 + 7 + 8 + 9 = 39

Since the total is 43, there are only 4 “extra” bags beyond this minimum. (1) also says the greatest count is greater than 12, so it must be at least 13. The only way to reach 13 with only 4 extra is to raise 9 to 13, which forces the full set of counts to be {4, 5, 6, 7, 8, 13}. But we still do not know which of these counts is Nora’s, so Nora could be 6 (No) or 7 (Yes). Not sufficient.

(2) Nora packed fewer snack bags than the median number of snack bags packed by the six volunteers.

Many different distributions are possible, so Nora could have packed more than 6 in some cases and 6 or fewer in others. Not sufficient.

(1)+(2) From (1), the counts must be {4, 5, 6, 7, 8, 13}, so the median is (6 + 7)/2 = 6.5. If Nora packed fewer than the median, Nora must be 4, 5, or 6, so she did not pack more than 6. Sufficient.

Answer: C.

thisisakr · Answer

Given: there are 6 student and 43 bag packs and No two students have same no of bag packs

1. Given the minimum is 4 bags and maximum is more than 12

We can have the following arrangement 
 4,5,6,7,8,13 —— however we aren’t given any information about Nora so this is  insufficient

2. Given Nora has less than the median value

Total number of bag packs 43

We can arrange in 0,1,3,12,13,14 or 7,7,7,7,7,8 
 Median for first arrangement is 15/2=7.5 so Nora can have 7 bags or less than 7 
 Arrangement 2 median is 7 so Nora can have 6 or less bags

This doesn’t help us answer the question if Nora has >6 bags or not —— so  insufficient

Together ,

We have 4,5,6,7,8,13 from statement 1 and 
 And median of 6.5 so Nora will always have 6 or less bags this answers our question  sufficient

Ans C

Edskore · Answer

The key insight on this one is hidden in Statement 1. Most people test a couple arrangements and call it insufficient. But there's actually only one valid arrangement, which is what makes this a great Data Sufficiency trap.

Statement 1: 6 distinct values, each >= 4, max > 12, total = 43.

Minimum with all distinct integers >= 4: 4+5+6+7+8+9 = 39. We need 4 more. And since max > 12, replace the highest with at least 13:

Try max = 13: 4+5+6+7+8+13 = 43. Fits perfectly.
Try max = 14: 4+5+6+7+8+14 = 44, but that's already over 43. You'd have to lower something else, but 4,5,6,7,8 are already the minimum. No valid arrangement with max = 14.

So Statement 1 locks in exactly one set: {4, 5, 6, 7, 8, 13}.
Still doesn't tell us which number is Nora's. She could be any of them. Nora's count could be 4 or could be 13. Insufficient alone.

Statement 2: Nora packed fewer bags than the median of the six volunteers.
Without knowing the actual values, we can't pin down whether Nora is above or below 6. Insufficient alone.

Both together:
Set is fixed as {4, 5, 6, 7, 8, 13}. Median = (6+7)/2 = 6.5.
Nora < 6.5, so Nora packed 4, 5, or 6. In all cases, Nora packed 6 or fewer.
The answer to "did Nora pack more than 6?" is a definitive NO.

Answer: C

The trap is giving up on S1 too early. Once you realize the constraints force exactly one set of values, the problem becomes much cleaner.

HK12! · Answer

Statement (1) says:
Minimum 4, max > 12
Possible set: 4, 5, 6, 7, 8, 13

Nora could be ≤6 or >6
So, It's Not sufficient.

Statement (2) says:
Nora < median
But without knowing numbers, she could still be ≤6 or >6
So, It's Not sufficient.

Combined statement (1) & (2) says,
From (1), numbers are: 4, 5, 6, 7, 8, 13
Median = (6 + 7)/2 = 6.5

Nora < 6.5 → Nora = 4, 5, or 6 → not > 6
Thus, it's sufficient and therefore the correct answer is option C.

At a community center, Nora and five other volunteers packed snack bag

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GMAT Data Sufficiency (DS) Questions

At a community center, Nora and five other volunteers packed snack bag

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