A craftsperson made 126 ornaments and put them all into boxes.

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A craftsperson made 126 ornaments and put them all into boxes.

by BTGmoderatorDC » Sat Apr 09, 2022 8:33 pm

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A craftsperson made 126 ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained 24 ornaments?

(1) Fewer than 4 of the boxes contained 6 ornaments

(2) More than 3 of the boxes contained 24 ornaments

OA A

Source: GMAT Prep

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Re: A craftsperson made 126 ornaments and put them all into boxes.

by [email protected] » Sun Apr 10, 2022 5:57 am

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BTGmoderatorDC wrote:
Sat Apr 09, 2022 8:33 pm
A craftsperson made 126 ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained 24 ornaments?

(1) Fewer than 4 of the boxes contained 6 ornaments

(2) More than 3 of the boxes contained 24 ornaments

OA A

Source: GMAT Prep
Given: A craftsperson made 126 ornaments and put them all into boxes. Each box contained either 6 ornaments or 24 ornaments.
In situations like this, where there aren't many possible cases, I like to invest a little time upfront to systematically list those cases.
case i: 0 24-ornament boxes and 21 6-ornament boxes
case ii: 1 24-ornament boxes and 17 6-ornament boxes
case iii: 2 24-ornament boxes and 13 6-ornament boxes
case iv: 3 24-ornament boxes and 9 6-ornament boxes
case v: 4 24-ornament boxes and 5 6-ornament boxes
case vi: 5 24-ornament boxes and 1 6-ornament boxes
Aside: I'd typically list the six possible outcomes in table form, which would take less than 15 seconds.

Target question: How many of the boxes contained 24 ornaments?

Statement 1: Fewer than 4 of the boxes contained 6 ornaments
This statement rules out cases i to v, leaving only case vi, which means 5 boxes contained 24 ornaments.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: More than 3 of the boxes contained 24 ornaments
This statement rules out cases i to iv, leaving cases v and vi, which means EITHER 4 boxes contained 24 ornaments OR 5 boxes contained 24 ornaments.
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT