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
A craftsperson made 126 ornaments and put them all into boxes.
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Given: A craftsperson made 126 ornaments and put them all into boxes. Each box contained either 6 ornaments or 24 ornaments.BTGmoderatorDC wrote: ↑Sat Apr 09, 2022 8:33 pmA 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
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
Answer: A
Cheers,
Brent