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
Answer: A
Cheers,
Brent
