swerve wrote:A craftsperson made 126 made ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained ornaments?
1) Fewer than 4 of the boxes contained 6 ornaments.
2) More than 3 of the boxes contained 24 ornaments.
The OA is A
Source: GMAT Prep
We can let a = the number of boxes containing 6 ornaments each and b = the number of boxes containing 24 ornaments each. We can create the equation:
6a + 24b = 126
6a = 126 - 24b
Dividing both sides of the equation by 6, we have: a = 21 - 4b
We see that the value of b could be 0, 1, 2, 3, 4 or 5, and the value of a would then be 21, 17, 13, 9, or 1, respectively.
Statement One Only:
Fewer than 4 of the boxes contained 6 ornaments.
In other words, a < 4. From the stem analysis, we see that if a < 4, then a must be 1 and hence b must be 5. So the total number of boxes is 1 + 5 = 6. Statement one alone is sufficient.
Statement Two Only:
More than 3 of the boxes contained 24 ornaments.
In other words, b > 3. From the stem analysis, we see that if b > 3, then b must be 4 or 5, and hence, a must be 9 or 1, respectively. In the former case, the total number of boxes is 4 + 9 = 13; however, in the latter case, the total number of boxes is 5 + 1 = 6. Statement two alone is not sufficient.
Answer: A
