Two-Part Analysis Data Insights Practice Questions

To solve this logic problem, first list the constraints:

- 12 hours = total hours available per day
- 4 hours = maximum hours for walking per day
- Minimum 4 art or architecture activities during the 2 days
- Maximum 1 art museum per day
- Minimum of 1 beach activity during the trip
- Minimum of 1 shopping activity each day

Now evaluate the activities the family has already planned to see which constraints are satisfied and which are not.

**Day 1:** The family has planned 11 hours of activities with 1 hour of walking. Therefore, only 1 hour remains, and a walking activity could be chosen if desired.

**Day 2:** The family has planned 10 hours of activities (3 + 2 + 4 + 1 = 10) with 4 hours of walking. This means that 2 hours remain for additional activities, but none can involve walking since the 4-hour walking limit has been reached.

Given these constraints, the only activities possible for each day are:

- **Day 1:** Mirador De Colon, Montserrat, or La Pedrera
- **Day 2:** Montserrat

Therefore, the family must choose the sightseeing trip to Montserrat on Day 2, leaving only Mirador De Colon and La Pedrera as options for Day 1.

Now consider the family preferences. Mom already has shopping on each day (Las Ramblas and Barri Gotico), and Little Brother has a beach activity on Day 2 (Nova Icària). However, Big Sister only has 3 of her required 4 art or architecture activities. Both Mirador De Colon and La Pedrera fit this category, but Dad will not go to more than 1 art exhibit on a single day, and the family will already visit Park Güell on Day 1. This means they cannot also visit La Pedrera. Therefore, the family will visit Mirador De Colon on Day 1.

To solve this fractions problem, we must find the ratio of the number of total boxes packed by the first-shift to the total number of boxes packed by both shifts together. From the information given, we know that there were 2/3 as many first-shift workers as second-shift workers and, inverting the second fraction, we know that each first-shift worker packed 3/4 as many boxes as each individual second-shift worker. From here, multiplying the ratio of workers by the ratio of work per individual gives the fraction of total first-shift boxes relative to the second shift. This is done as (2/3) × (3/4) = 6/12 = 1/2. Thus, the first shift packs half as many boxes as the second shift. We can compute the first-shift boxes relative to the total by:
(first-shift fraction) / (first-shift fraction + second-shift fraction) = 1 / (1+2) = 1/3.
Thus the first shift does 1/3 of the total work. We must look for two numbers in the table that are related by a factor of 3. The only two numbers are 12 and 36, meaning that the first shift packed 12 boxes, and the total number of boxes packed by both shifts was 3 × 12 = 36.

Alternatively, one could use numbers to establish the relationship between the number of total boxes packed by the first shift and the number of total boxes packed by the two shifts together. We use our fractional ratios to choose smart numbers and assign 2 workers to the first shift, 3 workers to the second shift, 3 boxes per individual on the first shift, and 4 boxes per individual on the second shift. This gives:
Total First-shift Boxes = (2 workers) × (3 boxes per worker) = 6 boxes
Total Second-shift Boxes = (3 workers) × (4 boxes per worker) = 12 boxes
Total Boxes Overall = 12 boxes + 6 boxes = 18 boxes.
Again, from this we can derive that the ratio of first-shift boxes to the total boxes packed is 6/18 = 1/3.
Column 1: The correct answer is C.
Column 2: The correct answer is E.

The conclusion of the argument is that the Dante 5000 is more reliable than the company's other stone-cutting machines and the premise is that there have been fewer customer complaints about the Dante 5000 than about the company's other industrial stone-cutting machines over the last six months.

This argument assumes a number of things! Do breakdowns in unreliable machines typically occur within the first six months? Have enough Dante 5000's been sold to make a reasonable comparison with the other stone-cutting machines?

Option A: The Dante 5000 is the most expensive stone-cutting machine produced by the company.
The argument is not about cost. This is out of scope.

Option B: There are other stone-cutting machines that are considered more reliable than the Dante 5000.
The argument is only about this company's stone-cutting machines. Other machines may be from other companies, so this is out of scope.

Option C: The Dante 5000 performed very well in initial testing.
The argument is reliability measured in terms of breakdowns, not about performance. This is out of scope.

Option D: Stone-cutting machines usually break down very quickly under industrial use if they are not reliable. - Strengthens
This option directly strengthens the conclusion that the Dante 5000 is more reliable than the company's other machines because it makes it more likely that six months would be enough time to see breakdowns if the machine were unreliable. Note that this statement does not plug all of the holes in the argument! It just makes this weak argument slightly stronger.

Option E: Very few customers have purchased a Dante 5000. - Weakens
This option directly weakens the conclusion by providing a good alternative interpretation of the low number of customer complaints. If very few customers have bought the machine, then a small number of complaints could actually represent a high rate (percent) of complaints. This choice points up the classic difference between absolute numbers and percents.

Option F: The Dante 5000 employs a new technology that is more precise than that used by our previous stone-cutting machines.
The argument is concerned with reliability measured in terms of breakdowns, not about precision. This choice is out of scope.

Column 1: The correct answer is D.
Column 2: The correct answer is E.