Julio is trying to decide between 4 different vendors for a new IT system

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Julio is trying to decide between 4 different vendors for a new IT system. Vendor D is less expensive than Vendor C. Vendor C is more expensive than Vendor B. Vendor B is less expensive than Vendor D. Vendor D is less expensive than Vendor A. If Julio wants to purchase the least expensive system, which Vendor will he pick?

Vendor A

Vendor B

Vendor C

Vendor D

Vendor A or B

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The Correct Answer and Explanation is:

To determine which vendor Julio should choose for the least expensive IT system, we must compare the relative costs of the four vendors based on the given information:

Given:

  1. Vendor D is less expensive than Vendor C.
    → D < C
  2. Vendor C is more expensive than Vendor B.
    → C > B → B < C
  3. Vendor B is less expensive than Vendor D.
    → B < D
  4. Vendor D is less expensive than Vendor A.
    → D < A

Step-by-step comparison:

From statement 3:

  • B < D

From statement 1:

  • D < C, and since B < D, we now know: B < D < C

From statement 4:

  • D < A, so now we can add A into the sequence:
    → B < D < C, and D < A
    → So B < D < C and D < A, meaning B < D < C, and A is highest.

So putting all together in order from least to most expensive:

  • B < D < C < A

Conclusion:

Since Vendor B is the least expensive of all, Julio should choose Vendor B.

✅ Correct Answer: Vendor B

300-Word Explanation:

To determine which vendor offers the least expensive IT system, we must analyze and compare the relative pricing given in the problem.

First, we’re told Vendor D is less expensive than Vendor C. This gives us D < C. Next, Vendor C is more expensive than Vendor B, or C > B, which implies B < C. Then, it is said that Vendor B is less expensive than Vendor D, giving us B < D.

Putting these relationships together:

  • From B < D and D < C, we can conclude: B < D < C

The last comparison states that Vendor D is less expensive than Vendor A, or D < A. Combining this with the previous relationships, we get:

  • B < D < C
  • And D < A, so Vendor A must be the most expensive.

Now we can build the full ranking of the vendors from least to most expensive:

  • Vendor B < Vendor D < Vendor C < Vendor A

From this, it’s clear that Vendor B is the cheapest option.

When faced with relative comparisons like these, a good strategy is to list the vendors and slowly establish relationships based on the given statements. Drawing a number line or simple inequality expressions can help you keep track.

Julio’s goal is to purchase the least expensive system. Based on the logical order we’ve established, the lowest-priced vendor is Vendor B, making it the best choice for his budget.

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