Five coffee–chicory blends—J, K, L, M, and N—are all priced differently. The blends are such that the greater the proportion...

## Understanding the Question

We have 5 coffee-chicory blends (J, K, L, M, and N), each priced differently. The key relationships are:
- More coffee → More expensive
- More chicory → Stronger flavor

Since coffee and chicory together make 100% of each blend, we can deduce:
- More expensive blends = More coffee = Less chicory = **Weaker** flavor
- Less expensive blends = Less coffee = More chicory = **Stronger** flavor

**Our task**: When the 5 blends are ranked by cost from most to least expensive, which blend occupies position 3 (the middle)?

For a statement to be **sufficient**, it must allow us to definitively identify which specific blend is in the 3rd position.

## Analyzing Statement 1

Statement 1 tells us: "Blend L has a higher proportion of coffee than the other blends except for Blend M."

This translates to:
- M has the most coffee → M is most expensive (position 1)
- L has the second most coffee → L is second most expensive (position 2)
- J, K, and N have less coffee than L → They occupy positions 3, 4, and 5

Our partial ranking: M (1st), L (2nd), then J, K, and N somewhere in positions 3-5.

**The problem**: We don't know the relative order of J, K, and N. Any of these three could be in position 3.
- If J > K > N, then J is 3rd
- If K > J > N, then K is 3rd
- If N > J > K, then N is 3rd

Since we cannot identify which specific blend is 3rd, Statement 1 is **NOT sufficient**.

**[STOP - Not Sufficient!]** This eliminates choices A and D.

## Analyzing Statement 2

**Important**: We now analyze Statement 2 independently, forgetting Statement 1 completely.

Statement 2 tells us: "Blend K and Blend N both have a stronger flavor than Blend J."

Since stronger flavor = more chicory = less coffee = less expensive:
- J has weaker flavor than K → J has more coffee than K → J is more expensive than K
- J has weaker flavor than N → J has more coffee than N → J is more expensive than N

This gives us: \(\mathrm{J} > \mathrm{K}\) and \(\mathrm{J} > \mathrm{N}\) (in terms of cost).

**What we still don't know**:
- Where J ranks compared to L and M
- The relative order of K and N
- Which position (1st through 5th) any blend occupies

J could be anywhere from 1st to 3rd position. For example:
- If \(\mathrm{M} > \mathrm{L} > \mathrm{J} > \mathrm{K} > \mathrm{N}\), then J is 3rd
- If \(\mathrm{J} > \mathrm{M} > \mathrm{L} > \mathrm{K} > \mathrm{N}\), then L is 3rd
- If \(\mathrm{M} > \mathrm{J} > \mathrm{L} > \mathrm{K} > \mathrm{N}\), then L is 3rd

Since we cannot determine which blend is in position 3, Statement 2 is **NOT sufficient**.

**[STOP - Not Sufficient!]** This eliminates choice B.

## Combining Statements

Now let's combine both statements.

**From Statement 1**:
- Position 1: M (most expensive)
- Position 2: L
- Positions 3, 4, 5: J, K, and N (in some order)

**From Statement 2**:
- J is more expensive than both K and N

**Combining the information**: 
Since J must occupy position 3, 4, or 5 (from Statement 1), and J is more expensive than both K and N (from Statement 2), J must be the most expensive among these three blends. Therefore:

- Position 3: **J**
- Positions 4 and 5: K and N (in either order)

The complete ranking becomes: M (1st), L (2nd), **J (3rd)**, then K and N in positions 4 and 5.

**[STOP - Sufficient!]** The combined statements allow us to determine that **J is the blend in the middle position**.

## The Answer: C

Neither statement alone tells us which blend is in the middle, but together they provide enough information to determine that J occupies the 3rd position.

**Answer Choice C**: "Both statements together are sufficient, but neither statement alone is sufficient."