For each of the last six years, the table shows the price, in Bangladeshi taka, of one unit for each...

Owning the Dataset

Let's start by understanding what we're working with. This table shows prices for four items (A, B, C, D) and a price index across 6 years.

Key insights from our initial scan:

• We have price data that varies across different years
• Multiple items with different pricing patterns
• A price index that may relate to the individual item prices
• The years serve as our reference points for all comparisons

Rather than trying to memorize all the numbers, let's focus on understanding relationships and patterns. This approach will help us evaluate the statements much more efficiently.

Analyzing Statement 1

Statement 1 Translation:

Original: "The years in which the Item B prices were highest were also the years for which the price index was least."

What we're looking for:

• Years with the highest Item B prices
• Years with the lowest price indices
• Whether these two sets of years match completely

In other words: Do the years with maximum Item B prices perfectly match the years with minimum price index values?

Let's tackle this using a sorting approach. Instead of manually checking each year's values, we can sort the data to immediately identify the patterns we need.

Step 1: Sort by Item B prices (highest to lowest)

SORT by Item B (descending):
→ Years 2 and 3 both have value 12 (highest)

We can immediately see that Years 2 and 3 have the highest Item B prices (both at 12).

Step 2: Sort by Price Index (lowest to highest)

SORT by Price Index (ascending):
→ Years 1, 2, 6 have lowest values (345, 347, 358)

The years with the lowest price indices are Years 1, 2, and 6.

Step 3: Check for matches

Looking at our two sets:

• Highest Item B prices: Years 2 and 3
• Lowest price indices: Years 1, 2, and 6

Only Year 2 appears in both sets. For the statement to be true, both Years 2 and 3 would need to appear in the lowest price index set, and Years 1 and 6 should not be in that set.

Statement 1 is FALSE

Teaching Note: Notice how sorting immediately revealed the answer patterns without requiring us to write down every single value. This approach dramatically reduces the chance of calculation errors while giving us a clearer picture of the data relationships.

Analyzing Statement 2

Statement 2 Translation:

Original: "The prices of Item A were positively correlated with the price index."

What we're looking for:

• Whether Item A prices tend to increase as the price index increases
• A general upward trend between these two variables

In other words: As Item A prices go up, does the price index also tend to go up?

Instead of performing a complex correlation calculation, we can use visual pattern recognition after sorting.

Step 1: Sort by Item A prices (ascending)

SORT by Item A (ascending):

Year	Item A	Price Index
1	3	345
2	3	347
3	5	407
6	6	358
4	8	415
5	8	420

Step 2: Analyze the pattern in the Price Index column

When we look at the sorted data, we can see a general upward trend in the Price Index as Item A increases:

• At Item A = 3: Price Index ranges from 345-347
• At Item A = 5: Price Index is 407
• At Item A = 6: Price Index is 358 (a slight dip)
• At Item A = 8: Price Index ranges from 415-420

Despite the slight anomaly with Year 6, the overall pattern shows a clear positive relationship. When Item A increases from 3 to 8, the Price Index generally increases from the 340s to the 410-420 range.

Statement 2 is TRUE

Teaching Note: We've avoided a time-consuming correlation calculation by using visual pattern recognition. On the GMAT, you rarely need to calculate exact correlation coefficients - recognizing the general pattern after sorting is usually sufficient and much faster.

Analyzing Statement 3

Statement 3 Translation:

Original: "The prices of Item C and the prices of Item D were positively correlated."

What we're looking for:

• Whether Item C prices tend to increase as Item D prices increase
• A general upward trend between these two variables

In other words: As Item C prices go up, do Item D prices also tend to go up?

Again, let's use sorting and visual pattern recognition to quickly evaluate this statement.

Step 1: Sort by Item C prices (ascending)

SORT by Item C (ascending):

Item C	Item D
5	6
6	5
7	4
8	5
9	3
10	1

Step 2: Analyze the pattern in the Item D column

Looking at the sorted data, we can observe that as Item C increases from 5 to 10, Item D generally decreases from 6 to 1. The pattern is quite clear:

• As Item C increases, Item D predominantly decreases
• The highest Item C value (10) corresponds to the lowest Item D value (1)
• The lowest Item C value (5) corresponds to the highest Item D value (6)

This shows a negative correlation, not a positive one. When one variable increases, the other tends to decrease.

Statement 3 is FALSE

Teaching Note: Sorting the data instantly revealed the relationship between these two variables. We didn't need to calculate any correlation coefficients - the visual pattern was sufficient to determine that the correlation is negative, not positive.

Final Answer Compilation

Evaluating all three statements:

• Statement 1: FALSE (Years with highest Item B prices don't all have the lowest price indices)
• Statement 2: TRUE (Item A prices and Price Index show a positive correlation)
• Statement 3: FALSE (Item C and Item D prices show a negative correlation, not positive)

Our answer is: No, Yes, No

Learning Summary

Skills We Used

1. Strategic Sorting: We sorted the data differently for each statement to reveal patterns instantly.
2. Visual Pattern Recognition: Instead of calculating correlation coefficients, we recognized trends visually after sorting.
3. Set Comparison: For Statement 1, we identified two sets and checked for complete overlap.

Strategic Insights

1. Sort First, Calculate Later (If At All): On table analysis questions, sorting should be your first instinct. It transforms the data to reveal patterns that might take minutes to find through calculation.
2. Correlation Shortcut: For correlation questions, simply sort by one variable and observe whether the other variable generally increases (positive), decreases (negative), or shows no pattern (no correlation).
3. Extreme Values Matter: For statements about "highest" or "lowest" values, sorting immediately identifies these extremes without searching the table.

Common Mistakes We Avoided

1. Calculating Correlation Coefficients: This is time-consuming and error-prone. Visual pattern recognition after sorting is sufficient for most GMAT questions.
2. Manual Checking: We avoided manually checking each year's values, which would have taken much longer and increased the chance of errors.
3. Over-Analysis: For Statement 2, despite one anomaly (Year 6), we correctly identified the predominant trend without getting caught up in perfect correlations.

Remember, on table analysis questions, your ability to reorganize data through sorting will often be more valuable than complex calculations. The approach we used here can be applied to virtually any GMAT table question to save significant time while improving accuracy.