Question: A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185. What is the sum of the 5 smallest integers of set A?

1. -165
2. -175
3. -195
4. -205
5. -215

Answer:
Solution with Explanation:

Approach Solution (1):

Average of largest 5 = -185/5 = -37
So the largest numbers are -41, -39, -37, -35, -33
Now if we consider smallest 5, we have to eliminate last 2 numbers, which are -35 and -33
Notice here that the numbers are equally spaced
So the average of smallest number will just shift 2 place to the left
Average = -41
Therefore, total = -41 * 5 = -205

Correct Option: D

Approach Solution (2):

Say 7 consecutive odd integers are:
x, x+2, x+4, x+6, x+8, x+10, x+12
Question: x + x + 2 + x + 4 + x + 6 + x + 8 = 5x + 20 = ?
Given: x + 4 + x + 6 + x + 8 + x + 10 + x + 12 = 5x + 40 = -185
x + 4 + x + 6 + x + 8 + x + 10 + x + 12 = 5x + 40 = -185
5x + 20 + 20 = -185
5x + 20 = -205

Correct Option: D

“A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185. What is the sum of the 5 smallest integers of set A?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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