SAT Math: Disguised Average Questions

Sometimes the challenge in the SAT Math section isn’t doing the math: it’s knowing what math to do. Consider this problem.

The sum of 7 consecutive even integers is 224. What integer has the least value in the list?

  1. 16
  2. 18
  3. 26
  4. 29
  5. 32

The simplest solution involves finding the average (arithmetic mean) of the seven numbers. But how would you know to calculate the average? After all, the question seems to be about numbers and operations, not descriptive statistics.

What else you can do inside qs leap ?

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Here are your clues: the words consecutive and sum. For any list of consecutive integers, the average will equal the median. And since the median will fall in the middle of the list, once you’ve found the median you can count down in the list to the lowest value.

Average = Sum of the Values ÷ The Number of Values

  • 32 = 224 ÷ 7
  • 32 = Median
  • 26, 28, 30, 32, 34, 36, 38
  • Thus, (C) is correct.

Did the list surprise you? You may have been expecting to see this: 29, 30, 31, 32, 33, 34, 35. But the question refers to a list of consecutive even integers.

Make sure you read—and reread—disguised average questions carefully. Keep an eye out for words like “even” and “odd.” If you’re not paying attention, you may end up picking a wrong answer like (D).

Try a few more problems for practice. Remember: when you’re given the sum of a set of consecutive integers—be they odd, even, or otherwise patterned—consider calculating the average of those integers. The average will give you the median, and the median will put you in the middle of the list.

  1. The sum of 7 consecutive integers is 406. If the numbers are arranged from least to greatest, what is the value of the second integer in the list?
    1. 56
    2. 57
    3. 58
    4. 59
    5. 60
  2. What is the greatest of 5 consecutive odd integers if the sum of these integers is 255?
    1. 51
    2. 53
    3. 55
    4. 57
    5. 59
  3. A list of 5 integers is made up of consecutive multiples of 5. If the sum of these five numbers is 675, what is the number with the least value in the list?
    1. 100
    2. 125
    3. 133
    4. 135
    5. 175

Answers: 1.(A) 2.(C) 3.(B)

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