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The product of two integers is between 137 and 149. Which of the following CANNOT be one of the integers?
  • a)
    15
  • b)
    13
  • c)
    11
  • d)
    10
  • e)
    7
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The product of two integers is between 137 and 149. Which of the follo...
The correct answer is a. For the product of two integers to lie between 137 and 149, a multiple of both integers must lie between 137 and 149. Of the answer choices, 15 is the only number without a multiple that lies between 137 and 149; 15 × 9 = 135, and 15 × 10 = 150. Thus, the only number that cannot be one of the integers is 15.
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The product of two integers is between 137 and 149. Which of the follo...
Explanation:

Given:
The product of two integers is between 137 and 149.

To find:
Which of the following CANNOT be one of the integers?

Analysis:
To find the integer that cannot be one of the factors, we need to consider the range of possible values for each integer based on the given product range.

Factors Analysis:
- The factors of 137 are 1 and 137.
- The factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138.
- The factors of 139 are 1 and 139.
- The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.
- The factors of 141 are 1, 3, 47, and 141.
- The factors of 142 are 1, 2, 71, and 142.
- The factors of 143 are 1, 11, 13, 143.
- The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
- The factors of 145 are 1, 5, 29, and 145.
- The factors of 146 are 1, 2, 73, and 146.
- The factors of 147 are 1, 3, 7, 21, 49, and 147.
- The factors of 148 are 1, 2, 4, 37, 74, and 148.

Conclusion:
From the above analysis, we can see that the integer 15 (option A) cannot be one of the integers as it does not fall within the factors of any of the numbers in the given product range. Therefore, option A (15) is the correct answer.
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The product of two integers is between 137 and 149. Which of the following CANNOT be one of the integers?a)15b)13c)11d)10e)7Correct answer is option 'A'. Can you explain this answer?
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