Question:

If \(-13<a<-2\) and \(1<b<9\), which of the following could be equal to the product of \(a\) and \(b\)? Indicate all possible values.

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For product range questions, calculate extreme values and then verify each option within that interval carefully.
Updated On: Sep 30, 2025
  • -20
  • -18
  • -15
  • -14
  • -13
  • -9
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The Correct Option is A

Solution and Explanation

Step 1: Define ranges.
Since \( -13<a<-2 \), possible integer values for \( a \) are: \(-12, -11, -10, -9, -8, -7, -6, -5, -4, -3\). Since \( 1<b<9 \), possible integer values for \( b \) are: \(2, 3, 4, 5, 6, 7, 8\).
Step 2: Product range.
Smallest product = \(-12 \times 8 = -96\).
Largest product = \(-3 \times 2 = -6\).
So possible values of \( ab \) are between -96 and -6.
Step 3: Check options.
- -20: Falls in range, possible.
- -18: Falls in range, possible.
- -15: Falls in range, possible.
- -14: Falls in range, possible.
- -13: Not possible (not divisible by given integers).
- -9: Not possible (since \(a\) is negative and \(b\) is positive, but no integer pair matches). Thus, correct answers are -20, -18, -15, -14.
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