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a and b are integers 1 < a < b < 10

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a and b are integers 1 < a < b < 10 [#permalink] New post   13 Jun 2022, 01:00
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a and b are integers

\(1 < a < b < 10\)


Quantity A
Quantity B
The number of multiples of a that are greater than 20 but less than 80
The number of multiples of b that are greater than 20 but less than 80



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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piorachid
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Re: a and b are integers 1 < a < b < 10 [#permalink] New post   13 Jun 2022, 04:47
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Since a and b are integers, we know the maximum values are a=8 and b=9
By using logic, we can see that the smaller number is going to have more multiples than the greater number within the same range.
multiples of a between 20-80 exclusive:
8(3)=24 - 8(9)=72
multiples of b between 20-80 exclusive:
9(3)=27 - 9(8)=56
The range of possible multiples of a is greater than that of b
A
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a and b are integers 1 < a < b < 10 [#permalink] New post   13 Jun 2022, 06:32
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Since both a and b are integers, then we should examine lower ends of a and b, since smallers numbers will have greater number of multiples

Let a=2 and b=3

multiples of a and b shall be bounded by 20 and 80, therefore:
Multiples of a = \(\frac{(80-20-2)}{2} = 29 \)
Multiples of b = \(\frac{(80-20-2)}{3} = 19 \)

The answer is (A)
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a and b are integers 1 < a < b < 10 [#permalink]
13 Jun 2022, 06:32
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