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The product of the consecutive integers from 20 through 73,
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13 Jul 2020, 07:47
13 Jul 2020, 07:47
1
Expert Reply
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Question Stats:
73% (00:46) correct
26% (00:23) wrong based on 34 sessions
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Quantity A |
Quantity B |
The product of the consecutive integers from 20 through 73, inclusive |
The product of the consecutive integers from 18 through 72, inclusive |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: The product of the consecutive integers from 20 through 73,
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13 Jul 2020, 07:56
13 Jul 2020, 07:56
1
Value A is equal to 20*21*22* ... * 72*73
Value B equals 18*19*20*...*72
Both of the values contain a common factor of 20*21*22*...*71*72
We can divide each number by that factor
Then Value A becomes 73 and Value B becomes 18*19
18*19 >> 73
Thus Value B is larger (Answer B)
Value B equals 18*19*20*...*72
Both of the values contain a common factor of 20*21*22*...*71*72
We can divide each number by that factor
Then Value A becomes 73 and Value B becomes 18*19
18*19 >> 73
Thus Value B is larger (Answer B)
Re: The product of the consecutive integers from 20 through 73,
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13 Jul 2020, 21:16
13 Jul 2020, 21:16
1
Carcass wrote:
Quantity A |
Quantity B |
The product of the consecutive integers from 20 through 73, inclusive |
The product of the consecutive integers from 18 through 72, inclusive |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Another way to do it. Bit longer.
A = 20 * 21 ... 73
B = 18 * 19 ... 72
Multiplying both sides by 18*19*73, we have
A = (18*19*20 * ... * 72) * 73 * 73
B = 18*19*(18*19*20 * ... * 72) * 73
Comparing, common multipliers cancel. Thus
73*73 < 18*19*73
73 < 18*19
A < B
Answer B.
