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31 Dec 2023, 08:59
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Which of the following has the greatest value?
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
03 Sep 2024, 06:49
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sumitjain123
The question is up to the highest GMAT standards. The solution provided is also fine and detailed enough. The use of "obviously" indicates that the reasoning is straightforward and doesn't require further elaboration. If it's not clear to you, I suggest you consider the following:
a. Re-read the solution carefully and invest more time in understanding it. b. Brush up on fundamental concepts. c. Practice easier questions, as this type of question may be more challenging for you at the moment.
Option D, \(120!^4 = (120!) * (120!) * (120!) * (120!)\).
Option B, \(480! = (120!) * (121 * ... * 240) * (241 * ... * 360) * (361 * ... * 480)\).
The number of terms is equal in both options (four in each, those within parentheses). The first terms are equal, and each of the remaining corresponding terms in option B is greater than in option D. So, once again, it is OBVIOUS that B > D. This should be elementary.
Hope this helps.
General Discussion
31 Dec 2023, 08:59
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Official Solution:
Which of the following has the greatest value?
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
Let's compare A and B:
\(480! = 400! * 401 * 402 * ... * 480\). Since \(401 * 402 * ... * 480\), the product of 80 numbers from 401 to 480, inclusive, is more than \(80!\), he product of 80 numbers from 1 to 80, inclusive, then B > A.
Similarly, we can conclude that B > C.
Option D, \(120!^4 = 120! * 120! * 120! * 120!\). While option B, \(480! = 120! * (121 * ... * 240) * (241 * ... * 360) * (361 * ... * 480)\). Obviously, B > D.
Similarly, we can conclude that B > E.
Therefore, among the options, B, \(480!\), has the greatest value.
Answer: B
Which of the following has the greatest value?
A. \(400!*80!\)
B. \(480!\)
C. \(360!*120!\)
D. \((120!)^4\)
E. \((240!)^2\)
Let's compare A and B:
\(480! = 400! * 401 * 402 * ... * 480\). Since \(401 * 402 * ... * 480\), the product of 80 numbers from 401 to 480, inclusive, is more than \(80!\), he product of 80 numbers from 1 to 80, inclusive, then B > A.
Similarly, we can conclude that B > C.
Option D, \(120!^4 = 120! * 120! * 120! * 120!\). While option B, \(480! = 120! * (121 * ... * 240) * (241 * ... * 360) * (361 * ... * 480)\). Obviously, B > D.
Similarly, we can conclude that B > E.
Therefore, among the options, B, \(480!\), has the greatest value.
Answer: B
