Hello,
Can you please tell me how to solve this:
During the 31-day month of May, a tuxedo shop rents a different number of tuxedos each day, including a store-record 55 tuxedos on May 23rd. Assuming that the shop had an unlimited inventory of tuxedos to rent, what is the maximum number of tuxedos the shop could have rented during May?
A) 1240
B) 1295
C) 1650
D) 1705
E) 1760
OA: A
Thanks a lot,
Sri
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During the 31-day month of May, a tuxedo shop rents
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Hi Sri,
This prompt is essentially about addition, but it presents a number of "rules" that we have to follow, so that we can figure out what numbers to "add up."
We're told that we'll have 31 numbers AND that they're all DIFFERENT. The highest number is 55 (since it was a "store-record"). We're asked for the maximum total possible, which means that we'll have to choose the 31 "biggest" numbers, starting at 55 and "working down."
55, 54, 53, 52.....
The first task is to figure out what would be the "smallest" number of this group. Since there are 55 positive integers from 1 to 55 (inclusive) and we want the 31 biggest numbers, we need to remove the 24 smallest. So, remove the numbers 1 to 24 (inclusive) and you're left with 25 to 55, inclusive.
Now, we have to add up the numbers from 25 to 55, inclusive. You can approach this process in a couple of different ways.
One way is to take the average of the largest and smallest, then multiply this value by the total number of terms:
(55 + 25)/2 = 80/2 = 40
40 x 31terms = 1240
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This prompt is essentially about addition, but it presents a number of "rules" that we have to follow, so that we can figure out what numbers to "add up."
We're told that we'll have 31 numbers AND that they're all DIFFERENT. The highest number is 55 (since it was a "store-record"). We're asked for the maximum total possible, which means that we'll have to choose the 31 "biggest" numbers, starting at 55 and "working down."
55, 54, 53, 52.....
The first task is to figure out what would be the "smallest" number of this group. Since there are 55 positive integers from 1 to 55 (inclusive) and we want the 31 biggest numbers, we need to remove the 24 smallest. So, remove the numbers 1 to 24 (inclusive) and you're left with 25 to 55, inclusive.
Now, we have to add up the numbers from 25 to 55, inclusive. You can approach this process in a couple of different ways.
One way is to take the average of the largest and smallest, then multiply this value by the total number of terms:
(55 + 25)/2 = 80/2 = 40
40 x 31terms = 1240
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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To maximize the sum for all 31 days, we must maximize the number of tuxedos rented per day.gmattesttaker2 wrote:Hello,
Can you please tell me how to solve this:
During the 31-day month of May, a tuxedo shop rents a different number of tuxedos each day, including a store-record 55 tuxedos on May 23rd. Assuming that the shop had an unlimited inventory of tuxedos to rent, what is the maximum number of tuxedos the shop could have rented during May?
A) 1240
B) 1295
C) 1650
D) 1705
E) 1760
A different number of tuxedos is rented each day, with the maximum number -- 55 -- rented on May 23.
Thus, the number of tuxedos rented per day must be a descending set of CONSECUTIVE INTEGERS, starting with 55:
55, 54, 53, 52...
If exactly 50 tuxedos are rented each today, the sum for all 31 days = 31*50 = 1550.
Since FEWER than 50 tuxedos are actually rented on most of the days, the sum for all 31 days must be LESS than 1550.
Eliminate C, D and E.
For any set of consecutive integers, median = (sum)/(number of integers).
Here, there are 31 consecutive integers, implying the following:
median = sum/31.
The median of an ODD number of consecutive integers will always be an INTEGER value.
Thus, the correct answer choice must be a multiple of 31.
Test A and B:
A: 1240/31 = 40.
B: 1295/31 = non-integer.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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