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29 Sep 2021, 08:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
46% (02:32) correct
54%
(02:47)
wrong
based on 107
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In a certain batch of guests in a museum, there are 50 guests; each guest buys either a $40 ticket or a $60 ticket, with at least one guest of each ticket type. The average (arithmetic mean) value of ticket-receipts from the batch is more than $50. If the average value of ticket-receipts is to be reduced to less than $50 by including few new guests with $40 tickets, what could definitely NOT be the number of new guests with $40 tickets that could be included?
I. 1
II. 2
III. 3
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. 1
II. 2
III. 3
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Capakki
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Joined: 21 Jun 2020
Last visit: 04 Apr 2024
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GMAT 1: 630 Q44 V32
GPA: 3.56
29 Sep 2021, 08:58
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I am not sure if my approach is correct. Giving a try.
if the split between $40 and $60 tickets is equal then (40x25)+(60x25)=2500. Avg=2500/50=50.
Now, to keep the avg above 50, number of people with $60 tickets needs to be increased.
New split: 24x40$ and 26x60$= 2520. Avg=2520/50=50.xy>50.0. Since its given that avg is more than 50, so we will solve further using this split, i.e. 24 tickets for 40$ and 26 tickets for $60.
To bring the avg below 50, lets add one to $40 ticket count
Split: 25x40$+26x60$=2560. Avg=2560/51=50.xy>50.00. Hence '1' can definitely not be included.
Adding one more to $40 count
Split: 26x40+ 26x60=2600. Avg=2600/52=50.00. Not less than 50. Hence '2' can definitely not be included.
Adding one more:
Split: 27x40 + 26x60=2640. Avg=2640/53=49.xy<50.00. Hence '3' can be there atleast in one of the possible case.
Therefore, option D is the answer.
It took me some time. A different approach might save some time.
if the split between $40 and $60 tickets is equal then (40x25)+(60x25)=2500. Avg=2500/50=50.
Now, to keep the avg above 50, number of people with $60 tickets needs to be increased.
New split: 24x40$ and 26x60$= 2520. Avg=2520/50=50.xy>50.0. Since its given that avg is more than 50, so we will solve further using this split, i.e. 24 tickets for 40$ and 26 tickets for $60.
To bring the avg below 50, lets add one to $40 ticket count
Split: 25x40$+26x60$=2560. Avg=2560/51=50.xy>50.00. Hence '1' can definitely not be included.
Adding one more to $40 count
Split: 26x40+ 26x60=2600. Avg=2600/52=50.00. Not less than 50. Hence '2' can definitely not be included.
Adding one more:
Split: 27x40 + 26x60=2640. Avg=2640/53=49.xy<50.00. Hence '3' can be there atleast in one of the possible case.
Therefore, option D is the answer.
It took me some time. A different approach might save some time.
rocky620
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GMAT 1: 590 Q49 V22
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29 Sep 2021, 09:07
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If the average is exactly was exactly $50 than equal number of guests must have bought $40 & $60 tickets (25 each). But, since the average is greater than $50, more than 25 guests bought $60 tickets. The minimum will be 26 guests, as per this 24 guests bought $40 tickets.
To bring the average below $50 we need to add minimum 3 guests who will buy $40 ticket.
So 1 & 2 cannot be the value.
Option D
To bring the average below $50 we need to add minimum 3 guests who will buy $40 ticket.
So 1 & 2 cannot be the value.
Option D
