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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Of 120 hotel rooms rented one night, some were suits rented for $115 e
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18 Oct 2022, 07:11
18 Oct 2022, 07:11
1
Expert Reply
00:00
Question Stats:
75% (02:15) correct
25% (01:18) wrong based on 4 sessions
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Of 120 hotel rooms rented one night, some were suits rented for $115 each and the rest were double rooms rented for $85 each. If the total revenue from the room rentals ffor this night was $10890, how many suits were rented?
A) 23
B) 35
C) 54
D) 94
E) 99
A) 23
B) 35
C) 54
D) 94
E) 99
GRE Whiz Representative
Joined: 25 May 2022
Posts: 25
Given Kudos: 1
Of 120 hotel rooms rented one night, some were suits rented for $115 e
[#permalink]
19 Oct 2022, 07:10
19 Oct 2022, 07:10
1
Expert Reply
Approach 1 (Stanard):
Let's assume the number of suits to be 'S' and double rooms to be 'D'.
So from the first part, we can form the equation,
Each suit costs 115$ and each double room costs 85$
So the equation we can get,
By "Equation (2)" \(-\) "Equation (1) \(× 17\)" we get,
The answer is A.
Approach 2: A different way
If you observe, the prices are given in such a way that one is 100 + 15 and another one is 100 - 15.
Now we can utilize this info to our advantage to do the calculation swiftly.
Had there been 60 rooms of each type the total rent would be \(60 × (115 + 85) = 12000\)
This is happening because we have fewer suits. And for each change of one suit to a double room, we lose out on \(115 - 85 = 30$\)
Let's assume the number of suits to be 'S' and double rooms to be 'D'.
So from the first part, we can form the equation,
- \(S + D = 120\)... (1)
Each suit costs 115$ and each double room costs 85$
So the equation we can get,
- \(115S + 85D = 10890
Or, 23S + 17D = 2178\)... (2)
By "Equation (2)" \(-\) "Equation (1) \(× 17\)" we get,
- \(23S + 17D - 17D - 17S = 2178 -\) \(120 ×17\) \(= 138\)
Or, \(6S = 138 \)
Or, \(S = 23\)
The answer is A.
Approach 2: A different way
If you observe, the prices are given in such a way that one is 100 + 15 and another one is 100 - 15.
Now we can utilize this info to our advantage to do the calculation swiftly.
Had there been 60 rooms of each type the total rent would be \(60 × (115 + 85) = 12000\)
- Now there is a gap of \(12000 - 10890 = $1110\)
This is happening because we have fewer suits. And for each change of one suit to a double room, we lose out on \(115 - 85 = 30$\)
- So we must have missed out on \(\frac{1110}{30}\) \(= 37\) rooms.
- So the number of suits should be 60 - 37 = 23
gmatclubot
Of 120 hotel rooms rented one night, some were suits rented for $115 e [#permalink]
19 Oct 2022, 07:10
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