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At a certain reception, punch is served in glasses of two sizes, small

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sahildesai360
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At a certain reception, punch is served in glasses of two sizes, small [#permalink] At a certain reception, punch is served in glasses of two sizes, small   14 Nov 2023, 10:00
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77% (02:28) correct 23% (02:45) wrong based on 144 sessions
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At a certain reception, punch is served in glasses of two sizes, small and large. If a bowl of a certain size, when filled with punch will 24 small glasses or 15 large glasses, then 10 such bowls, when filled with punch, will fill 72 small glasses and how many large glasses?

A) 90
B) 105
C) 120
D) 135
E) 150
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B
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Navnit99
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Re: At a certain reception, punch is served in glasses of two sizes, small [#permalink] At a certain reception, punch is served in glasses of two sizes, small   06 Dec 2023, 07:24
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24 small glass = 1 bowl, so 72 small glass = 3 bowls

Now there are 7 bowls for large glasses.

1 bowl = 15 large glasses, so 7x15= 105 large glasses

Ans = 105 glasses option "B"
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gmatophobia
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Re: At a certain reception, punch is served in glasses of two sizes, small [#permalink] At a certain reception, punch is served in glasses of two sizes, small   14 Nov 2023, 11:32
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sahildesai360 wrote:
At a certain reception, punch is served in glasses of two sizes, small and large. If a bowl of a certain size, when filled with punch will 24 small glasses or 15 large glasses, then 10 such bowls, when filled with punch, will fill 72 small glasses and how many large glasses?

A) 90
B) 105
C) 120
D) 135
E) 150


Let's assume that the volume of the bowl = LCM (24, 15) = \(8 * 3 * 5\)

As the bowl of punch can fill \(15\) large glasses, the volume of each large glass = \(8\) cubic units, and the volume of each small glass = \(5\) cubic units.

The volume of punch in \(10\) bowls = \(8 * 3 * 5 * 10 = 1200\) cubic units.

The volume of punch that can be accommodated by \(72\) small glasses = \(72 * 5 = 360\) cubic units.

Remaining volume of punch= \(1200 - 360 = 840\) cubic units

Number of large glasses required to fill \(840\) cubic units of punch = \(\frac{840}{8} = 105\)

Option B
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Re: At a certain reception, punch is served in glasses of two sizes, small [#permalink] At a certain reception, punch is served in glasses of two sizes, small   16 Nov 2023, 02:50
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Given: At a certain reception, punch is served in glasses of two sizes, small and large.
Asked: If a bowl of a certain size, when filled with punch will 24 small glasses or 15 large glasses, then 10 such bowls, when filled with punch, will fill 72 small glasses and how many large glasses?

I bowl will filll punch in = 24 small glasses = 15 large glasses
10 bowls will fill punch in = 240 small glasses = 150 large glasses

72 small glasses = 45 large glasses

10 bowls will fill punch in 72 small glasses and (150-45=105) large glasses.

IMO B
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At a certain reception, punch is served in glasses of two sizes, small [#permalink] At a certain reception, punch is served in glasses of two sizes, small   23 Nov 2023, 01:04
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Simple Logical Approach

Bowls can either fit 24 small (x) or 15 large (y). There are 10 bowls, so x+y=10.

STEM says some of these 10 bowls fit 72 small glasses.

72 small glasses / 24 small glasses (which is the capacity per bowl x) = 3. You are now left with 7 bowls since --> 3+y=10 ---> y=7.

7 bowls * 15 large glasses = 105 large glasses.

Voila.
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mooh
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Re: At a certain reception, punch is served in glasses of two sizes, small [#permalink] At a certain reception, punch is served in glasses of two sizes, small   16 May 2024, 13:52
The question wants us to find the no of large glasses required to fill 10 bowls in addition to 72 small glasses

24 small glasses will fill 1 bowl
x small glasses will fill 10 bowls

x = 240, so 240 small glasses will fill 10 bowls and we already have 72 of those

so there are (240-72)small glasses left to fill the bowl and this equals 168small glasses left

Now we need to determine how many large glasses is equal to 168 small glasses

From the question 24 small glasses = 15 large glasses
therefore 168 small glasses = x large glasses

with cross multiplication, x= 105 large glasses
Answer = B­
gmatclubot
Re: At a certain reception, punch is served in glasses of two sizes, small [#permalink]
16 May 2024, 13:52
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