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A group ticket for admission to art gallery A costs $p for up to 10 pe

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A group ticket for admission to art gallery A costs $p for up to 10 pe [#permalink]

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New post 22 Nov 2017, 01:15
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[GMAT math practice question]

A group ticket for admission to art gallery A costs $p for up to 10 people. Each additional person is charged an admission fee of $q. A group ticket for admission to museum M costs $r for up to 15 people. Each additional person is charged an admission fee of $s. If a group of 20 people visit both the art gallery A and the museum M, is the total cost of their admission to the art gallery less than the total cost of their admission to the museum?

1) \(p<r\)
2) \(q<s\)
[Reveal] Spoiler: OA

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A group ticket for admission to art gallery A costs $p for up to 10 pe [#permalink]

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New post 22 Nov 2017, 01:33
MathRevolution wrote:
[GMAT math practice question]

A group ticket for admission to art gallery A costs $p for up to 10 people. Each additional person is charged an admission fee of $q. A group ticket for admission to museum M costs $r for up to 15 people. Each additional person is charged an admission fee of $s. If a group of 20 people visit both the art gallery A and the museum M, is the total cost of their admission to the art gallery less than the total cost of their admission to the museum?


A.G -> 10p + 10q
M -> 15r + 5s

10p + 10q < 15r + 5s ?

Quote:
1) \(p<r\)
2) \(q<s\)


S1) p < r
We don't know the value of q or s.
Insufficient.

S2) q < s
We don't know the value of p or r.
Insufficient

Quote:
Combining both statements


p = 10, q = 1
r = 11, s = 2
10p + 10q < 15r + 5s (Yes)

p = 10, q = 20
r = 11, s = 21
10p + 10q < 15r + 5s (No)

Insufficient.

E is the answer.
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Last edited by akshayk on 22 Nov 2017, 12:53, edited 1 time in total.

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Re: A group ticket for admission to art gallery A costs $p for up to 10 pe [#permalink]

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New post 22 Nov 2017, 06:12
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If 20 people visit art gallery => Cost for admission to art gallery = A = 10p + 10q

If 20 people visit museum => Cost for admission to museum = M = 15r +5s

From 1: p <r => 10p<10r. To compare M and A, now, we have to compare 10q and (5r+5s) or more simplier 2q and (r+s). We do not have any relationship among q, r and s => (1) is not sufficient

From 2: q<s => 5q<5s. To compare M and A, now, we have to compare (10p+5q) and 15r; or more simplier (2p+q) and 3r. We do not have any relationship among p,q,r => (2) is not sufficient

Combine 1 and 2:
From 1, we need that we have to compare 2q and (r+s). From 2, we know that q<s => we need to continue to compare between q and r. However, we do not have any relationship between q and r => 1 and 2 combined is not sufficient.

Answer is E

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Re: A group ticket for admission to art gallery A costs $p for up to 10 pe [#permalink]

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New post 24 Nov 2017, 00:20
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The question asks if \(p + (20 – 10)q = p + 10q\) is smaller than \(r + ( 20 – 15 )s = r + 5s\).

Since we have 4 variables (\(p, q, r\), and \(s\)) and 0 equations, E is most likely to be the answer.
Therefore, we should consider both conditions together first.

Conditions 1) & 2)
If \(p = 10, q = 20, r = 100\), and \(s = 200\), then\(p+10q=210<1,100=r+5s\). The answer is ‘yes’.
If \(p = 10, q = 20, r = 11\), and \(s = 21\), then \(p+10q=210>116=r+5s\). The answer is ‘no’.
So, conditions 1) & 2) are NOT sufficient when taken together.

Therefore, the answer is E, as expected.


In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Answer: E
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Re: A group ticket for admission to art gallery A costs $p for up to 10 pe   [#permalink] 24 Nov 2017, 00:20
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