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22 Nov 2017, 02:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:15) correct
30%
(02:26)
wrong
based on 56
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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) \(q<s\)
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) \(q<s\)
MathRevolution
A.G -> 10p + 10q
M -> 15r + 5s
10p + 10q < 15r + 5s ?
Quote:
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:
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.
22 Nov 2017, 07:12
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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
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
