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06 Oct 2025, 01:12
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:05) correct
33%
(02:13)
wrong
based on 124
sessions
History
Date
Time
Result
Not Attempted Yet
Each of the 30 first graders in a class bought one of three kinds of dictionaries, pocket edition, at price of $15; compact edition, at price of $18; and ordinary edition, at price of $20. How many students bought the compact edition?
(1) The total cost of all dictionaries bought by the students is 540 dollars.
(2) The students who bought pocket edition are twice as many as the students who bought the compact edition.
(1) The total cost of all dictionaries bought by the students is 540 dollars.
(2) The students who bought pocket edition are twice as many as the students who bought the compact edition.
06 Oct 2025, 02:32
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Bookmarks
Let P = number of pocket editions, C = number of compact editions, O = number of ordinary editions.
We know:
P + C + O = 30
Q: Find C.
(1) 15P + 18C + 20O = 540
We have 2 equations:
P + C + O = 30
15P + 18C + 20O = 540
That’s 2 equations with 3 variables → multiple solutions. Not sufficient.
(2) P = 2C
So P + C + O = 30 → 2C + C + O = 30 → 3C + O = 30.
Still 2 variables, no unique solution. Not sufficient.
(1) + (2):
P = 2C.
Then equations:
2C + C + O = 30 → 3C + O = 30 → O = 30 – 3C.
Plug in cost equation:
15(2C) + 18C + 20(30 – 3C) = 540
→ 30C + 18C + 600 – 60C = 540
→ (30C+18C–60C) + 600 = 540
→ –12C + 600 = 540
→ –12C = –60
→ C = 5. Unique.
(1) alone not sufficient.
(2) alone not sufficient.
Together sufficient.
Answer: C.
We know:
P + C + O = 30
Q: Find C.
(1) 15P + 18C + 20O = 540
We have 2 equations:
P + C + O = 30
15P + 18C + 20O = 540
That’s 2 equations with 3 variables → multiple solutions. Not sufficient.
(2) P = 2C
So P + C + O = 30 → 2C + C + O = 30 → 3C + O = 30.
Still 2 variables, no unique solution. Not sufficient.
(1) + (2):
P = 2C.
Then equations:
2C + C + O = 30 → 3C + O = 30 → O = 30 – 3C.
Plug in cost equation:
15(2C) + 18C + 20(30 – 3C) = 540
→ 30C + 18C + 600 – 60C = 540
→ (30C+18C–60C) + 600 = 540
→ –12C + 600 = 540
→ –12C = –60
→ C = 5. Unique.
(1) alone not sufficient.
(2) alone not sufficient.
Together sufficient.
Answer: C.
06 Oct 2025, 10:12
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Bunuel
Let the number of pocket edition, compact edition and ordinary edition be a,b,c respectively.
The price of pocket edition = $15
The price of compact edition = $18
The price of ordinary edition = $20
Given that a + b + c =30
We need to find the value of b.
Statement 1:
(1) The total cost of all dictionaries bought by the students is 540 dollars.
15 a + 18 b + 20 c = $540
Without knowing the values of the variables. Insufficient.
Statement 2:
(2) The students who bought pocket edition are twice as many as the students who bought the compact edition.
a = 2b
a + b + c =30
3b + c = 30
if c = 0, b = 10. And the values of b can be anywhere from 10 to 1. Whereas, the value of c , can be multiples of 3 from 0,3,6,9 till 27.
Hence , insufficient.
Combining Statements 1 and Statements 2, we get
15 a + 18 b + 20 c = $540
substitute a = 2b
48b + 20c = 540
12 b + 5 c = 135
3b + c = 30, multiply this equation by 5 , we get
15 b + 5 c = 150
12 b + 5 c = 135
subracting both, we get 3 b = 15 , b = 5
Sufficient.
Option C
