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13 Oct 2025, 00:44
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D
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Difficulty:
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Question Stats:
87% (01:33) correct
13%
(01:33)
wrong
based on 91
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Sam's Grocery store sells potatoes only in 5-pound bags and 10-pound bags. Yesterday, if the store sold 130 pounds of potatoes, how many 5-pound bags were sold?
(1) The number of 5-pound bags sold was 2 more than 4 times the number of 10-pound bags sold.
(2) The store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
(1) The number of 5-pound bags sold was 2 more than 4 times the number of 10-pound bags sold.
(2) The store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
13 Oct 2025, 02:50
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Let x be the number of 5-pound bags sold, and y be the number of 10-pound bags sold.
The store sold a total of 130 pounds:
5x + 10y = 130
Statement 1:
The number of 5-pound bags sold was 2 more than 4 times the number of 10-pound bags sold.
x = 4y + 2
Substituting into the total weight equation:
5(4y+2) + 10y = 130
20y + 10 + 10y = 130
30y = 120 implies y = 4
x = 4*4+2 = 18
Statement 1 alone is sufficient.
Statement 2:
The store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
5x = 10y + 50
Again, using the total weight equation:
5x + 10y = 130
Substitute 5x = 10y + 50:
(10y + 50) + 10y = 130
20y + 50 = 130
20y = 80
y = 4
Then,
5x = 10*4 + 50 = 90 implies x = 18
Statement 2 alone is also sufficient.
Each statement alone is sufficient to answer the question.
Hence, (D)
The store sold a total of 130 pounds:
5x + 10y = 130
Statement 1:
The number of 5-pound bags sold was 2 more than 4 times the number of 10-pound bags sold.
x = 4y + 2
Substituting into the total weight equation:
5(4y+2) + 10y = 130
20y + 10 + 10y = 130
30y = 120 implies y = 4
x = 4*4+2 = 18
Statement 1 alone is sufficient.
Statement 2:
The store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
5x = 10y + 50
Again, using the total weight equation:
5x + 10y = 130
Substitute 5x = 10y + 50:
(10y + 50) + 10y = 130
20y + 50 = 130
20y = 80
y = 4
Then,
5x = 10*4 + 50 = 90 implies x = 18
Statement 2 alone is also sufficient.
Each statement alone is sufficient to answer the question.
Hence, (D)
13 Oct 2025, 08:13
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Bunuel
Let the number of 5 pound bags and 10 pound bags sold by Sam grocery store is a and b respectively.
The grocery store sold a total number of 130 pounds.
5a + 10 b = 130. , which can be re written as : a + 2b = 26
We need to find: a
Statement 1:
(1) The number of 5-pound bags sold was 2 more than 4 times the number of 10-pound bags sold.
a = 2 + 4b
substitute in the above bolded equation, we get
2 + 4b + 2b = 26
b = 4, then a = 18.
Hence, Sufficient
Statement 2:
(2) The store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
5a = 50+10b ,
From the bolded equation, a = 26 - 2b
5a = 130 - 10b
130 - 10b = 50+10b
80 = 20b
b = 4, then a = 18.
Hence, Sufficient
Option D
