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Difficulty:
25%
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Question Stats:
80% (01:22) correct
20%
(00:57)
wrong
based on 56
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Bill bought several binders. If each binder was either a $2.20 binder or a $4.40 binder, how many $4.40 binders did Bill buy?
(1) The total value of the binders Bill bought was $22.00.
(2) Bill bought twice as many $4.40 binders as $2.20 binders.
(1) The total value of the binders Bill bought was $22.00.
(2) Bill bought twice as many $4.40 binders as $2.20 binders.
01 Feb 2026, 22:50
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Bill bought several binders. If each binder was either a $2.20 binder or a $4.40 binder, how many $4.40 binders did Bill buy?
(1) The total value of the binders Bill bought was $22.00.
(2) Bill bought twice as many $4.40 binders as $2.20 binders.
Let the number of $2.20 binders bought be x and the number of $4.40 binders bought be y. We need to figure out the value of y.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: The total value of the binders Bill bought was $22.00.
Thus, 2.2x + 4.4y = 22
22/10 x + 44/10 y = 22
Dividing both the sides of the equation by 22:
x/10 + 2y/10 = 1 => x+2y = 10
However, as you can see, we cannot arrive at any unique value for y using this equation, as multiple values of y are possible. Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Bill bought twice as many $4.40 binders as $2.20 binders.
Given: y = 2x
Even in this case, we cannot arrive at any unique value for y, as multiple values are possible. Hence, Statement 2 alone is insufficient too.
Now, let's look at the combination of both the statements together:
x+2y = 10
y = 2x
Essentially, we have 2 equations and 2 variables. We should be able to arrive at a single value of y. Let's see:
As y = 2x, x+2(2x) = 10 => 5x = 10
Thus, x = 2 and so, y = 4
Therefore, we are able to arrive at a unique value for y using both the statements together.
Hence, the correct answer is Option C - BOTH statements together are sufficient, but NEITHER statement alone is sufficient.
Hope this helps!
(1) The total value of the binders Bill bought was $22.00.
(2) Bill bought twice as many $4.40 binders as $2.20 binders.
Let the number of $2.20 binders bought be x and the number of $4.40 binders bought be y. We need to figure out the value of y.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: The total value of the binders Bill bought was $22.00.
Thus, 2.2x + 4.4y = 22
22/10 x + 44/10 y = 22
Dividing both the sides of the equation by 22:
x/10 + 2y/10 = 1 => x+2y = 10
However, as you can see, we cannot arrive at any unique value for y using this equation, as multiple values of y are possible. Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Bill bought twice as many $4.40 binders as $2.20 binders.
Given: y = 2x
Even in this case, we cannot arrive at any unique value for y, as multiple values are possible. Hence, Statement 2 alone is insufficient too.
Now, let's look at the combination of both the statements together:
x+2y = 10
y = 2x
Essentially, we have 2 equations and 2 variables. We should be able to arrive at a single value of y. Let's see:
As y = 2x, x+2(2x) = 10 => 5x = 10
Thus, x = 2 and so, y = 4
Therefore, we are able to arrive at a unique value for y using both the statements together.
Hence, the correct answer is Option C - BOTH statements together are sufficient, but NEITHER statement alone is sufficient.
Hope this helps!
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