Percents: Percent Translation
Jim and Julia bought a bag of jellybeans and ate some of them. If the bag originally contained 350 jellybeans, how many were left after Jim and Julia were done eating?
>(1) The number of jellybeans Jim and Julia ate equals 250% of the number of jellybeans they left in the bag.
>(2) Jim ate 32% as many jellybeans as Julia did.
According to Stat. (2), Jim ate 32% as many jellybeans as Julia did. This percentage allows us to determine the ratio between the two numbers.
However, it gives us no information about the real number of jellybeans the two ate or about the percent of eaten jellybeans out of the total number of jellybeans in the bag. Therefore, this statement is insufficient, **Stat.(2) → IS → A**.
Incorrect.
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According to Stat. (2), Jim ate 32% as many jellybeans as Julia did. This percentage allows us to determine the ratio between the two numbers.
However, it gives us no information about the real number of jellybeans the two ate or about the percent of eaten jellybeans out of the total number of jellybeans in the bag. Therefore, this statement is insufficient, **Stat.(2) → IS → A**.
Incorrect.
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According to Stat. (1), the number of jellybeans Jim and Julia ate equals 250% of the number of jellybeans they left in the bag. Since
>$$250\% =\frac{250}{100} = \frac{5}{2}$$,
this statement effectively supplies the size ratio between the number of jellybeans _eaten_ and the number of jellybeans _left_ in the bag. Since we know the total number of jellybeans that were originally in the
bag, this is sufficient to calculate the exact number of
jellybeans left.
The algebraic calculation of this (although not strictly necessary to know that the statement is sufficient) is as follows: define $$x$$ as the number of jellybeans left in the bag. According to the rules of percent translation, the number of jellybeans Jim and Julia ate is $$250\% \times x$$, which is equal to $$\frac{5}{2}x$$.
The total number of jellybeans that were originally in the bag can now be expressed as $$x+\frac{5}{2}x$$. This should come to 350 jellybeans in total, so
>$$x+\frac{5}{2}x = 350$$.
This is a one-variable equation and can thus be solved. Therefore, this statement is sufficient, and **Stat.(1) → S → AD**.
Incorrect.
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According to Stat. (2), Jim ate 32% as many jellybeans as Julia did. This percentage allows us to determine the ratio between the two numbers.
However, it gives us no information about the real number of jellybeans the two ate or about the percent of eaten jellybeans out of the total number of jellybeans in the bag. Therefore, this statement is insufficient, **Stat.(2) → IS → A**.
Incorrect.
[[snippet]]
According to Stat. (1), the number of jellybeans Jim and Julia ate equals 250% of the number of jellybeans they left in the bag. Since
>$$250\% =\frac{250}{100} = \frac{5}{2}$$,
this statement effectively supplies the size ratio between the number of jellybeans _eaten_ and the number of jellybeans _left_ in the bag. Since we know the total number of jellybeans that were originally in the
bag, this is sufficient to calculate the exact number of
jellybeans left.
The algebraic calculation of this (although not strictly necessary to know that the statement is sufficient) is as follows: define $$x$$ as the number of jellybeans left in the bag. According to the rules of percent translation, the number of jellybeans Jim and Julia ate is $$250\% \times x$$, which is equal to $$\frac{5}{2}x$$.
The total number of jellybeans that were originally in the bag can now be expressed as $$x+\frac{5}{2}x$$. This should come to 350 jellybeans in total, so
>$$x+\frac{5}{2}x = 350$$.
This is a one-variable equation and can thus be solved. Therefore, this statement is sufficient, and **Stat.(1) → S → AD**.
Correct.
[[snippet]]
According to Stat. (1), the number of jellybeans Jim and Julia ate equals 250% of the number of jellybeans they left in the bag. Since
>$$250\% =\frac{250}{100} = \frac{5}{2}$$,
this statement effectively supplies the size ratio between the number of jellybeans _eaten_ and the number of jellybeans _left_ in the bag. Since we know the total number of jellybeans that were originally in the
bag, this is sufficient to calculate the exact number of
jellybeans left.
The algebraic calculation of this (although not strictly necessary to know that the statement is sufficient) is as follows: define $$x$$ as the number of jellybeans left in the bag. According to the rules of percent translation, the number of jellybeans Jim and Julia ate is $$250\% \times x$$, which is equal to $$\frac{5}{2}x$$.
The total number of jellybeans that were originally in the bag can now be expressed as $$x+\frac{5}{2}x$$. This should come to 350 jellybeans in total, so
>$$x+\frac{5}{2}x = 350$$.
This is a one-variable equation and can thus be solved. Therefore, this statement is sufficient, and **Stat.(1) → S → AD**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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