# Word Problems - Ratio Percents : Data Sufficiency

Exercise caution while solving questions of this kind. It is important to evaluate each statement independently and meticulously. Quite often, students end up making mistakes with questions of this kind.

## Directions

• DS
• This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether:

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

## Question

A candy manufacturer decided to decrease the weight of each candy bar, while retaining the price. By how many cents did the per kilogram cost of candy change after the reduction in weight?
Statement 1: The weight of each piece of candy bar reduced by 9 grams.
Statement 2: The weight of each piece of candy bar reduced by 9%

• Correct Answer
Choice E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

## Explanatory Answer

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## Detailed Solution

Answer the following questions before you read the statements.

#### 1. What kind of an answer will the question fetch?

The question asks us to find the change in per kilogram cost of the candy in cents after the weight of each candy was reduced.
The data provided in the statements will be sufficient if we get a unique value in cents.

#### 2. When is the data not sufficient?

If after using the information given in the statements, we are not able to determine a unique value in cents for the change in cost per kilogram of the candy, the data is NOT sufficient.

#### Let us assign the following variables.

Let the initial cost per kilogram be x cents; let the cost per kilogram after reducing the weight be y cents, where y > x.
We need to find (y-x).

Now let us evaluate each statement independently.

Statement 1: The weight of each piece of candy bar reduced by 9 grams.

We do not know either x or y from this statement.

We cannot find a unique value for (y - x). Hence, statement 1 is NOT Sufficient.

Therefore, we can eliminate choices A and D. We can narrow down the choices to this DS question to B, C, or E.

Statement 2: The weight of each piece of candy bar reduced by 9%

All that we can deduce is that the new weight of the candies is 9% lesser than its original weight or that the new weight is 91% of the original weight.

Statement 2 also does not provide us with either x or y.

Because we are not able to get a unique value for (y - x) using statement 2, statement 2 is also NOT Sufficient.

Therefore, we can eliminate choice B as well. We are down to C or E.

Combining the two statements

"The weight of each piece of candy bar reduced by 9 grams" and "The weight of each piece of candy bar reduced by 9%"

9% reduction is 9 grams

We can deduce that the weight of each candy bar was 100 grams before the reduction.

We still do not have any information on x and y.

Even after combining the information given in the two statements, we are not able to get a unique value for (y - x). Therefore, the statements together are NOT Sufficient.

The Answer

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Choice E is the correct answer.