GMAT 700+ Quant Question 7 | Ratios - Word Problem

The given question is a GMAT Data sufficiency Word problem. 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.

GMAT Data Sufficiency | Directions | Click Here ▼

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 a leap year or the meaning of the word counterclockwise), you must indicate whether -

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

Numbers

All numbers used are real numbers.

Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question 7: 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%.

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Video Explanation

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Explanatory Answer | GMAT Ratios DS

Step 1: Decode the Question Stem and get clarity

Q1. 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.

Q2. 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).

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Step 2: Evaluate Statement 1 ALONE

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.
Eliminate answer options A and D.

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Step 3: Evaluate Statement 2 ALONE

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.

We are not able to get a unique value for (y - x) using statement 2, statement 2 is also NOT Sufficient.
Hence, statement 2 is not sufficient.
Eliminate answer options B.

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Step 4: Evaluate Statements TOGETHER

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.

We are not able to get a unique value for (y - x) despite combining the two statements, the data provided is NOT sufficient..
Hence, statements together are not sufficient.
Eliminate answer option C.

Choice E is the correct answer.