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Word Problem Ratio, percentsData Sufficiency – Question 7

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?

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

grams.

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

CombineStatement 2Statement 1ApproachQuestion StemQuestion

◴Answer these questions before evaluating the statements.

Determine approach to solve the question

Step 1

Spend a few seconds answering the following questions

Before going to the statements

When is the data sufficient? Assign variables

The data is sufficient when we are able to find a unique value for the change in cost per kilogram of the candy.




When is the data sufficient? When is it not sufficient? Assign variables


The data is NOT sufficient either when we get more than one value or we are not able to determine the value.




When is the data sufficient? When is it not sufficient? Assign variables


The data is NOT sufficient either when we get more than one value or we are not able to determine the value.

Let x be the initial cost per kilogram of the candies.

Let y be the cost per kilogram after the weight of the candies are reduced. So, y > x


Meticulously evaluate the statements to see whether we can find values for x and y

Approach to solve the question

Does statement 1 provide values for x and y or (y – x)?



Meticulously evaluate the statements to see whether we can find values for x and y

Approach to solve the question




If the answer to the previous 2 questions were NO, combine the data in the two statements to

see whether we can find values of x and y or (y – x).

◴Evaluate Statement 1 alone

Step 2

By how many cents did the per kilogram cost of candy change?

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

Yes

1

Can we find x

using statement 1?




Yes

1

Can we find x

using statement 1?


NO



Yes

1

Can we find x

using statement 1?


2

Can we find y

using statement 1?

NO



Yes

1

Can we find x

using statement 1?


2

Can we find y

using statement 1?

NONO



Yes

1 3

Can we find x

using statement 1?


2

Can we find y

using statement 1?

NO

Can we find

(y – x) using (1)?

NO



Yes

1 3

Can we find x

using statement 1?

NO


2

Can we find y

using statement 1?

NO

Can we find

(y – x) using (1)?

NO



Yes

1 3

Can we find x

using statement 1?

NO

Choices narrow down to B, C or E.

Eliminate choices A and D

Statement 1 alone is NOT sufficient


2

Can we find y

using statement 1?

NO

Can we find

(y – x) using (1)?

NO

◴Evaluate Statement 2 alone

Step 3

Yes


1

Can we find x

using statement 2?

By how many cents did the per kilogram cost of candy change?Statement 2 : The weight of each piece of candy bar reduced by 9%

Yes


1

Can we find x

using statement 2?

NO


Yes


1

Can we find x

using statement 2?

2

Can we find y

using statement 2?

NO


Yes


1

Can we find x

using statement 2?

2

Can we find y

using statement 2?

NONO


Yes


1

Can we find x

using statement 2?

2

Can we find y

using statement 2?

NO

Can we find

(y – x) using (2)?

NO


3

Yes


1

Can we find x

using statement 2?

NO

2

Can we find y

using statement 2?

NO

Can we find

(y – x) using (2)?

NO


3

Yes

Choices narrow down to C or E.

Eliminate choice B as well

Statement 2 alone is NOT sufficient


1

Can we find x

using statement 2?

NO

2

Can we find y

using statement 2?

NO

Can we find

(y – x) using (2)?

NO


3

◴Evaluate the data given in the two statements together

Step 4

Yes


What can we deduce? Do we have the answer for (y – x)?

9% reduction is 9 grams .

Therefore, weight of each candy bar before the reduction in weight is 100 grams.

By how many cents did the per kilogram cost of candy change?Combine the statements : The weight of each piece of candy bar reduced by 9 grams & The

weight of each piece of candy bar reduced by 9%

.

Yes





We still do not know x and y or (y – x )



.

Yes





We still do not know x and y or (y – x )



.

Answer Choice E

Eliminate choice C.

Statements together are NOT sufficient

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