1/3 of the Cookies in a Jar are Chocolate Chip, 2/3 of the Remaining Cookies are Peanut Butter GMAT Problem Solving

Question: 1/3 of the cookies in a jar are chocolate chip, 2/3 of the remaining cookies are peanut butter, and the rest of the cookies are white chocolate. If 20 cookies are white chocolate, how many cookies are in the jar?

1. 40
2. 60
3. 70
4. 90
5. 100

”1/3 of the Cookies in a Jar are Chocolate Chip, 2/3 of the Remaining Cookies are Peanut Butter GMAT Problem Solving” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution:

This question has only 1 approach to answer the question through algebraic equations.

Based on the given scenario, it can be identified that 1/3 of the cookies in a jar are chocolate chip. Further, 2/3 of the remaining cookies are peanut butter, and the rest of the 4x cookies are white chocolate.

Considering that there are 20 white chocolate cookies in the jar, the total number of cookies in the jar needs to be identified.

Accordingly, let the total number of cookies in the jar be x. This would imply that the number of different types of cookies in the jar are as follows:

Chocolate chip cookies, as stated is ⅓ of the total cookies. This equals to \(\frac{1}{3}x\).

This simply implies that number of chocolate chip cookies are x/3

The remaining of the cookies in the jar is stated to be ⅔ of the total cookies. This equals to\(\frac{2}{3}x\) 

This implies that the number of peanut butter cookies in the jar is 2x/3

The number of peanut butter cookies in the jar can be evaluated to be \(\frac{2x}{3} X \frac{2}{3}\). The value of the same can be evaluated as-

\(\frac{2x}{3} X \frac{2}{3} = \frac{4x}{9}\)

The remaining number of cookies in the jar can be identified from the aspect of the following evaluation-

\(\frac{2x}{3} - \frac{4x}{9} = \frac{2x}{9}\)

The remaining number of cookies in the jar were the white chips hence,\(\frac{2x}{9}\)  is the number of white chip cookies.

However, the number of white chip cookies is given to be 20 in number. So the total number of cookies in the jar apart from the white chips can be evaluated from the same equation. This implies as follows:

\(\frac{2x}{9}\) = white chips

\(\frac{2x}{9}\)= 20

2x = 20 X 9 = 180

x = \(\frac{180}{2}\)

x = 90

Thus, the total number of cookies in the jar can be stated to 90 cookies which evaluates that option D is the correct answer.

Correct Answer: D

Suggested GMAT Problem Solving Questions

• A contractor estimated that his 10-man crew could complete the construction GMAT Problem Solving
• A circle is inscribed in a square with the diagonal of 4 centimeters GMAT Problem Solving
• At a dog competition, a dog is awarded 10 points if it runs through 4 pipes GMAT Problem Solving
• Two consultants, Mary and Jim, can type up a report in 12.5 hours GMAT Problem Solving
• Machine A can do a certain job in 12 days working 2 full shifts GMAT Problem Solving
• What is the remainder when 333^222 is divided by 7? GMAT Problem Solving
• In a college of 300 students, every student reads 5 newspapers GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200 GMAT Problem Solving
• Find The Value Of x GMAT Problem Solving
• 4 Out Of 15 Apples Are Rotten GMAT Problem Solving
• Last Year 26 Members of a Certain Club Traveled to England GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines GMAT Problem Solving
• A conference room is equipped with a total of 45 metal or wooden chairs GMAT Problem Solving
• A welder received an order to make a 1 million litre cube-shaped tank GMAT Problem Solving
• After 6 games, Team B had an average of 61.5 points per game GMAT Problem Solving
• If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water GMAT Problem Solving
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving
• If 4 people are selected from a group of 6 married couples GMAT Problem Solving
• If the equation |x|+|y|= 5 encloses a certain region on the graph GMAT Problem Solving
• If x = ¾ and y = ⅖ , what is the value of (x^2+ 6x+ 9) - (y^2-2y+ 1)? GMAT Problem Solving