There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving

Question: There are 100 apples in a bag of which 98% are green and rest are red. How many green apples do you need to remove so that only 96% of the apples are green?

1. 40
2. 8
3. 15
4. 25
5. 50

“There are 100 apples in a bag of which 98% are green and rest are red.”- 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 number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

This question has only one approach.

Given that there are 100 apples in the bag. Of those 100 apples, 98% of the apples are green and the rest are of red colour. We are asked to find out the number of green apples to be removed so that the number of green apples will be 96% of the total apples.
So out of 100 apples, first we should find out how many apples are green and how many are red.
No of green apples = 98% of total apples
                                 = 98% of 100 apples
                                 = 98/100 * 100 apples
                                 = 98 apples.
There are 98 green apples in the bag.
No of red apples = total number of apples - number of green apples
                            = 100 - 98
                            = 2
There are two red apples in the bag.
Now we have to remove some green apples so that the total number of green apples is 96% of the total apples.
Let the number of green apples which are removed be x
Now the total number of apples in the bag = total number of apples before removal- x
                                                                     = 100 -x
The total number of green apples in the bag = no of green apples before removal - x
                                                                        = 98 - x
The percentage of the total number of green apples in the bag is now 96
So we can write it as,
Percentage of green apples in the bag = 96%
No of green apples/ total number of apples * 100 = 96
Putting the values of green apples and total apples after removal we get,
( (98 - x) / (100 -x) ) * 100 = 96
=> (98 - x) * 100 = 96 * (100 - x) (taking 100 - x to the right side )
=> 9800 - 100x = 9600 - 96x
=> 9800 - 9600 = 100x - 96x ( taking 9600 to left and 100x to right )
=> 200 = 4x
=> x = 200 / 4
=> x = 50
Therefore in order to have a bag of apples having 96% green apples we have to remove 50 green apples from the bag.
For cross-verification, find the percentage of green apples in the bag after removal.
After removal, total apples = 100 - 50 - 50
After removal, total green apples = 98 - 50 = 48
Percentage of green apples = 48 / 50 * 100 = 48 * 2 = 96%

Correct Answer: E

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