Among 200 People, 56% like Strawberry Jam, 44% like Apple Jam, and 40% like Raspberry Jam GMAT Problem Solving

Question: Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?

1. 20
2. 60
3. 80
4. 86
5. 92

“Among 200 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?”- 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.

Answer:

Approach Solution 1

Assume total to be 100
100 = 56 + 44 + 40 – (30 – x) – 2x
100 = 110 – x
x = 10

Now double the total and value of x, we will get:
Total = 2*100 = 200
x = 10*2 = 20
Final answer: 40*2 – 20 = 60

Correct option: B

Approach Solution 2

Your equation

Total = R + A + S – (Sum of exactly 2 group overlap) – 2(All 3)
As Bunuel stated, “Notice that “30% of the people like both strawberry and apple jam” doesn’t mean that among these 30% (60) cannot be some people who like raspberry as well.”
Key Error: It was wrong for you 60 as “exactly those who like apple and strawberry only”. The sixty could include those who like Strawberry, Apple, and Raspberry. This error led you to multiply the number of those who like all (All 3) by 2.
Your equation should have been:

Total = R + A + S – (Sum of 2 groups) – (All 3)
200 = 112 + 88 + 80 – 60 – x
x = 20

This means that of the 60 who like both apple and strawberry, 20 like raspberry too.
Therefore number of people who like raspberry only is 80 – 20 = 60

Correct option: B

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