GMAT Problem Solving - A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice

Question: A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. What is the value of x?

1. 5
2. 6
3. 7
4. 8
5. 9

“ A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice.” - this is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.
In the GMAT Problem Solving section, examiners measure how well the candidates make analytical and logical approaches to solve numerical problems. In this section, candidates have to evaluate and interpret data from a given graphical representation. In this section, mostly one finds out mathematical questions. Five answer choices are given for each GMAT Problem solving question.

Approach Solution 1:

There is x kg of rice in the store:

1st customer buys half of the total rice + ½ kg of rice. Hence, the equation comes as: 
x/2+1/2=(x+1)/2

2nd customer buys half of the remaining amount + ½ kg of rice. Hence, the equation stands as: 
(x−(x+1)/2)/2+1/2=(x−1)/4+1/2=(x+1)/4

3rd customer: Half the remaining amount plus 1/2 kg of rice --then, no rice is left.

--> that means the remaining amount must be 1 kg after the first 2 customers bought it.

---> (x+1)/2+(x+1)/4+1=x
—>(3x+7)/4=x
—>(3x+7)/4=x 
—>x=7

Correct Answer: C

Approach Solution 2:

Let us consider the reverse calculation. The third customer is getting 'k' amount of rice.
Hence, as per the problem statement, the equation becomes:

k/2=½
k= 1Kg

Second customer will get = 1+1= 2kg

First customer will get = (1+2) + 1= 4Kg

Hence, the total amount will be:
x= 1+2+4=7Kg

Correct Answer: C

Approach Solution 3:

Let us consider that there is x kg of rice
The first customer buys x/2+ 0.5
So the remaining is x/2-0.5 = y
The Second customer buys y/2+ 0.5
So the remaining is y/2-0.5 = z
The third customer buys z/2+0.5
So the remaining is 0 = z/2-0.5

So the value of z = 1

then, 1=y/2-0.5
that implies y=3

So, 3= x/2-0.5
hence, the value of x = 7

Correct Answer: C

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