There was a Series of Two Successive Discounts of y% on the Price of Laptop.

Question: There was a series of two successive discounts of y% on the price of Laptop. The final price of the laptop was tagged at 64% of the original price. What is the value of y?

A) 18%
B) 20%
C) 24%
D) 36%
E) 82%

“There was a series of two successive discounts of y% on the price of Laptop. The final price of the laptop was tagged at 64% of the original price. What is the value of y?” - this is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Approach 1

This question can be solved by assuming $100 as the price of the laptop. Then we need to work backward to obtain the final price of the laptop as $64.

Since we have to calculate the value of ‘y’, we will take a look at the options.

Clearly, options D and E cannot be the answers.

1. The discount of 82% will take the price of the laptop much below $64. Hence, there is no question of applying another 82% and getting $64.
2. A similar thing happens with option D. 36% of 100 is 36. Hence, after the first discount itself, the price reduces to $64. Now, if we apply another 36% discount, the price will not stay at $64.

Hence, options D and E are out of our way.

Now, we will check the remaining options.
Let us pick 20% since this is clearly an easy number to deal with,

Now, considering the price of the laptop as 100:
When we apply the first discount of 20%, 100 becomes:
100-20
=>80.
When we apply the second discount of 20%, 80 becomes:
80-16
=>64.
This matches the provided amount.

Hence, the correct answer is B.

Approach 2

Let us consider the discount percent = x%
Let the initial price be 100
As per the given question, the discounted price is 64

We get the equation:
=> 100 * (1-(x/100))^2 = 64
=> (1-(x/100)) = 64/100= 8/10
=> x/100 = 1-(8/10) = 2/10
=> x = 20%

Hence, B is the correct answer.

Approach 3

Let us consider p as the original price of the laptop.
We can create the equation:
p x (100- y)/100 x (100 - y)/100 = p x 64/100
=>(100 - y)^2/100^2 = 64/100
Multiplying both sides of the equation by 100^2, we have:
(100 - y)^2 = 64(100)
√[(100 - y)^2] = +/-√6400
100 - y = 80 or 100 - y = -80
y = 20 or y = 180
We will ignore y = 180 because an item cannot be discounted more than 100%.

Thus we get, y = 20.

Correct Answer: B

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