On a particular day, a shop sold 3 fewer laptops of brand X than two

Question

On a particular day, a shop sold 3 fewer laptops of brand X than two times the number of laptops of brand Y. If a customer who bought a laptop of X brand had purchased a laptop of Y brand instead of X brand, the number of brand X and the number of brand Y sold would have been the same. What is the total number of laptop sold?

A. 8
B. 9
C. 10
D. 12
E. None of these

A. 8 
B. 9 
C. 10 
D. 12 
E. None of these

Kinshook · Answer

Given: On a particular day, a shop sold 3 fewer laptops of brand X than two times the number of laptops of brand Y.
If a customer who bought a laptop of X brand had purchased a laptop of Y brand instead of X brand, the number of brand X and the number of brand Y sold would have been the same.

Asked: What is the total number of laptop sold?

Let the number of laptops sold of brand X be x and brand Y be y.

On a particular day, a shop sold 3 fewer laptops of brand X than two times the number of laptops of brand Y.
x = 2y - 3

If a customer who bought a laptop of X brand had purchased a laptop of Y brand instead of X brand, the number of brand X and the number of brand Y sold would have been the same. 
x - 1 = y + 1
x = y + 2 = 2y - 3
y = 5
x = 7

Total laptops sold = x+ y = 5+7 = 12

IMO D

HarshaBujji · Answer

We can go by options;

As the total should be multiple of 3 from the first condition, So B or D or E

Validate these 2 options

IMO D

farha_01 · Answer

As it is said that the customer didn't buy a laptop from x company instead bought form y company shouldn't the laptops from x company remain same and 1 laptop from y company subtracted?
I mean shouldn't the equation be-
x = y-1?

piermacabj · Answer

You basically have two scenarios here.

In the scenario 1 you know that the total of laptops sold are in the form of 3y-3 ( 2y-3 + y) which means that your answer should be a multiple of 3. You now are only left with alternatives B (9) and D (12).

In the scenario 2 they tell you that now the laptops sold are equals, which only leaves alternative D (12) as a possibility (6 laptops brand x +6 laptops brand y).

To verify that answer E (None of these) is the answer you can plug 12 into the equation of the first scenario:

3y - 3 = 12 (total laptops sold)
y = 5 (quantity of brand y)
And the replace in the equation of brand x sold 
2(5) - 3 = 7 (quantity of brand x)

If you rest 1 of brand x (7-1) and you give it to brand y (5+1) you end with equal laptops sold just like the scenario 2 indicates, so it's valid.

I know this seams like a lot of work but once you understand the logic it's actually very easy and fast to find the answer.

On a particular day, a shop sold 3 fewer laptops of brand X than two

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On a particular day, a shop sold 3 fewer laptops of brand X than two

Prep Toolkit

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