Bunuel wrote:
Mini and Vinay are quiz masters preparing for a quiz. In x minutes, Mini makes y questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes mini would make 2y questions more than Vinay. How many questions does Mini make in x minute?
A. \(\frac{1}{4}(2(x + y) - \sqrt{2x^2 + 4y^2})\)
B. \(\frac{1}{4}(2(x - y) - \sqrt{2x^2 + 4y^2})\)
C. \(\frac{1}{4}(2(x - y) - \sqrt{2x^2 - 4y^2})\)
D. \(\frac{1}{4}(2(x + y) + \sqrt{2x^2 + 4y^2})\)
E. \(\frac{1}{4}(2(x + y) - \sqrt{2x^2 - 4y^2})\)
Whenever variables are involved in both question stem and answer choices, I feel its best to use smart numbers and solve and then plug those smart numbers in the answer choices to match which one matches with the answer you got.
So we need x to be a number which is divisible by 2 numbers (a, b) and also to be divisible by (a-2, b-2). Some number which has multiples of 2 as factors
How about 24? It has 2,4,6 and 8 as factors which gives us 4 possible number and the -2 combination as well
So let x=24 minutes
Mini (time/question)=6, So Mini(questions/24m)=4
Vinay (time/question)=8, So Vinay(questions/24m)=3
y=4-3=1
Now let us reduce time taken per question by 2 minutes for both:
Mini (time/question)=4, So Mini(questions/24m)=6
Vinay (time/question)=6, So Vinay(questions/24m)=4
y=6-4=2(2y)
Now, let us plug in the values of x(24) and y(1) in the answer choices and see which gives us the answer of 4 (because in 24 minutes, Mini solves 24/6=4 questions)
1) 1/4 * [2*(24+1) - Root(2*24*24 + 4*1*1)] = 1/4 * [50 - Root(1156)] = 1/4 * [50 - Root(2*2*17*17)] = 1/4 * [50-34] = 1/4*16 = 4
We got our answer on the first try, no need to try other options
Answer - A