Problem Solving

A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x,what is the value of x?

A)9/4
B)3/2
C)4/3
D)2/3
E)1/2

x is multiplied by 2 ---- 2x

this product is then divided by 3 ---- 2x/3

sqrt(2x/3) = x ---- raise everything to the second power to get:

2x/3 = x^2 ---- subtract the left side from the right side

x^2 - 2x/3 = 0

x(x - 2/3) = 0 ---- has two solutions: 0 and 3/2. You'll have to pick 2/3, since 0 is not positive.

Let the digit be x

1.................digit is multiplied by 2,it becomes 2x.

2................2x is divided by 3,it becomes 2x/3.

3.................the square root of 2x/3 that 4x^2/9 is equal to x.

then when we solve this we x=9/4. thats option A.

abhinav85 wrote:
3.................the square root of 2x/3 that 4x^2/9 is equal to x.

youre squaring it instead of taking the square root. thats why you end up with the wrong answer

DanaJ's approach would be the easiest. For this prob we can always reverse engineer(doesnt take much time) to verify the answer we have choosen is indeed right. Just a suggestion....

Regards,
CR