VJesus12 wrote:Each of the numbers w, x, y, and z is equal to either 0 or 1. What is the value of w + x + y + z ?
(1) w/2 + x/4 + y/8 + z/16 = 11/16
(2) w/3 + x/9 + y/27 + z/81 = 31/81
The OA is the option D.
Could someone explain this DS question for me? I am confused. I don't know how to use the given statements. <i class="em em-cold_sweat"></i>
We are given that each of the numbers w, x, y, and z is equal to either 0 or 1.
We have to get the value of w + x + y + z .
Let's take each statement one by one.
(1) w/2 + x/4 + y/8 + z/16 = 11/16
Taking LCM (16) , and canceling it, we get,
$8w+4x+2y+z=11$
=> w cannot be 0; since if w = 0 and even if each of x, y, and z is 1, then 8*0 + 4*1 + 2*1 + 1 = 7 < 11. Thus, w = 1.
=> x cannot be 1; since w = 1 and if x = 1 and even if each of y, and z is 0, then 8*1 + 4*1 + 2*0 + 0=12 > 11. Thus, x = 0
At w = 1 and x = 0, we have 8w + 4x + 2y + z = 11 => 8*1 + 4*0 + 2y + z = 8 + 2y + z =11=> 2y + z = 3 => y = z = 1$
Thus, the value of w + x + y + z = 1 + 0 + 1 + 1 = 3. Sufficient.
(2) w/3 + x/9 + y/27 + z/81 = 31/81
Hope you can now deal with this statement in a similar manner as I dealt Statement 1.
The correct answer:
D
Hope this helps!
-Jay
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