Two-part Analysis (TPA) | Re: The chair of the board of directors for a certain company is planning

"­The chair correctly determined that the measure would not pass if all members voted as they said they would"

x < (3/4)*(x + y)
4x < 3x +3y
x <3y ..............(1)

"but the measure would pass if the chair could convince just one member who said she would vote against the measure to instead vote for the measure"

x + 1 >= (3/4)*(x + y)
4x + 4 >= 3x +3y
x + 4 >=3y .................(2)

From (1) and(2),

x < 3y < x +4

For 3 times y to still be less than x + 4, y should be small. For instance, if y = 19, 3 x 19 = 57. No value of x from the choices will give an x + 4 that is greater than 3y.

So,
for y, consider the smaller values and see what happens.

(1) y = 4
Then 3y = 12
x<3y => x can only be 4 or 7. But in both these cases, x + 4 will be < 3y (8, 11 are both < 12). We need x+4 to be greater than 3y.
Hence y= 4 can be rejected.

(2) y = 7.
Then 3y = 21.
All the choices here will work for x (all are < 21). But there
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Statistics : Posted by HarshR9 • on 28 Jun 2024, 06:36 • Replies 2 • Views 169

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