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11 May 2020, 19:52
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
24% (02:35) correct
76%
(02:51)
wrong
based on 142
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From any two numbers x and y, we define x* y = x + 0.5y - xy. Suppose that both x and y are greater
than 0.5. If x*x<y* y then which of the following must be true :
A. 1 > x > y
B. x > 1 > y
C. 1 > y > x
D. y > 1 > x
E. none of the above
than 0.5. If x*x<y* y then which of the following must be true :
A. 1 > x > y
B. x > 1 > y
C. 1 > y > x
D. y > 1 > x
E. none of the above
12 May 2020, 00:14
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Bookmarks
\(x*x = x+0.5x-x^2 = 1.5x-x^2\)
\(y*y= y+0.5y-y^2 = 1.5y-y^2\)
\(x*x<y* y\)
\(1.5x-x^2 < 1.5y-y^2\)
\(1.5(y-x) + x^2-y^2 >0\)
\(1.5(y-x)-(y^2-x^2) > 0\)
\(1.5(y-x) - (y+x)(y-x) > 0\)
\((1.5-y-x) (y-x) > 0\)
2 cases possible.
Case 1- y>x and y+x<1.5
Case 2- x>y and y+x>1.5
Option A-
x=0.8 and y=0.6; x*x>y*y (Eliminate)
Option B -
Since x>1 and y>0.5; x+y>1.5
Also x>y (Always true) [Case 2]
We don't need to check further tho.
Option C-
y=0.9 and x=0.8; x*x>y*y
(Eliminate)
Option D-
x+y>1.5 and y>x
Opposite of Case 2 (Eliminate)
\(y*y= y+0.5y-y^2 = 1.5y-y^2\)
\(x*x<y* y\)
\(1.5x-x^2 < 1.5y-y^2\)
\(1.5(y-x) + x^2-y^2 >0\)
\(1.5(y-x)-(y^2-x^2) > 0\)
\(1.5(y-x) - (y+x)(y-x) > 0\)
\((1.5-y-x) (y-x) > 0\)
2 cases possible.
Case 1- y>x and y+x<1.5
Case 2- x>y and y+x>1.5
Option A-
x=0.8 and y=0.6; x*x>y*y (Eliminate)
Option B -
Since x>1 and y>0.5; x+y>1.5
Also x>y (Always true) [Case 2]
We don't need to check further tho.
Option C-
y=0.9 and x=0.8; x*x>y*y
(Eliminate)
Option D-
x+y>1.5 and y>x
Opposite of Case 2 (Eliminate)
preetamsaha
12 May 2020, 02:22
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preetamsaha
Given: From any two numbers x and y, we define x* y = x + 0.5y - xy. Suppose that both x and y are greater than 0.5.
Asked: If x*x<y* y then which of the following must be true :
x*y = x + .5y - xy
x*x = x + .5x - x^2 = 1.5x - x^2
y*y = y + .5y - y^2 = 1.5y - y^2
Since x*x < y*y
1.5x - x^2 < 1.5y - y^2
x^2 - y^2 +1.5y- 1.5x > 0
(x-y){(x+y) - 1.5} > 0
Case 1: x-y>0 & x+y-1.5>0;
Case 2: x-y<0 & x+y-1.5<0;
A. 1 > x > y
B. x > 1 > y ; x>y & x+y>1.5; MUST BE TRUE
C. 1 > y > x
D. y > 1 > x
E. none of the above
IMO B
