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25 Jun 2019, 02:06
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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:
65%
(hard)
Question Stats:
59% (02:01) correct
41%
(01:36)
wrong
based on 332
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If \(x>2\) and \(y>-1\), then which of the following statements must be true?
A. \(xy>-2\)
B. \(-x<2y\)
C. \(xy<-2\)
D. \(-x>2y\)
E. \(x<-2y\)
A. \(xy>-2\)
B. \(-x<2y\)
C. \(xy<-2\)
D. \(-x>2y\)
E. \(x<-2y\)
25 Jun 2019, 06:52
Kudos
Bookmarks
Bunuel
If \(x>2\) and \(y>-1\), then which of the following statements must be true?
A. \(xy>-2\)
B. \(-x<2y\)
C. \(xy<-2\)
D. \(-x>2y\)
E. \(x<-2y\)
A. \(xy>-2\)
B. \(-x<2y\)
C. \(xy<-2\)
D. \(-x>2y\)
E. \(x<-2y\)
Strategy: Try to find exceptions for each option!!
A. \(xy>-2\)
--> x = 10, y = -0.5 xy = -5 (<-2)
-- NO
B. \(-x<2y\)
--> Possible values of 2y are -1.9, -1, 0, 2, 5, 100;
Possible values of -x are -2, -2.5, -3, -4 etc
-- YES
C. \(xy<-2\)
--> x = 3, y = -0.5 xy = -1.5 (>-2)
-- NO
D. \(-x>2y\)
--> Possible values of 2y are -1.9, -1, 0, 2, 5, 100;
Possible values of -x are -2, -2.5, -3, -4 etc
-- NO
E. \(x<-2y\)
--> x = 100, y = 0
--> (x, -2y) = (100, 0)
-- NO
IMO Option B
Pls Hit Kudos if you like the solution
General Discussion
Nice question!
Constraint x > 2 so we know x is always +ve
Also, y > -1 so we know y is -ve (non-integer),+ve or 0
(a) xy > -2 —> +ve•+ve >-2 (true), +ve•-ve(non-integer) >-2 (not always true) so this option is not necessarily true
(b) -x < 2y —> x > -2y ,now the LHS of the inequality is always +ve and RHS y can be zero(0),-ve(non-integer) or +ve( but ends up being negative eg. -2•(2)=-4)
(Always true in all cases )
(c) xy < -2 —> +ve•+ve >0 so when xy is +ve (not true)
(d) -x > 2y —> Here x is -ve and can never be greater than 2y when y=+ve (not true)
(e) x <-2y —> not true when y is +ve
Answer B
Posted from my mobile device
Constraint x > 2 so we know x is always +ve
Also, y > -1 so we know y is -ve (non-integer),+ve or 0
(a) xy > -2 —> +ve•+ve >-2 (true), +ve•-ve(non-integer) >-2 (not always true) so this option is not necessarily true
(b) -x < 2y —> x > -2y ,now the LHS of the inequality is always +ve and RHS y can be zero(0),-ve(non-integer) or +ve( but ends up being negative eg. -2•(2)=-4)
(Always true in all cases )
(c) xy < -2 —> +ve•+ve >0 so when xy is +ve (not true)
(d) -x > 2y —> Here x is -ve and can never be greater than 2y when y=+ve (not true)
(e) x <-2y —> not true when y is +ve
Answer B
Posted from my mobile device
