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01 Oct 2020, 02:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:19) correct
17%
(01:28)
wrong
based on 517
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If \(x < 0\) and \(0 < y < |x|\), which of the following must be true?
A. \(y^2 − x^2 < 0\)
B. \(x^2 − y^2 < 0\)
C. \((y − x)^2 < 0 \)
D. \((x − y)^2 < 0 \)
E. \((x + y)^2 < 0 \)
A. \(y^2 − x^2 < 0\)
B. \(x^2 − y^2 < 0\)
C. \((y − x)^2 < 0 \)
D. \((x − y)^2 < 0 \)
E. \((x + y)^2 < 0 \)
yashikaaggarwal
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Joined: 19 Jan 2020
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01 Oct 2020, 03:02
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Given: If x<0 and 0<y<|x|,
To find: which of the following must be true?
Solution: Y is less than |x| and X is negative
Let Y = 1 and X = -2
A. y^2−x^2<0
1^2 - (-2)^2 < 0
1-4 < 0
-3 < 0 (TRUE)
B. x^2−y^2<0
(-2)^2 - 1^2 < 0
4-1 < 0
3 < 0 (WRONG)
C. (y−x)^2<0
(1+2)^2 < 0
3^2 < 0
9 < 0 (Wrong)
D. (x−y)^2<0
(-2-1)^2 < 0
(-3)^2 < 0
9 < 0 (Wrong)
E. (x+y)^2<0
(-2+1)^2 < 0
1^2 < 0
1 < 0 (Wrong)
Answer is A
To find: which of the following must be true?
Solution: Y is less than |x| and X is negative
Let Y = 1 and X = -2
A. y^2−x^2<0
1^2 - (-2)^2 < 0
1-4 < 0
-3 < 0 (TRUE)
B. x^2−y^2<0
(-2)^2 - 1^2 < 0
4-1 < 0
3 < 0 (WRONG)
C. (y−x)^2<0
(1+2)^2 < 0
3^2 < 0
9 < 0 (Wrong)
D. (x−y)^2<0
(-2-1)^2 < 0
(-3)^2 < 0
9 < 0 (Wrong)
E. (x+y)^2<0
(-2+1)^2 < 0
1^2 < 0
1 < 0 (Wrong)
Answer is A
01 Oct 2020, 04:01
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A.
Only A and B are possible even if we were to skip the details relevant to the question because a square of any number is always >=0
C, D, and E are impossible.
Between B and D, |x|>y so, x^2 - y^2 >0 (B is wrong.)
Left with A.
Only A and B are possible even if we were to skip the details relevant to the question because a square of any number is always >=0
C, D, and E are impossible.
Between B and D, |x|>y so, x^2 - y^2 >0 (B is wrong.)
Left with A.
