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13 Feb 2023, 00:32
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E
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:
43% (01:46) correct
57%
(01:28)
wrong
based on 37
sessions
History
Date
Time
Result
Not Attempted Yet
13 Feb 2023, 01:03
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TBT
Question
Is \(xy > 0\), in other words, we need to find whether x and y have the same sign (are they on the same side of zero) ?
Statement 1
(1) \(x-y=2\)
Case 1: x and y can be on the same side of zero.
---------- y ---------- x ----------- 0 -------------- y ----------------- x ----------
Ex:
y = 2 ; x = 4
y = -4 ; x = -2
In both cases, Is \(xy > 0\) - Yes !
Case 2: x and y can be on the opposite side of zero.
--------- y ------- 0 -------- x --------
Ex: x = 1 and y = -1
Is \(xy > 0\) - No !
The statement is not sufficient.
We can eliminate A and D.
Statement 2
(2)\( (\frac{x}{y}) < 1\)
Case 1: x and y can be on the same side of zero.
---------- y ---------- x ----------- 0 --------------
Ex:
y = -4 ; x = -2
Is \(xy > 0\) - Yes !
Case 2: x and y can be on the opposite side of zero.
--------- y ------- 0 -------- x --------
Ex: x = 1 and y = -1
Is \(xy > 0\) - No !
The statement is not sufficient.
Eliminate B
Combined
The statements combined don't help either as both cases mentioned in statement 2 is applicable for statement 1.
Option E
P.S = The indicated answer is incorrect. Should be E and not C.
13 Feb 2023, 02:10
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Is \(xy > 0\) ?
The question basically asks whether x and y have the same sign.
(1) \(x-y=2\)
One number (x) is 2 greater than another (y). This is clearly insufficient to say whether x and y have the same sign.
(2) \(\frac{x}{y} < 1\).
Not sufficient.
(1)+(2) From (1) \(x = y + 2\) so from (2) we get:
So, the question becomes whether x and y are both negative.
Not sufficient.
Answer: E.
The question basically asks whether x and y have the same sign.
(1) \(x-y=2\)
One number (x) is 2 greater than another (y). This is clearly insufficient to say whether x and y have the same sign.
(2) \(\frac{x}{y} < 1\).
- If x = 1 and y = 2, then the answer is YES.
If x = 1 and y = -2, then the answer is NO.
Not sufficient.
(1)+(2) From (1) \(x = y + 2\) so from (2) we get:
- \(\frac{(y + 2)}{y} < 1;\\
1 + \frac{2}{y} < 1;\\
\frac{2}{y} < 0;\\
y < 0.\)
So, the question becomes whether x and y are both negative.
- If y = -10 and x = -8, then the answer is YES.
If y = -1 and x = 1, then the answer is NO.
Not sufficient.
Answer: E.
