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Is the value of x less than 0? (1) The product of x and y is negative
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17 Oct 2019, 21:19
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Competition Mode Question Is the value of x less than 0? (1) The product of x and y is negative. (2) The difference between x and its reciprocal is positive.
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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17 Oct 2019, 21:27
Is the value of x less than 0? Is x<0? (1) The product of x and y is negative. xy is negative. So one of x or y is negative and other positive. If y>0, x<0, but if y<0, x>0. (2) The difference between x and its reciprocal is positive. \(x\frac{1}{x}>0...\frac{x^21}{x}>0\) If \(x>0..x^21>0..x>1\)....\(x=2....2\frac{1}{2}=\frac{3}{2}\)....x>0 If \(x<0..x^21<0....x<0\)...\(x=\frac{1}{2}...\frac{1}{2}(2)=\frac{3}{2}\)....x<0 Combined.. x<0 or x>1 Insuff E
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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17 Oct 2019, 21:41
Is the value of x less than 0? (1) The product of x and y is negative. it means x and y are of opposite sign. but since no other info is given, it is NOT SUFFICIENT. (2) The difference between x and its reciprocal is positive. The difference between any 2 numbers is always nonnegative. It is zero if the numbers are equal. Otherwise always positive. The difference between two numbers is defined as the distance between the two numbers on the number line. Statement 2 states that the x is not equal to 1/x or x is not equal to 1 or 1. No other info, hence NOT SUFFICIENT. Even after combining 2 statements, we are unable to conclude anything. Hence it is E
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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17 Oct 2019, 21:51
We are to determine if x is less than 0.
Statement 1: xy<0 Clearly insufficient. This is because x can be either positive or negative depending on whether y is positive or negative. When y is positive, x is negative, and when y is negative, x is positive. The answer is, therefore, yes and no.
Statement 2: The difference between x and it's reciprocal is positive. Statement 2 is not sufficient. This is because x can be 51, implying its reciprocal is 15. 5115=36, leading to answer No to the question posed. X can also be 15, and its reciprocal is 51. 1551=36 satisfying the given condition and this now leads to the answer Yes to the question posed.
1+2 Still insufficient. Both statements do not restrict the value of x to less than 0, equal to 0, or greater than 0. When y is negative, x=51 satisfies statement 1 and statement 2, and leads to the answer No to the question asked. On the other hand, when y>0 x can equal 15, which satisfies both statements and leads to the answer Yes.
The right answer in my view is E.



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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Updated on: 19 Oct 2019, 02:11
(1) The product of x and y is negative.....Clearly insufff.....Either of x,y can be +ve,ve (2) The difference between x and its reciprocal is positive.....x1/x can be positive if x is positive(1,2...) also for x=1/2,4/3....So instuff
OA:E
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Originally posted by madgmat2019 on 17 Oct 2019, 21:57.
Last edited by madgmat2019 on 19 Oct 2019, 02:11, edited 1 time in total.



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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17 Oct 2019, 23:06
(1) The product of x and y is negative. > x & y have opposite signs (If x > 0, y < 0 or of x <0, y > 0) > Insufficient
(2) The difference between x and its reciprocal is positive. > x  1/x > 0 > (x^2  1)/x > 0
Formula: If A/B > 0 > Either both A>0 & B>0 or both A<0 & B<0 Similarly, if (x^2  1)/x > 0
Case 1: x^2  1 > 0 & x > 0 > x > 1 (x is positive)
Case 2: x^2  1 < 0 & x < 0 > 1 < x < 0 (x is negative) > Insufficient
Combining (1) & (2),
Also, x can be either positive or negative > Insufficient
IMO Option E



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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17 Oct 2019, 23:20
Is the value of x less than 0? x < 0 ? (1) The product of x and y is negative. \(x.y < 0\) (+).(), x < 0 NO OR ().(+), x < 0 YES INSUFFICIENT. (2) The difference between x and its reciprocal is positive \(x  \frac{1}{x}\) > 0 It's possible only when x > 0 since x < 0 results in a negative difference. Let x = 2 then \(2  \frac{1}{2} = \frac{3}{2}\) > 0 x = 2 then \(2  \frac{1}{(2)} = \frac{3}{2}\) < 0 Hence x has to be positive. x < 0 NO SUFFICIENT. IMO Answer B.
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 01:09
Is the value of x less than 0?
Is x < 0?
(1) The product of x and y is negative. xy < 0 x < 0 or y < 0 insufficient
(2) The difference between x and its reciprocal is positive.
x  1/x > 0 x2 1 > 0 (x+1)(x1) >0 x< 1 or x> 1  we get that x can be both positive or negative
insufficient
taken (1) + (2) together, x can still be both positive and negative  insufficient Thus, E is the correct answer



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 01:18
#1 The product of x and y is negative. either of x&y is ve insufficient #2
The difference between x and its reciprocal is positive. x=2 ; reciprocal 1/2 ∆ ; 21/2 ; 3/2 x=1/2 ; reciprocal ; 2 ∆ 1/2+2 ; 3/2 insufficient from 1 &2 nothing conclusive IMO E
Is the value of x less than 0?
(1) The product of x and y is negative. (2) The difference between x and its reciprocal is positive.



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 02:14
Quote: Is the value of x less than 0?
(1) The product of x and y is negative. (2) The difference between x and its reciprocal is positive. We have to find whether or not x<0. (1) xy<0 => Either of x and y is negative and the other is positive. So, we do not have sufficient information to find out whether or not x<0. Thus, insufficient. (2) x\(\frac{1}{x}\)<0 => \(\frac{(x^21)}{x}\)<0 => x>1 or 1<x<0 So, x can be positive or negative. Thus, insufficient. From (1) and (2) together, we do not have sufficient information to find out whether or not x<0. Thus, insufficient. Therefore, the correct answer is option E.



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 02:22
Asked: Is the value of x less than 0? (1) The product of x and y is negative. xy < 0 x<0;y>0 or y<0;x>0 NOT SUFFICIENT (2) The difference between x and its reciprocal is positive. x  1/x > 0 (x^2  1)/x > 0 (x1)(x+1)/x >0 x> 1 or 1<x<0 NOT SUFFICIENT (1) + (2) (1) The product of x and y is negative. xy < 0 x<0;y>0 or y<0;x>0 (2) The difference between x and its reciprocal is positive. x  1/x > 0 (x^2  1)/x > 0 (x1)(x+1)/x >0 x> 1 or 1<x<0 x may or may not be <0 NOT SUFFICIENT IMO E
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 03:53
Imo. E Is the value of x less than 0? Is x = ve? (1) The product of x and y is negative. xy<0, x can or can not be ve. Insufficient. (2) The difference between x and its reciprocal is positive. x1/x = +ve x can be 2 or 1/2, So x can be or can not be ve. Insufficient. 1 + 2) X can be or can not be ve. Insufficient.
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 05:27
Q : x<0 ? Q type: Y/N
a) xy<0 => x and y have opposite signs. Either of them can be negative. Insufficient
b) The difference between x and its reciprocal is positive. => (x  1/x) > 0 => (x^2 1) > 0 or, x^2 >1 x can be positive or negative. (e.g. If x^2 =4, the x can have two values +2 or 2) Insufficient
a) + b) = x can be positive or negative.
Correct answer: E



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 06:43
Quote: Is the value of x less than 0?
(1) The product of x and y is negative. (2) The difference between x and its reciprocal is positive.
(1) The product of x and y is negative. insufic.\(xy<0:[x>0,y<0]…or…[x<0,y>0]\) (2) The difference between x and its reciprocal is positive. insufic.\(x\frac{1}{x}>0…\frac{x^21}{x}>0…\frac{(x1)(x+1}{x}>0…[x<1,x>1]\) (1 & 2): insufic.Answer (E)



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 13:27
x< 0 ???
(Statement1): x*y< 0 —> either x or y could be positive or negative to get this inequality correct. Insufficient
(Statement2): \(x—\frac{1}{x}\)>0
\(\frac{(x^{2}—1)}{x}\)>0
\(\frac{(x+1)(x—1)}{x}\)> 0 —> —1<x <0 and x>1 Clearly insufficient
Taken together 1&2, —> it depends on statement1 If x< 0, then Yes If x>0, then No
Insufficient
The answer is E.
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 21:49
Is the value of x less than 0?
is X negative?
(1) The product of x and y is negative. meaning either x or y is negative. we don't know which one. Therefore, insuffucient
(2) The difference between x and its reciprocal is positive. x (1/x) is positive (1/x)x is positive there is no such number that will give those both statement true insufficient
together, we know y doesn't give anything and with those statement in b doesn't add any value.
Therefore, E



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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 22:47
1. xy<0 means either x or y is negetive. so it is not enough
2. the reciprocal of x is 1/x so x1/x is positive. here this is positive result as x is larger then 1/x. but if the value of x is negetive then the result will be negetive. so this is also wrong
so answer is E
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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18 Oct 2019, 23:11
The trap here is to blindly assume value of X to be an integer.
Statement 1 is clearly not sufficient as X can be greater than 0 or less than 0. Not sufficient.
Statement 2.. tricky part.
Let's see , X 1/X >0 (X^21)/X > 0, at first one might think for this expression to be true, X has to be positive.. and if one thinks that way, he/she has made a wrong assumption of X to be a positive integer..
Take X = 4 (161)/4 > 0, I get a no Take X = 0.5 (0.251)/0.5 > 0, but X is less than 0 and I get a yes . This statement is not sufficient as well .
Combining both statements is of no use because X can be positive or X can be negative.. eliminate C and E is the right answer..
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Re: Is the value of x less than 0? (1) The product of x and y is negative
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