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On the number line, there are 4 points w,x,y and z, in an ascending
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05 Jul 2017, 09:31
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62% (01:44) correct 38% (01:52) wrong based on 183 sessions
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On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive? 1) wx 2) xy 3) yz A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only
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Re: On the number line, there are 4 points w,x,y and z, in an ascending
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05 Jul 2017, 10:14
roastedchips wrote: On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive?
1) wx 2) xy 3) yz
A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only for wxyz<0 two cases on number line is possible case 1 : w<0 & z>y>x>0 case 2: w<x<y<0 & z>0 A) wx wx results >0 with case 2 & wx<0 with case 1.........Discard B)xy both cases we have xy>0.........Keep it C) yz yz results >0 with case 1 & yz<0 with case 2.........Discard Only B satiesfies Ans B



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On the number line, there are 4 points w,x,y and z, in an ascending
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05 Jul 2017, 11:47
roastedchips wrote: On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive?
1) wx 2) xy 3) yz
A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only For the product of two or more numbers to be negative, there must be an odd number of negative factors. Here there are four numbers. Either only one is negative, or three are negative. I assigned values. Ascending order, smallest to greatest, is w<x<y<z. Case A: if only one factor is negative, we have: w<x<y<z ==> 1 < 2 < 3 < 4 Here, w is the one negative factor, and x, y, and z are positive Case B: If there are three negative factors, we have w<x<y<z ==> 4 < 3 < 2 < 1 Here, w,x, and y are negative, and z is positive. Assess options for "must be positive." I. wx  In Case A, wx is negative. Reject. II. xy  In both Case A and B, xy is positive because x and y have the same sign. Keep. III. yz  In Case B, yz is negative. Reject. Only II is true. Answer B.
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Re: On the number line, there are 4 points w,x,y and z, in an ascending
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05 Jul 2017, 11:52
roastedchips wrote: On the number line, there are 4 points w,x,y and z, in an ascending order. If wxyz<0, which of the following must be positive?
1) wx 2) xy 3) yz
A) 1 only B) 2 only C) 3 only D) 1 and 3 only E) 2 and 3 only w,x,y and z are on the number line in ascending order. Since wxyz is <0, none of w,x,y,z can be 0. 0 can take 5 different places but we need to find cases when wxyz <0 Case 1 w<x<y<z<0 => wxyz>0 => discard case Case 2 w<x<y<0<z => wxyz<0 => wx is +ve, xy is +ve yz is ve Case 3 w<x<0<y<z => wxyz>0 => discard case Case 4: w<0<x<y<z => wxyz<0 => wx is ve, xy is +ve, yz is +ve Case 5 0<w<x<y<z => wxyz>0 => Discard Only for cases 2 and 4, wxyz<0. Now we will check the signs of wx, xy and yz wx ve for case 4 => Not always +ve => 1) must not be true xy +ve for both cases => xy is always +ve => 2) must be true yz ve for case 2 => not always +ve => 3) must not be true. Only 2) must be true Answer B



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Re: On the number line, there are 4 points w,x,y and z, in an ascending
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05 Jul 2017, 13:33
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On the number line, there are 4 points w,x,y and z, in an ascending
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11 Jul 2018, 18:40
chetan2u pikolo2510 VeritasPrepKarishma Bunuel pushpitkc niks18Any other option than testing cases?
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Re: On the number line, there are 4 points w,x,y and z, in an ascending
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11 Jul 2018, 22:36
adkikani wrote: hi adkikaniYou will have to work through case based scenarios as \(wxyz<0\) so \(z>0\) and a situation where \(x<0\) and \(y>0\) is not possible. because in that case \(wxyz>0\) So Now only two cases remain Case 1: \(w,x,y<0\) & \(z>0\) This case will give Option 1 & Option 2 as positive solutions. Case 2: \(w<0\) & \(x,y,z>0\) This case will give Option 2 as the only Solution. As this is a Must be true question, so only Option 2 holds in all the scenarios.



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Re: On the number line, there are 4 points w,x,y and z, in an ascending
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12 Jul 2018, 00:52
I did it in this way Only two possible cases satisfy the above condition w x y z 1)    + 2)  + + + In the both the above cases, only xy is positive. Hence answer is B
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Re: On the number line, there are 4 points w,x,y and z, in an ascending
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