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# On the number line, there are 4 points w,x,y and z, in an ascending

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Intern
Joined: 18 Apr 2013
Posts: 33
On the number line, there are 4 points w,x,y and z, in an ascending  [#permalink]

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05 Jul 2017, 09:31
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55% (hard)

Question Stats:

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
Director
Joined: 05 Mar 2015
Posts: 990
Re: On the number line, there are 4 points w,x,y and z, in an ascending  [#permalink]

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05 Jul 2017, 10:14
1
1
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

B)xy
both cases we have xy>0.........Keep it

C) yz
yz results >0 with case 1

Only B satiesfies

Ans B
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Joined: 22 May 2016
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On the number line, there are 4 points w,x,y and z, in an ascending  [#permalink]

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05 Jul 2017, 11:47
1
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  [#permalink]

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05 Jul 2017, 11:52
1
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

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

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Re: On the number line, there are 4 points w,x,y and z, in an ascending  [#permalink]

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05 Jul 2017, 13:33
1
1
Attachment:

FullSizeRender (7).jpg [ 61.7 KiB | Viewed 2087 times ]

+B
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On the number line, there are 4 points w,x,y and z, in an ascending  [#permalink]

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11 Jul 2018, 18:40
chetan2u pikolo2510 VeritasPrepKarishma Bunuel pushpitkc niks18

Any 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  [#permalink]

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11 Jul 2018, 22:36
chetan2u pikolo2510 VeritasPrepKarishma Bunuel pushpitkc niks18

Any other option than testing cases?

You 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  [#permalink]

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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   [#permalink] 12 Jul 2018, 00:52
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