On the number line above, is the product of w, x, y and z negative?

Follow posting guidelines (link in my signatures). Do add the OA with your questions and format the analyses in the main question. Any and all analyses should either be put in the next post or put under "spoilers".

Refer below for the solution. The concepts tested are : Number properties (number line).

You are given the number line with the following important interpretation: w<x<y<z. Now, without knowing where is 0 wrt these 4 variables, we can not know what will be the sign of w*x*y*z .

Per statement 1, z>0 doesnt help. What if w,x,y are all positive ---> you will get wxyz >0 , so a "no" to the question asked "is wxyz < 0" but if w,x,y are all negative , then you will get wxyz < 0 , giving you a "yes" to the question asked. Also do note that this statement also tells you that z \(\neq\) 0 . Not sufficient.

Per statement 2, wx>0 ---> both w and x are of same sign (++ or - - ). Also do note that this statement also tells you that w or x \(\neq\) 0 . Again, relative signs of w and x are not sufficient to answer the question asked.

Combining the 2 statements we get, z>0 and wx>0 ---> 2 cases ( with the 3rd case not important for this question but might be for some other similar question)

Case 1: z>0, wx>0, y >0 ---> wxyz >0 , "no" to the question asked.

Case 2: z>0, wx>0 , y< 0 ---> wxyz < 0 , "yes" to the question asked.

Case 3: z>0, wx>0, y=0 ---> wxyz=0 . "no" to the question asked. Do note here that 0 is neither positive nor negative.

Thus, you still do not get a unambiguous yes or no for the question asked ---> E is thus the correct answer.

Hope this helps.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive


In the original condition and the question, there are 4 variables(w,x,y,z), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), if 0 is in between x and y, it is no. If o is in between y and z, it is yes, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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niks18 gmatbusters Bunuel VeritasPrepKarishma amanvermagmat

Please validate below approach:
Clearly statements when individually taken are insufficient.

When together:
Product of w and x is positive, implies either both w and x are positive or
both are negative. Now since y lies between x and z, it can take a positive or
negative value. Hence irrespective of z being positive, we can still have final product
as positive or negative.
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On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
it gives no info about the nature of sign of w, x, y . hence insufficient.

(2) The product of w and x is positive
it means either :
i)both w & x are positive : now y and z should also be positive, since they are on right side of w & x. hence product is positive.

ii)or both w & x are negative.: here there are 3 cases,
a) w, x, y, z = negative. product = positive
b) w, x, y = negative, z = positive. product = negative.
c) w, x= negative, y, z = positive. product = positive.

Hence insufficient.

No even after combining St 1 & 2 , we get
w, x, y = negative, z = positive. product = negative.
OR, w, x= negative, y, z = positive. product = positive.

so it is still INSUFFICIENT.

Answer = E



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Yes your logic is correct.
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Your Query :
"When together:
Product of w and x is positive, implies either both w and x are positive or both are negative. Now since y lies between x and z, it can take a positive or negative value. Hence irrespective of z being positive, we can still have final product as positive or negative."


If Z is negative, We can conclude that w,x,y,z all are negative, or the product WXYZ is positive.

So your understanding, irrespective of z being positive, we can still have final product
as positive or negative, doesn't seem right.

VeritasPrepKarishma, Please correct me.


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Similar question https://gmatclub.com/forum/on-the-numbe ... 40206.html

Hi everyone,

Here is the approach i took to solve.

wxyz = Negative (-) --> Sign of each number or relative position of number with respect to zero required to know is product is negative

(1) - insuff. no info about w,x,y
(2) - insuff. no info about y,z

(1) and (2) -

W .......... X........ Y.................... ......Z
(-) ......... (-)........no info....................(+) --> things change to either positive or negative based on Y's sign
OR
(+) ........(+)........no info....................(+) ---> things change to either positive or negative based on Y's sign