On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
(1) xyz<0
(2) xy< 0
OA E
Regards,
Uva.
Distance between X,Y and Z
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Given: Distance between x&y is GREATER than the distance between x&z, ie. on a number line xy is a bigger line segment and xz is a smaller one.Uva@90 wrote:On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
(1) xyz<0
(2) xy< 0
Q: We need to find out whether z lies between x and y or not
St1:
xyz < 0
product is negative so either all could be -ive or two could be -ive and one could be +ive
There could be many possibilities with these combinations and z MAY or MAY not lie inside:
INSUFFICIENT
(All the possibilities need not be visualized here only a few should suffice)
St2:
xy< 0
Either x = +ive & y = -ive
or x = -ive & y = +ive
We know nothing about Z and z could lie inside or outside.
INSUFFICIENT
St1+St2:
Combining the two inequalities we know that Z is +ive
Case1 (x = +ive & y = -ive & Z = +ive) :
Case2 (x = -ive & y = +ive & Z = +ive):
More than one possibility, thus INSUFFICIENT
[spoiler]Answer : E[/spoiler]
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When no order is specified, consider different -- especially NON-ALPHABETIC -- orderings of the given points.On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
a) xyz < 0
b) xy < 0
The following case satisfies all of the constraints in the problem:
y=-10..............................0..................z=9.....x=10
Here, z lies between x and y.
The following case satisfies all of the constraints in the problem:
y=-10..............................0..............................x=10....z=11
Here, z does NOT lie between x and y.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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