DS Queries - Need Expert help One day left for the GMAT

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Dear All

Plz hep with the explanations of the following.Thanks

q1) Is m+z >0

1)m-3z >0

2)4z-m >0

q2)Are x and y both positive

1) 2x-2y = 1

2) x/y > 1

q3) In xy plane what is the y-interceptof line

1)Slope of line l is 3 times the y intercept

2) x intercept of line is -1/3

q4) Six countries in a certain region sent a total of 75 representatives to sn international congress and no two countries sent the same number of people.Of the sic countries A sent the second greatest number of people.Did A send atleast 10m representatives??

1)One of the countries sent 41

2)Country A sent fewer than 12 representatives

q5)On the number line the distance between x and y is greater than x and z.Does z lie between x and y o the number line

1)xyz<0

2)xy<0

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by Anurag@Gurome » Wed Oct 31, 2012 10:16 pm
soni_pallavi wrote:Dear All

Plz hep with the explanations of the following.Thanks

q1) Is m+z >0

1)m-3z >0

2)4z-m >0
(1) m - 3z > 0; NOT sufficient.
(2) 4z - m > 0; NOT sufficient.

Combining (1) and (2), adding inequalities in statements (1) and (2), (m - 3z) + (4z - m) > 0 or z > 0 (we can add inequalities with the sign in the same direction) or z is positive. So, m is also positive. Hence m + z > 0; SUFFICIENT.

The correct answer is C.
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by Anurag@Gurome » Wed Oct 31, 2012 10:17 pm
soni_pallavi wrote:Dear All

Plz hep with the explanations of the following.Thanks

q2)Are x and y both positive

1) 2x-2y = 1

2) x/y > 1
(1) 2x - 2y = 1
x and y both positive means that point (x, y) is in the first quadrant.
2x - 2y = 1 implies y = x - 1/2, and it's an equation of a line and the question asks whether this line is only in first quadrant, which is not possible; NOT sufficient.

(2) x/y > 1
x and y have the same sign. But we don't know whether they are both positive or both negative; NOT sufficient.

Combining (1) and (2), 2x - 2y = 1 implies x = y + 1/2
x/y > 1 implies (x - y)/y > 0
Substituting the value of x, 1/y > 0 implies y is positive and since x = y + 1/2, so x is also positive; SUFFICIENT.

The correct answer is C.
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by Anurag@Gurome » Wed Oct 31, 2012 10:20 pm
soni_pallavi wrote:Dear All

Plz hep with the explanations of the following.Thanks

q3) In xy plane what is the y-intercept of line

1) Slope of line l is 3 times the y intercept.

2) x intercept of line is -1/3.
Equation of a line in point intercept form is y = mx + b, where m is the slope of the line,
b is the y-intercept of the line.

The question is to find the value of b.

(1) The slope of line l is 3 times its y-intercept implies m = 3b, which is not enough to find b; Not SUFFICIENT.

(2) The x-intercept of line l is -1/3.
x-intercept is the value of x when y = 0
0 = (-1/3)m + b
m = 3b, which is the same as statement 1; Not SUFFICIENT.

Combining (1) and (2), gives no new information; NOT sufficient.

The correct answer is E.
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by Anurag@Gurome » Wed Oct 31, 2012 10:24 pm
soni_pallavi wrote:Dear All

Plz hep with the explanations of the following.Thanks

q5)On the number line the distance between x and y is greater than x and z.Does z lie between x and y o the number line

1)xyz<0

2)xy<0
Consider the following two cases,
x = 2, y = -1, z = 1 ---> YES
x = 2, y = -1, z = 3 ---> NO

Both of the above cases satisfy both the statements but the answer is first case is YES and in the second is NO.

Hence, both statements together is also NOT sufficient.

The correct answer is E.
Anurag Mairal, Ph.D., MBA
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