2 DS Qs

Expert replies

Adas: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 29, 2009 7:07 am

by Adas » Sat Jul 04, 2009 9:46 am

Question the first:

Are x and y both positive?

1) 2x - 2y = 1
2) x/y > 1

The answer is that both statements together are sufficient but neither statement alone is sufficient...can someone please show me how to arrive at this conclusion?

Question the second:

If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

1) The coordinates of C are (a, 1-b)
2) The coordinates of D are (1-a, b)

The answer is that both statements together are sufficient but neither statement alone is sufficient...is it enough to express the midpoint using a and b as follows?

((1-a)-a)/2 , (b-(1-b))/2 --->
(1-2a)/2 , (2b-1)/2

Source: Beat The GMAT — Data Sufficiency | Sat Jul 04, 2009 9:46 am

GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Sat Jul 04, 2009 8:57 pm

Question 1

(1) 2x - 2y = 1
2(x - y) = 1
x - y = 1/2
x = y + 1/2

This can also mean x > y.

(2) x/y > 1
x/y - 1 > 0
(x - y)/y > 0

When you combine the two statements, we know x > y and (x-y)/y > 0. Then y > 0. Therefore x > y > 0.

C is your answer.

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GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Sat Jul 04, 2009 9:00 pm

Question 2.

The mid point formula is ( (x_1 + x_2)/2 , (y_1 + y_2)/2).

Adas: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 29, 2009 7:07 am

by Adas » Sun Jul 05, 2009 7:25 am

GMATQuantCoach wrote:Question 2.

The mid point formula is ( (x_1 + x_2)/2 , (y_1 + y_2)/2).

And in the case of this question (in my first post) is it enough to arrive at an answer with a and b still in the equation?

GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Sun Jul 05, 2009 1:52 pm

Adaś wrote:
GMATQuantCoach wrote:Question 2.

The mid point formula is ( (x_1 + x_2)/2 , (y_1 + y_2)/2).

And in the case of this question (in my first post) is it enough to arrive at an answer with a and b still in the equation?

When combining statement 1 and 2, the mid point of CD is ( ((1-a)+a)/2 , (b +(1-b))/2 ) which is (1/2,1/2) regardless of a and b.

C is your answer.

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