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GMAT - Data Sufficiency - Number Theory

Of the four numbers represented on the number line above, is r closest to zero?

Of the four numbers represented on the number line above, is r closest to zero?

(1) q = –s
(2) –t < q

from the number line we can conclude that q < r < s < t

to prove that r is closest to zero we need to prove that |r| < |q|,  |r| < |s|,  |r| < |t|

Statement 1:

 q = –s

=> |q| = |s| ... (i)

the statement also implies that s is positive and q is negative. So, s >0 

=> t > 0

hence |s| < |t|

we know that q < r < s

-s < r < s

|r| < |s|

therefore:

|r| < |q|,  |r| < |s|,  |r| < |t|

sufficient.

 

Statement 2:

Insufficient because t could be very large and -t could be very negative. No knowledge about p, q and r's relative position to zero.