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GMAT - Data Sufficiency - Number Theory

If x=6m^2 + 4n^2, what is the greatest even number that must be a factor of x? (more)

(1) m and n are even.

(2) gcf (m,n) = 2. 

 

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

C) BOTH statements together are sufficient, but NEITHER statement alone is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) together are not sufficient.

 

If m equals to n, then the expression becomes 10m^2. Since both statements mean that 2 is factor . The greatest factor would be 20. Correct me if I am wrong :)

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

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.