Princeton DS problem

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moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

Princeton DS problem

by moneyman » Wed May 09, 2007 6:37 am

Pls explain the answer

If figures M and N are circles, what is the circumference of N?

(1) If the radius of N were 4 times as long, the areas of M and N would be equal.
(2) The difference between the diameter of M and the diameter of N is 12.

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT SUFFICIENT

Maxx

Quote

Source: Beat The GMAT — Data Sufficiency | Wed May 09, 2007 6:37 am

mschling52: Master | Next Rank: 500 Posts; Posts: 105; Joined: Mon Sep 18, 2006 12:34 pm; Location: OH; Thanked: 7 times; GMAT Score:780

by mschling52 » Wed May 09, 2007 7:15 am

Is the answer C?

(1) If we call m the radius of circle M and n the radius of circle N, then from (1) we have that 4n = m, which is clearly not sufficient to know the circumference of N since we know nothing about the actual values of m and n.

(2) This gives us that |2m-2n|=12, but again, nothing about the values of either radius (they could be 13 and 1 or 90 and 77). In addition we don't even know which circle is the bigger of the two.

(1)&(2) From (1) we know that M is the bigger circle, that 4n = m, and from (2) we know that 2m-2n=12. Substituting the first equation into the second we can solve for

n = 2
m = 8

So the circumference of N is 4(pi).