Problem 14 Section 11 of 100DS

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isisalaska: Community Manager; Posts: 363; Joined: Sun Dec 10, 2006 12:24 pmFollowed by: 3 members; Location: St. Louis; Thanked: 7 times

by isisalaska » Thu Jan 25, 2007 3:44 pm

If a and b are positive integers, is a/b=2/3?

(1) 3a = 2b
(2) For integers m and n, a = 2m and b = 3n

Is not D the the answer? if you substitute 2m by a and 3n by b the result is m=n.

Isis Alaska

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Source: Beat The GMAT — Data Sufficiency | Thu Jan 25, 2007 3:44 pm

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Stacey Koprince: GMAT Instructor; Posts: 2228; Joined: Wed Dec 27, 2006 3:28 pmFollowed by: 694 members; Location: Montreal, Canada; Thanked: 639 times; GMAT Score:780

by Stacey Koprince » Wed Jan 31, 2007 5:08 pm

yes/no: is a/b = 2/3

(1) 3a = 2b. Can be rearranged to a/b = 2/3. Yes.

(2) a = 2m, b = 3n, m and n are integers. So a/b = 2m/3n. We don't know what m and n are; we only know they are integers.

Nor do we know that m = n; we can't just substitute into the equation given in the question stem b/c we don't know that that equation is true - the point is that we're being asked to determine whether it is true. m could equal n IF that equation is true (that is, if a/b = 2/3 is true). But if it isn't true, then m and n can be any integers. So can't tell for sure.

Answer is A.

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Wed Mar 28, 2007 5:15 am

If a and b are positive integers, is a/b=2/3?

(1) 3a = 2b
(2) For integers m and n, a = 2m and b = 3n

3a = 2b

Thus a/b = 2/3

Hence I is sufficient

a = 2m and b = 3n

Thus a/ b = 2m/3n

But here a/b will be equal to 2/3 if m = n

Hence it may or may not be true

Hence II is insufficient

Thus A

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