Problem 14 Section 11 of 100DS

[isisalaska]

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.

[Stacey Koprince]

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.

[Cybermusings]

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