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.
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Problem 14 Section 11 of 100DS
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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.
(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
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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
(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
