if r-s=3p, is p an integer?
1) r is divisible by 735
2) r+s is divisible by 3
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vaibhav101
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Hi vaibhav101,
We're told that R - S = 3P. We're asked if P is an integer. This is a YES/NO question and can be solved by TESTing VALUES (and knowledge of a rarer Number Property rule also helps).
1) R is divisible by 735
IF....
R=735 and S = 0, then 735 = 3P and P = 245. The answer to the question is YES.
R=735 and S = 1, then 734 = 3P and P = 244 2/3. The answer to the question is NO.
Fact 1 is INSUFFICIENT.
2) (R+S) is divisible by 3
IF....
R=3 and S = 0, then 3 = 3P and P = 1. The answer to the question is YES.
R=2 and S = 1, then 1 = 3P and P = 1/3. The answer to the question is NO.
Fact 2 is INSUFFICIENT.
Combined, we know:
R is divisible by 735
(R+S) is divisible by 3
735 is a multiple of 3; from out prior work, we know its (3)(245). Since R is divisible by 735, it MUST be a multiple of 3. We're also told that (R+S) is a multiple of 3; since R is already a multiple of 3, the ONLY way for the (R+S) to be a multiple of 3 is if S is ALSO a multiple of 3. Thus, we know that BOTH R and S MUST be multiples of 3.
R - S would give us a multiple of 3 'minus' another multiple of 3.... and that resulting number will ALSO ALWAYS be a multiple of 3. In the end, we would have 3P = some multiple of 3. Dividing both sides by 3 would give us P = an integer... and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that R - S = 3P. We're asked if P is an integer. This is a YES/NO question and can be solved by TESTing VALUES (and knowledge of a rarer Number Property rule also helps).
1) R is divisible by 735
IF....
R=735 and S = 0, then 735 = 3P and P = 245. The answer to the question is YES.
R=735 and S = 1, then 734 = 3P and P = 244 2/3. The answer to the question is NO.
Fact 1 is INSUFFICIENT.
2) (R+S) is divisible by 3
IF....
R=3 and S = 0, then 3 = 3P and P = 1. The answer to the question is YES.
R=2 and S = 1, then 1 = 3P and P = 1/3. The answer to the question is NO.
Fact 2 is INSUFFICIENT.
Combined, we know:
R is divisible by 735
(R+S) is divisible by 3
735 is a multiple of 3; from out prior work, we know its (3)(245). Since R is divisible by 735, it MUST be a multiple of 3. We're also told that (R+S) is a multiple of 3; since R is already a multiple of 3, the ONLY way for the (R+S) to be a multiple of 3 is if S is ALSO a multiple of 3. Thus, we know that BOTH R and S MUST be multiples of 3.
R - S would give us a multiple of 3 'minus' another multiple of 3.... and that resulting number will ALSO ALWAYS be a multiple of 3. In the end, we would have 3P = some multiple of 3. Dividing both sides by 3 would give us P = an integer... and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
