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If r and s are positive numbers and θ is one of the operations, +, −,
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26 Apr 2019, 02:30
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If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ? (1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r. DS37502.01 OG2020 NEW QUESTION
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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26 Apr 2019, 04:32
From S1: r = s (both positive numbers) r θ s = 0, then θ can only be subtraction. Sufficient. From S2: r ≠ s, then r θ s ≠ s θ r Let r = 3 s = 4 addition and multiplication will be the same. but, 34 ≠ 43 also, 3/4 ≠ 4/3 Hence θ can be  or / Insufficient. A is the answer.
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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27 Apr 2019, 07:04
Bunuel wrote: If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?
(1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r.
DS37502.01 OG2020 NEW QUESTION #1 If r = s, then r θ s = 0 only subtraction possible ; sufficeint #2 f r ≠ s, then r θ s ≠ s θ r. then addition , multiplication possible insufficient IMO A



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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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27 Apr 2019, 07:35
Bunuel wrote: If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?
(1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r.
DS37502.01 OG2020 NEW QUESTION We know that \(r\) and \(s\) are positive numbers and θ is one of the 4 basic operations. The original question: Which operation is θ ? 1) If \(r=s\), then \(r+s=r+r>0\) \(rs=rr=0\) \(r\cdot s=r\cdot r>0\) \(\frac{r}{s}=\frac{r}{r}=1\neq 0\) θ must be subtraction. Thus, we can get a definite answer to the original question. \(\implies\) Sufficient2) If \(r\neq s\), then \(r+s=s+r\) \(rs\neq sr\) since the two sides have different signs. \(r\cdot s=s\cdot r\) \(\frac{r}{s}\neq \frac{s}{r}\) since one of the sides has a value greater than 1, while the other side has a value less than 1. θ can be either subtraction or division. Thus, we can't get a definite answer to the original question. \(\implies\) InsufficientAnswer: A
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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30 Apr 2019, 08:06
Bunuel wrote: If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?
(1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r.
DS37502.01 OG2020 NEW QUESTION Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷ Target question: Which operation is θ ? Statement 1: If r = s, then r θ s = 0 Keep in mind that r and s are POSITIVE So, we have POSITIVE θ POSITIVE = 0 POSITIVE + POSITIVE ≠ 0 So, θ cannot represent addition POSITIVE  POSITIVE = 0 So, θ COULD represent subtraction POSITIVE × POSITIVE ≠ 0 So, θ cannot represent multiplication POSITIVE ÷ POSITIVE ≠ 0 So, θ cannot represent division The answer to the target question is θ represents subtractionSince we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: If r ≠ s, then r θ s ≠ s θ rLet's test some values for each possible operation. 1 ≠ 2, yet 1 + 2 = 2 + 1. So, θ cannot be addition 1 ≠ 2, yet 1 x 2 = 2 x 1. So, θ cannot be multiplication If r and s are DIFFERENT positive numbers, then r  s will never equal s  r. So, θ COULD represent subtraction If r and s are DIFFERENT positive numbers, then r ÷ s will never equal s ÷ r. So, θ COULD represent division Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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06 May 2019, 20:19
Bunuel wrote: If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?
(1) If r = s, then r θ s = 0. (2) If r ≠ s, then r θ s ≠ s θ r.
DS37502.01 OG2020 NEW QUESTION Statement One Alone: If r = s, then r θ s = 0. If r = s, then the only way for r θ s = 0 is for θ to represent subtraction. Statement one alone is sufficient to answer the question. Statement Two Alone: If r ≠ s, then r θ s ≠ s θ r. We can let r = 2 and s = 3. We see that 2  3 does not equal 3  2 and 2/3 does not equal 3/2, thus θ could represent subtraction or division. Statement two alone is not sufficient to answer the question. Answer: A
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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21 May 2019, 15:58
Hi All, We're told that R and S are POSITIVE NUMBERS and θ is one of the operations add, subtract, multiply or divide. We're asked which operation is θ. This question comes down to some basic Arithmetic and TESTing VALUES. (1) If R =S, then R θ S = 0. With the information in Fact 1, we have to check the 4 possible operations to see which one(s) fit the given equation. IF.... R=S=1.... 1 + 1 = 2 this is NOT a match 1  1 = 0 this IS a match (1)(1) = 1 this is NOT a match 1/1 = 1 this is NOT a match The ONLY operation that fits is SUBTRACTION, so that is the answer to the question. Fact 1 is SUFFICIENT (2) If R ≠ S, then R θ S ≠ S θ R Just as we did with Fact 1, we have to check the 4 possible operations to see which one(s) fit the given equation (meaning that the two calculations do NOT equal one another). IF.... R=1 and S=2.... 1 + 2 = 3 IS equal to 2 + 1 = 3 this is NOT a match 1  2 =  1 DOES NOT equal 2  1 = 1 this IS a match for the given information (1)(2) = 2 IS equal to (2)(1) = 2 this is NOT a match 1/2 = 1/2 DOES NOT equal 2/1 = 2 this IS a match for the given information. Thus, the operation could be either SUBTRACTION OR DIVISION. Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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10 Jul 2019, 09:17
Hi
But it can be either rs or sr or sr. It is still insufficient



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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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15 Jul 2019, 00:48
A alone is sufficient. For B,  and / two signs are possible.
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Re: If r and s are positive numbers and θ is one of the operations, +, −,
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