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If t#0, is r greater than zero?
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20 Feb 2014, 00:19
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf \(t\neq{0}\), is r greater than zero? (1) rt = 12 (2) r + t = 7 Data Sufficiency Question: 105 Category: Arithmetic; Algebra Arithmetic operations; Properties of numbers; Simultaneous equations Page: 160 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: If t#0, is r greater than zero?
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20 Feb 2014, 00:20



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Re: If t#0, is r greater than zero?
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20 Feb 2014, 02:22
is r greater than zero?
(1) rt = 12
both r=2 and t=6 and r=2 and t=6 satisfy this equation
hence not sufficient
(2) r + t = 7
if r=0, t=7 also r=1 and t=6 satisfy this equation. hence not sufficient
combining 1 and 2 we have t=(7r) r(7r)=12 since product is positive thus r and 7r must have the same sign. if r= ve then 7r will be positive. If r= +ve then 7r will be positive for all values less than seven. hence r will be greater than zero and its value will be less than 7 hence sufficient therefore C.



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Re: If t#0, is r greater than zero?
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20 Feb 2014, 03:08
If \(t\neq{0}\), is r greater than zero? (1) rt = 12 (2) r + t = 7 1  insufficient. If t<0 > r<0, if t>0 > r>0. 2  insufficient. Could be r=1 and t=8, or r=1 and t=6. 2 and 2: \(r+\frac{12}{t}7=0\) \(r^2 7r+12=0\) \((r1)(r6)=0\) So r=1 or 6. That are >0. Ans C
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Re: If t#0, is r greater than zero?
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20 Feb 2014, 23:32
Option C From S1:r * t=12 r=3;t=4 could be one sol. r=3;t=4 could be another sol.Not suff.
From S2:r+t=7.Infinite no. of both pos. and neg. sol possible for a linear equation. Not suff.
Combining,we get r*t=12 and r+t=7.We can solve these two to get unique values of r and t. t=12/r Replacing t in other equation; r^27r+12=0 (r3)(r4)=0 r=3/4>0 Hence suff.



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Re: If t#0, is r greater than zero?
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21 Feb 2014, 03:11
t#0; Is r>0?
Statement (1): rt = 12; Here, either both r & t need to be positive or both need to be negative in order to get a positive number. There are 6 possibilities each in both positive and negative: r = 1 & t =12; r = 2 & t = 6; r = 3 & t = 4; ....
Not sufficient, as negative value for r is possible.
Statement (2): r + t = 7;
Yes, if r = 4 & t = 3; No, if r = 3 & t = 10;
Insufficient;
Combining 2 statements, substitute t = 7  r in (1); rt = 12; r(7  r) = 12; 7r  r^2 = 12; r^2  7r + 12 = 0; (r  4)(r  3) = 0; r = 3, 4;
So, r is positive when 2 statements are combined.
Ans is (C).



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Re: If t#0, is r greater than zero?
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02 Jun 2014, 17:05
No calculations approach:If t#0, is r greater than zero? (1) rt = 12 (2) r + t = 7 St1: Both r and t could be positive or both r and t could be negative. Not Suff St2: Both r and t could be positive or either of r and t could be negative. Not Suff 1+2 > common possibility is both r and t are positive. So r is positive i.e. greater than 0. Ans:C
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Re: If t#0, is r greater than zero?
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10 Nov 2017, 06:11
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Re: If t#0, is r greater than zero? &nbs
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