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Is 2a – b < 7?
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02 Dec 2011, 06:22
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61% (01:49) correct 39% (01:37) wrong based on 289 sessions
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Is \(2a – b < 7\)? (1) \(2a – b < 7\) (2) \(a = b + 3\) Guyz, I can't agree with official answer. What are your thoughts on this?
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Re: Is 2a – b < 7?
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10 Jul 2014, 12:55
PathFinder007 wrote: Postal wrote: Is 2a – b < 7? (1) 2a – b < 7 (2) a = b + 3
Guyz, I can't agree with official answer. What are your thoughts on this? Hi Bunnel, Could you please provide your comments on this. I am using following logic is 2ab <7 is 7<2ab<7 here in st1 2ab <7 but we dont know lower limit of 2ab so clearly not sufficient. in St2 a= b+3 . ( nothing new information) I want to know how to combine both the statement and proceed further? Thanks Actually this is a 30 second question. Is 2a – b < 7?(1) 2a – b < 7. If 2a  b = 0, then 2a  b = 0 < 7 but if 2a  b = 10, then 2a  b = 10 > 7. Not sufficient. (2) a = b + 3. Clearly insufficient. (1)+(2) Clearly 2a  b = 0 and a = b + 3 as well as 2a  b = 10 and a = b + 3, have solutions, so both cases are still possible. Not sufficient. Answer: E. Hope it helps.
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Re: Is 2a – b < 7?
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03 Dec 2011, 05:01
What was your answer, and why?
I get E.
From 1: 2a – b < 7 AND 2a – b < 7 WHERE 2a b > 7 2a – b < 7 BUT 2a – b > 7 WHERE 2a b < 7 INSUFFICIENT
to confirm this you can find values of a & b that satisfy the condition 2a – b < 7 but provide different answers for 2a – b < 7 ? A: a = 3, b = 0 2a  b = 6  0 = 6 6 < 7 and 6 < 7 B: a = 10, b = 1 2a  b = 20  1 = 21 21 < 7 but 21 > 7
From 2 you can refactor the original question: Is 2(b + 3)  b < 7? => is b + 6 < 7? This is true for 13 < b < 1 but false for value outside of this range. Again INSUFFICIENT.
Together, we can further combine in a similar manner as above to see that b + 6 < 7 so we find that b < 1, but we still don't know if b > 13.
So together is INSUFFICIENT.
Again, to see that this is the case, you can substitute numbers that satisfy both 1 & 2, but give different answers to the main question:
A: a = 3, b = 0 2a – b < 7 : 2a  b = 6  0 = 6 < 7 a = b + 3 : 3 = 0 + 3 2a – b < 7 ? : 6 < 7 TRUE
B: a = 20, b = 17 2a – b < 7 : 2a  b = 40  (17) = 23 < 7 a = b + 3 : 20 = 17 + 3 2a – b < 7 ? : 23 < 7 FALSE



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Re: Is 2a – b < 7?
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05 Dec 2011, 05:45
I ended up with C though.When you combined both statements. the statement is true



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Re: Is 2a – b < 7?
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05 Dec 2011, 14:00
Can you see from my explanation above that when you combine both statementsiit is true for some values (a=3, b=0), but not all values (a=20, b=17)?
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Re: Is 2a – b < 7?
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16 Apr 2014, 07:05
Is Is 2a – b < 7? Statement 1 Clearly insufficient we need to know if 2a>b for this to be true Statement 2 Here we have that a=b+3 But still nothing useful up to this point Both together Here's were the magic happens. 2a = 2b+6 So we need to know is 2a>b, is 2b+6>b? Is b>6? We don't have information to answer this question so clearly answer will be E Hope this helps Cheers! J



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Re: Is 2a – b < 7?
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10 Jul 2014, 03:50
Postal wrote: Is 2a – b < 7? (1) 2a – b < 7 (2) a = b + 3
Guyz, I can't agree with official answer. What are your thoughts on this? Hi Bunnel, Could you please provide your comments on this. I am using following logic is 2ab <7 is 7<2ab<7 here in st1 2ab <7 but we dont know lower limit of 2ab so clearly not sufficient. in St2 a= b+3 . ( nothing new information) I want to know how to combine both the statement and proceed further? Thanks



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Re: Is 2a – b < 7?
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10 Jul 2014, 21:57
But when we open the mod we get 2 options: 2ab < 7 OR 2ab > 7 When A mentions the first option, how come it's not sufficient? Please help Posted from GMAT ToolKit
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Re: Is 2a – b < 7?
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11 Jul 2014, 05:26
smit29may wrote: But when we open the mod we get 2 options: 2ab < 7 OR 2ab > 7 When A mentions the first option, how come it's not sufficient? Please help Posted from GMAT ToolKitSee there lies your fallacy.. Both can be possible so it is NOT possible ( SUFFICIENT) to answer conclusively. Had there been some other condition outlining that 2ab is always greater than 0 , then it would have been SUFFICIENT. Right now as it is stands , it is ambiguous. Hope this helps



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Re: Is 2a – b < 7?
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11 Jul 2014, 11:42



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Re: Is 2a – b < 7?
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12 Jan 2015, 15:08
Is 2 a – b < 7? (1) 2 a – b < 7 (2) a = b + 3



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Re: Is 2a – b < 7?
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12 Jan 2015, 15:52
Hi viktorija, We can answer this DS question by TESTing VALUES. We just have to make sure to be thorough with what we're TESTing: We're asked if 2A  B < 7. This is a YES/NO question. Fact 1: 2A  B < 7 IF... A = 0 B = 1 0  1 = 1 = 1 and the answer to the question is YES IF... A = 0 B = 10 0  10 = 10 = 10 and the answer to the question is NO Fact 1 is INSUFFICIENT Fact 2: A = B + 3 IF... B = 0 A = 3 6  0 = 6 = 6 and the answer to the question is YES IF.... B = 1 A = 4 8  1 =  7 = 7 and the answer to the question is NO Fact 2 is INSUFFICIENT Combined, we know: 2A  B < 7 A = B + 3 We can substitute in the value of A and get... 2(B+3)  B < 7 2B + 6  B < 7 B < 1 So whatever we TEST for B, it MUST be < 1 IF.... B = 0 A = 3 6  0 = 6 = 6 and the answer to the question is YES B can be ANY negative number though, so what happens if we take B to an 'extreme'....? IF.... B = 100 A = 97 194  (100) = 94 = 94 and the answer to the question is NO Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: Is 2a – b < 7?
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12 Jan 2015, 17:55



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Re: Is 2a – b < 7?
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16 Feb 2016, 20:01
Postal wrote: Is 2a – b < 7? (1) 2a – b < 7 (2) a = b + 3
Guyz, I can't agree with official answer. What are your thoughts on this? went with E. 1. 2ab< 7 suppose 2ab=4  in this case, both answers are yes. but if 2ab=20? 1 is satisfied, but the answer to the question is no. not sufficient. 2. we can rewrite b+6<7? if b for ex is 2 > b+6=4 and the answer is yes. if b=20 > then we have 14 and 14>7 and the answer is no. 1+2 b+6<7 b=2  yes b=20  no E



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Re: Is 2a – b < 7?
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23 Mar 2017, 17:09
Postal wrote: Is \(2a – b < 7\) ? (1) \(2a – b < 7\) (2) \(a = b + 3\) OFFICIAL SOLUTION Absolute value can be understood as distance from zero on the number line. The quantity 2 a – b has an absolute value less than 7 if (and only if) that quantity is less than 7 units away from 0 on a number line. (1) INSUFFICIENT: This statement tells us that 2 a – b is less than 7, but this does not tell us whether it is less than 7 units away from 0. For instance, 2 a – b could be equal to –20. (2) INSUFFICIENT: We can manipulate the equation a = b + 3 so that it tells us the value of 2 a – b: a = b + 3 2 a = 2 b + 6 2 a – b = b + 6 Since there is no restriction on the value of b, b + 6 can be anywhere on the number line. This implies that 2 a – b can be anywhere on the number line, making both “yes” and “no” answers possible. (1) & (2) INSUFFICIENT: Statement (2) does not restrict the value of 2 a – b at all, so combining it with statement (1) yields the same result as for statement (1) alone. In a sense, the catch in this problem is that there is no catch: we should be suitably suspicious when a problem seems easier than it ought to be, but we should then trust our analysis and choose confidently. The correct answer is E.
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