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If a+1=b1, what is the value of ab? (1) ab>0
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Updated on: 18 Feb 2017, 06:21
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Challenging Question! If \(a+1=b1\), what is the value of \(ab\) ? (1) \(ab>0\) (2) \(\frac{a}{b}≠ 1\)
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Originally posted by hazelnut on 18 Feb 2017, 05:15.
Last edited by hazelnut on 18 Feb 2017, 06:21, edited 2 times in total.




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Re: If a+1=b1, what is the value of ab? (1) ab>0
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18 Feb 2017, 10:00
ziyuenlau wrote: Challenging Question! If \(a+1=b1\), what is the value of \(ab\) ? (1) \(ab>0\) (2) \(\frac{a}{b}≠ 1\) Hi... Let us solve \(a+1=b1\)... Square both sides.. \(a^2+2a+1=b^22b+1\).. \(a^2b^2+2a+2b=0.....(ab)(a+b)+2(a+b)=0.....(ab+2)(a+b)=0\).. So either (ab)=2 OR a=b or both.. Let's see the statements.. (1) \(ab>0\) So both a and b are of same sign.. If they are of same sign, ab=2.. Sufficient (2) \(\frac{a}{b}≠ 1\)[/quote] So a ≠ b.. As per conditions if a is not equal to b, ab=2.. Sufficient D
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Re: If a+1=b1, what is the value of ab? (1) ab>0
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18 Feb 2017, 08:09
ziyuenlau wrote: Challenging Question! If \(a+1=b1\), what is the value of \(ab\) ? (1) \(ab>0\) (2) \(\frac{a}{b}≠ 1\) Similar question: https://gmatclub.com/forum/x2y2what ... 72994.html
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Re: If a+1=b1, what is the value of ab? (1) ab>0
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18 Feb 2017, 09:28
Either of the statements is sufficient. If a+1=b1 then there can be two cases 1. a and b both are of same sign, in this case the difference ab will be 2 always 2. a and b are of different sign, in this case absolute value of a and b will be same
Now let's look at statements: 1. ab>0: so a and b are of same sign (both positive or negative)  sufficient 2. Frac{a}{b}!= 1: so a and b are of same sign  sufficient
So either statement is sufficient
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If a+1=b1, what is the value of ab? (1) ab>0
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25 Mar 2017, 15:52
Hello Chetan, Unable to understand how S1 and S2 are sufficient. From question I infer ab = 2 or a+b =0. But not sure how to relate this to S1, S2. It looks I am skipping a simple point. Request your help.
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Re: If a+1=b1, what is the value of ab? (1) ab>0
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25 Mar 2017, 20:01
coolkl wrote: Hello Chetan,
Unable to understand how S1 and S2 are sufficient. From question I infer ab = 2 or a+b =0. But not sure how to relate this to S1, S2. It looks I am skipping a simple point. Request your help. Hi There are two possiblities as you have also mentioned.. 1) ab=2 2) a=b Now SI tells us that ab>0, so both a and b are of same sign that is either BOTH are NEGATIVE or both are POSITIVE.. So a=b is not TRUE... Only possibility left is ab=2, so we can say ab is 2 & this is what we have to find this sufficient SII tells us a/b \(\neq{1}\) or \(a \neq{b}\) So only second case possible is ab=2, again we can tell what ab is.. Hope it helps
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If a+1=b1, what is the value of ab? (1) ab>0
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18 Sep 2019, 07:05
chetan2u wrote: coolkl wrote: Hello Chetan,
Unable to understand how S1 and S2 are sufficient. From question I infer ab = 2 or a+b =0. But not sure how to relate this to S1, S2. It looks I am skipping a simple point. Request your help. Hi There are two possiblities as you have also mentioned.. 1) ab=2 2) a=b Now SI tells us that ab>0, so both a and b are of same sign that is either BOTH are NEGATIVE or both are POSITIVE.. So a=b is not TRUE... Only possibility left is ab=2, so we can say ab is 2 & this is what we have to find this sufficient SII tells us a/b \(\neq{1}\) or \(a \neq{b}\) So only second case possible is ab=2, again we can tell what ab is.. Hope it helps Hi chetan2u, This looks wrong. I believe the correct answer is A (ie. only statement (1) is sufficient alone). The Q states: \(a+1=b1\) If \(\frac{a}{b}≠−1\), then there are two solutions, either \(ab=2\) or \(ab=0\) Example,\(a=3\) and\(b=5\), then both the original condition \(3+1=51\) and\(\frac{3}{5}≠−1\)are satisfied. But also consider \(a=b=0\): \(0+1=01\) is satisfied. \(\frac{0}{0}≠−1\) is also satisfied, as \(\frac{0}{0}\) is indeterminate. Hence statement 2 is not sufficient independently, as you do not have a unique solution for (\(ab\)).



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Re: If a+1=b1, what is the value of ab? (1) ab>0
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18 Sep 2019, 13:23
chetan2u  Can we multiply a variable in an inequality?.. i suppose not and then a/b!= 1 could be lot of things Statement A should only be sufficient Posted from my mobile device



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Re: If a+1=b1, what is the value of ab? (1) ab>0
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18 Sep 2019, 18:42
dushyanta wrote: chetan2u  Can we multiply a variable in an inequality?.. i suppose not and then a/b!= 1 could be lot of things Statement A should only be sufficient Posted from my mobile device Hi, Yes, we cannot multiply inequality < or >, but we can always do it for = or \(\neq\) For example \(\frac{a}{b}\neq{1}\) when is \(\frac{a}{b}=1\)... ONLY when a=b. Now, opposite of above when will a/b NOT be 1  when a is NOT equal to b SO, if a =2, then for \(\frac{a}{b}\neq{1}\), b should not be (2) or (a) or a
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Re: If a+1=b1, what is the value of ab? (1) ab>0
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18 Sep 2019, 18:44
ngmat12 wrote: chetan2u wrote: coolkl wrote: Hello Chetan,
Unable to understand how S1 and S2 are sufficient. From question I infer ab = 2 or a+b =0. But not sure how to relate this to S1, S2. It looks I am skipping a simple point. Request your help. Hi There are two possiblities as you have also mentioned.. 1) ab=2 2) a=b Now SI tells us that ab>0, so both a and b are of same sign that is either BOTH are NEGATIVE or both are POSITIVE.. So a=b is not TRUE... Only possibility left is ab=2, so we can say ab is 2 & this is what we have to find this sufficient SII tells us a/b \(\neq{1}\) or \(a \neq{b}\) So only second case possible is ab=2, again we can tell what ab is.. Hope it helps Hi chetan2u, This looks wrong. I believe the correct answer is A (ie. only statement (1) is sufficient alone). The Q states: \(a+1=b1\) If \(\frac{a}{b}≠−1\), then there are two solutions, either \(ab=2\) or \(ab=0\) Example,\(a=3\) and\(b=5\), then both the original condition \(3+1=51\) and\(\frac{3}{5}≠−1\)are satisfied. But also consider \(a=b=0\): \(0+1=01\) is satisfied. \(\frac{0}{0}≠−1\) is also satisfied, as \(\frac{0}{0}\) is indeterminate. Hence statement 2 is not sufficient independently, as you do not have a unique solution for (\(ab\)). In GMAT, we deal with ONLY real numbers... That is why you will never see a case in GMAT when the denominator is 0... Although, the statement II could have mentioned \(b\neq{0}\)
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Re: If a+1=b1, what is the value of ab? (1) ab>0
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19 Sep 2019, 05:11
Hi! Can anyone explain this with plotting the number line approach?



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Re: If a+1=b1, what is the value of ab? (1) ab>0
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23 Sep 2019, 01:37
hazelnut wrote: Challenging Question! If \(a+1=b1\), what is the value of \(ab\) ? (1) \(ab>0\) (2) \(\frac{a}{b}≠ 1\) We can also solve by making use of the below concept: if a=b , then a=b OR a=b Applying the above concept we get: a+1=b1 a+1=b1 OR a+1=1b => ab=21) OR a=b2) now, first says: ab>0, thus eqn 2 cannot satisfy as both are of opposite signs and hence eqn 1 suffices.  Sufficient second says : a/b not equal to 1, thus eqn 2 again cannot satisfy and hence eqn 1 suffices here too Sufficient. D it is.
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Re: If a+1=b1, what is the value of ab? (1) ab>0
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