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If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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27 Feb 2013, 13:17
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If a is not equal to b, is 1/(ab) > ab ? (1) a > b (2) a < b
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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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27 Feb 2013, 22:22
mun23 wrote: If a is not equal to b, is 1/(ab) > ab ?
(1) a > b (2) a < b From F.S 1, let's assume a = 3 and b = 2. Thus, 1/(ab) = 1 and a*b = 6. Thus, as 1<6, the answer to the question stem is No. Again, pick a = 3 and b = 2, and 1/(ab) = 0.2, and a*b = 6. In this case we see that 0.2>6, thus the answer to the question stem is a YES. Insufficient. From F.S 2, lets again assume a = 3 and b = 2. Just as above we still get a NO. Again choosing the same set for a = 3 and b = 2, we get a YES to the question stem. Insufficient. Combining both, we know that ba>0 and mod(a)mod(b)>0. Thus lets choose a=7 and b=2. We get 1/(ab) = 0.2 and a*b = 14. Thus a NO. Again, choosing b=3 and a=5, we get a YES . Insufficient. Basically, the two fact statements given together mean that (a+b)<0. It's because from F.S 1, we get a^2b^2>0 or (ab)*(a+b)>0. We have from F.S 2 that ab<0. Thus, (a+b) has to be negative. E.
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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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01 Jan 2014, 23:44
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Value substitution is good to solve this: 1. a>b we can say a can not be zero bcz mod of b will always be positive or equal to zero thus a must be anything but not zero. We can do value substitution to test all cases:  a  b  ab  1/(ab)  ab  Pass/ Fail for option (1)  3  2  1  1  6  Fail  3  2 . 5  1/5  6  Pass  3 . 2  1  1  6  Fail  3 . 2  5  1/5  6  Pass  3 . 0  3  1/3  0  Fail  3 . 0  3  1/3  0  Pass Multiple Pass / Fail inconsistent result, option one not sufficient. Option (2) a < b Not sufficient. Combine option 1 + 2 a<b  a  b  ab  1/(ab)  ab  Pass/ Fail for option (1)  3  2  1  1  6  Fail  3  2  5  1/5  6  Pass  3  0  3  1/3  0  Fail Again inconsistent result, thus both option also not sufficient. Answer E.
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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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18 Feb 2014, 03:10
(1) a > b Clearly IS. Look at this:
a > b a > b  a > b a > b
Would give you various answers for the YES/NO Question. IS!
(2) a<b. Here, a could be 1 and b 2. then we had 1/1 = 1 and 1 * 2 = 2. Hence 1/(ab) < a*b. But if a = 1 and b = 2 then 1/(ab) = 1/3 and a*b = 1 * 2 = 2. Thus 1/(a+b) > a*b. IS.
Answer E.



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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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26 Apr 2014, 08:26
So let's see. I think fastest way is to pic numbers. Statement 1, let's first say a=2, b=1 then we have a YES answer. Let's also say that a=2 and b=1 then we have a NO answer. Insufficient. Statement 2, we can use a=2 and b=1 again for a YES answer. For a NO answer we could use b=3 and a=1. Insufficient. Both statements together we have that we can still use a=2 and b=1 for a YES answer. Additionally, we could also have that both 'a' amd 'b' are negative. As in a=3 and b=2, giving a NO answer. Therefore answer is E Hope this helps Cheers! J



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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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30 Apr 2014, 13:07
Hey Karishma & Bunuel, Is there a faster way to solve this problem? I tried picking numbers but it took me more than 2 mins to arrive at the answer. Thanks, Prasoon



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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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01 May 2014, 00:58
prsnt11 wrote: Hey Karishma & Bunuel, Is there a faster way to solve this problem? I tried picking numbers but it took me more than 2 mins to arrive at the answer. Thanks, Prasoon For this problem I'd still advice to use number plugging at one point or another. If a is not equal to b, is 1/(ab) > ab ?(1) a > b. This statement implies that a is further from 0 then b. We can have 4 cases: 0ba b0a a0b ab0 For the second case the LHS is positive, while RHS is negative: 1/(ab) > ab; For the fourth case the LHS is negative, while RHS is positive: 1/(ab) < ab. Two different answers. Not sufficient. (2) a < b > a  b < 0. The LHS is negative: If a=2 and b=1, then (1/(ab)=1/3) > (ab=2); If a=2 and b=1, then (1/(ab)=1) < (ab=2). Two different answers. Not sufficient. (1)+(2) We can have only the third or fourth cases from (1): a0b ab0 We can use the same example as for (2): If a=2 and b=1, then (1/(ab)=1/3) > (ab=2); If a=2 and b=1, then (1/(ab)=1) < (ab=2). Two different answers. Not sufficient. Answer: E. Hope it helps.
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Re: If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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22 May 2014, 02:49
Alternative approach
Is 1/(ab)  ab>0?
Is (ab)(1ab) / (ab)> 0?
Statement 1 we have that a^2  b^2 >0, or (a+b)(ab) > 0
But still insufficient, we don't know anything about 'ab'
Statement 2 we have that ab<0
Same here, we are missing information regarding the sign of (1ab)
Both together
Since (a+b)(ab)>0 and ab<0, then a+b>0
Therefore a<0, but we don't know about 'b' hence again impossible to figure out sign of (1ab)
Answer: E



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If a is not equal to b, is 1/(ab) > ab ? [#permalink]
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08 Oct 2016, 19:47
If a ≠ b, is 1/ (ab) > ab? (1) a > b (2) a < b Please provide explanation for your answer choice. I do not fully understand OA
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Last edited by Vyshak on 08 Oct 2016, 20:11, edited 1 time in total.
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Re: If a ≠ b, is 1/ (ab) > ab? [#permalink]
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08 Oct 2016, 20:18
sidoknowia wrote: If a ≠ b, is 1/ (ab) > ab? (1) a > b (2) a < b
Please provide explanation for your answer choice. I do not fully understand OA Rephrasing the question.. 1/(ab)ab>0 or, ab(ab)<1 (1) if a=5 b=1 ........Yes but if a=5 && b=3.......No Hence insuff..... (2) a=3 && b=5.........No but if a=5 && b= 1.......Yes Hence insuff... Combining both we know from (1) a > b consider same ex. as in (1) Again insufff........ Ans E




Re: If a ≠ b, is 1/ (ab) > ab?
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