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If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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20 Dec 2006, 14:21
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If a and b are integers, and a not= b, is ab > 0? (1) a^b > 0 (2) a^b is a nonzero integer
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(E) for me.
a*b > 0 ?
<=> b > 0 ?
From (1)
a^b > 0
o If b=1 and a=1, 1 > 0 and b < 0
o If b=1 and a=1, 1 > 0 and b > 0
INSUFF.
From (2)
a^b is a non zero integer implies that b must be positive or equal to 0 in order to not create a real number such as 2^1.
So, we remains with the cases of b = 0 and b > 0.
INSUFF.
Both (1) and (2)
It brings nothing more.
INSUFF.



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my answer is E
Given: a , b are ints. and a is different from b
asking: a * b > 0
what the question is really asking if b > 0 [ a is always >0 ]
(1) a^b >0

says nothing, cuz x is always > 0
statement 1 is insufficient
(2) a^b is not zero

also says nothing .. we know a^b > 0
b could be ve or +ve
statement 2 is insufficient
(1) and (2) together

both statements really say nothing about b
final answer is E



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is ab > 0 is same as, is b > 0
stat 1 is not sufficient since all it says is that a <> 0
from stat 2 b>= 0 since a only negative value of b can cause a^b to be not a non zero integer
so E ?



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Re: DS_If a and b.... [#permalink]
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16 Jan 2007, 21:39
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mm007 wrote: If a and b are integers, and a not= b, is ab > 0? (1) a^b > 0 (2) a^b is a nonzero integer
First of all, the question is equivalent to: is a<>0 AND b>0?
(1) For a^b > 0, a could be <>0 but b could be <0 OR b>0 => insuff => B, C, or E.
(2) This is a similar case to (1): b, similarly to a, could be <>0 => insuff => C or E.
(1&2) Again, similar case to (1) and (2): b could be +ve or ve => insuff => E.



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Quote: If a and b are integers, and a not= b, is ab > 0? (1) a^b > 0 (2) a^b is a nonzero integer
E2
I rephrased the stem to "is a>0 and is b ve, 0 or +ve?"
1) a^b will always be +ve. But here, b can be greater than or equal to 0 and a^b will still be +ve
INS
2) a^b. Here, a cannot be 0 but B can be 0 or 1. b can't be ve b/c a^b will become a noninteger, 1/a^b.
INS
Taken together, we're still not told anything about b. If we can't figure what b is we can't do much with this prob.
INS



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Can anybody chime in? Although I agree with the answer, I don't think the bold statement below is correct. B does not have to be 0 or greater. It can be 4 if A is 1. If b= 4 and a=1. this satisfiies the conditions: 1) a,b are integers 2) a is not equal to b 3) statement 2; 1^(4)=1. that is a nonzero integer. So you can't say B is definitely positive or 0. Combining statement 1 and 2. You can't determine if A is a 1 or not so E. Please correct me if I am wrong. Thanks. Fig wrote: (E) for me.
a*b > 0 ? <=> b > 0 ?
From (1) a^b > 0
o If b=1 and a=1, 1 > 0 and b < 0 o If b=1 and a=1, 1 > 0 and b > 0
INSUFF.
[b]From (2) a^b is a non zero integer implies that b must be positive or equal to 0 in order to not create a real number such as 2^1.
So, we remains with the cases of b = 0 and b > 0.[/b] INSUFF.
Both (1) and (2) It brings nothing more.
INSUFF.



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Re: DS_If a and b.... [#permalink]
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26 Nov 2009, 19:34
mm007 wrote: If a and b are integers, and a not= b, is ab > 0?
(1) a^b > 0
(2) a^b is a nonzero integer Clearly E. a^b and a^b are always >0, no matter what b is, because absolute value is always greater than 0. Thus, we can't know if b>0 or not.
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Re: DS_If a and b.... [#permalink]
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21 Dec 2009, 08:22
mm007 wrote: If a and b are integers, and a not= b, is ab > 0?
(1) a^b > 0
(2) a^b is a nonzero integer Question is ab>0 this can be proved if we can prove that a not=0 and b>0. 1. a^b > 0 implies that a not = 0. a can be +ve or ve, and be can be 0, +ve or ve....but we are sure that a not=0 else a^b = 0. Statement 1 itself is insuff. 2. a^b is a non zero integer. we already know a,b both are integers....a is > 0, so b >= 0. No clear value of b... So ans E.



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Mishari wrote: my answer is E
Given: a , b are ints. and a is different from b asking: a * b > 0
what the question is really asking if b > 0 [ a is always >0 ]
(1) a^b >0  says nothing, cuz x is always > 0 statement 1 is insufficient
(2) a^b is not zero  also says nothing .. we know a^b > 0 b could be ve or +ve statement 2 is insufficient
(1) and (2) together  both statements really say nothing about b
final answer is E >>Please tell me how can a be taken as positive in the above steps without knowing its sign..I mean if a is negative,then a wil be negative..Right?Am i missing anythin badly?



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ravitejapandiri wrote: >>Please tell me how can a be taken as positive in the above steps without knowing its sign..I mean if a is negative,then a wil be negative..Right?Am i missing anythin badly? Absolute value of of an expression is alway nonnegative: \(some \ expression\geq{0}\). Please check Walker's post on Absolute Value at: mathabsolutevaluemodulus86462.htmlAs for the question: If a and b are integers, and a does not equal to b, is a*b > 0? (1) a^b > 0 (2) a^b is a nonzero integer. \(a*b>0\) is true when \(b>0\) and \(a\) does not equal to zero. (1) \(a^b > 0\) > \(a\) does not equal to zero, but we don't know about \(b\), it can be any value, positive or negative. Not sufficient. (2) \(a^b\) is a nonzero integer > \(a\) can be 1 and \(b\) any integer, positive or negative. Not sufficient. (1)+(2) If \(a=1\) and \(b=2\), then \(a*b>0\), but if \(a=1\) and \(b=2\), then \(a*b<0\). Not sufficient. Answer: E. Other discussion of this question at: goodsetofds85413.html Similar question: thepowerofabsolutesmanhattanchallengeproblem101661.htmlHope it helps.
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Re: DS question : need help [#permalink]
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28 Oct 2010, 18:20
Basically just need to find out if b is positive or negative, since a will always be positive as it is inside of the  .
1) Doesn't give you anything because everything is inside of the  , so you can't tell if b is positive or negative, so insufficient.
2) Tells you that b is not negative since that would result in a noninteger. However, b could be 0 since a number raised to the 0 is 1, which is a noninteger number. Also insufficient.
Using both statements still doesn't provide anything because b can still be equal to 0, in which case ab > 0 is false. However, b can also be any positive number which would make ab > 0 true. Thus E.



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Re: If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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04 Jun 2014, 18:35
The reason why s2 alone or taken together with s1 is not sufficient bcos we need info on the signs that is, a is +ve or ve and whether b is +ve or ve & not wether they are zero or nonzero integers.



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Re: If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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02 Sep 2014, 03:43
Bunuel wrote: ravitejapandiri wrote: >>Please tell me how can a be taken as positive in the above steps without knowing its sign..I mean if a is negative,then a wil be negative..Right?Am i missing anythin badly? Absolute value of of an expression is alway nonnegative: \(some \ expression\geq{0}\). Please check Walker's post on Absolute Value at: mathabsolutevaluemodulus86462.htmlAs for the question: If a and b are integers, and a does not equal to b, is a*b > 0? (1) a^b > 0 (2) a^b is a nonzero integer. \(a*b>0\) is true when \(b>0\) and \(a\) does not equal to zero. (1) \(a^b > 0\) > \(a\) does not equal to zero, but we don't know about \(b\), it can be any value, positive or negative. Not sufficient. (2) \(a^b\) is a nonzero integer > \(a\) can be 1 and \(b\) any integer, positive or negative. Not sufficient. (1)+(2) If \(a=1\) and \(b=2\), then \(a*b>0\), but if \(a=1\) and \(b=2\), then \(a*b<0\). Not sufficient. Answer: E. Other discussion of this question at: goodsetofds85413.html Similar question: thepowerofabsolutesmanhattanchallengeproblem101661.htmlHope it helps. Hi Bunuel, I've always struggled when to consider 0 as an integer and when not. Is there any concept that you can share? Appreciate your help!!



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If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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02 Sep 2014, 03:49
shahPranay14 wrote: Bunuel wrote: ravitejapandiri wrote: >>Please tell me how can a be taken as positive in the above steps without knowing its sign..I mean if a is negative,then a wil be negative..Right?Am i missing anythin badly? Absolute value of of an expression is alway nonnegative: \(some \ expression\geq{0}\). Please check Walker's post on Absolute Value at: mathabsolutevaluemodulus86462.htmlAs for the question: If a and b are integers, and a does not equal to b, is a*b > 0? (1) a^b > 0 (2) a^b is a nonzero integer. \(a*b>0\) is true when \(b>0\) and \(a\) does not equal to zero. (1) \(a^b > 0\) > \(a\) does not equal to zero, but we don't know about \(b\), it can be any value, positive or negative. Not sufficient. (2) \(a^b\) is a nonzero integer > \(a\) can be 1 and \(b\) any integer, positive or negative. Not sufficient. (1)+(2) If \(a=1\) and \(b=2\), then \(a*b>0\), but if \(a=1\) and \(b=2\), then \(a*b<0\). Not sufficient. Answer: E. Other discussion of this question at: goodsetofds85413.html Similar question: thepowerofabsolutesmanhattanchallengeproblem101661.htmlHope it helps. Hi Bunuel, I've always struggled when to consider 0 as an integer and when not. Is there any concept that you can share? Appreciate your help!! 0 is neither positive nor negative even integer.Check for more here: numberpropertiestipsandhints174996.html
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Re: If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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20 Oct 2014, 22:23
If a and b are integers, and a does not equal to b, is a*b > 0? (1) a^b > 0 (2) a^b is a nonzero integer. to check whether a*b > 0, we need to identify whether b>0 1  This statement has to be positive, irrespective of the value of a and b. This is insufficient 2. a^b is nonzero integer  Possibilities  a = .5 or .5 and b = 1 The value of expression would be 2 a = any number and b = 0. The value will be 1 a = any positive / negative number and b = any positive number Thus the result will be a positive number. Thus insufficient. Combining two, We'll get positive values for y, and zero. Thus combining two will not give solution. Thus Ans  E
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Re: If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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If a and b are integers, and a not= b, is ab > 0? (1) [#permalink]
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20 Mar 2017, 19:51
mm007 wrote: If a and b are integers, and a not= b, is \(ab > 0\)?
(1) \(a^b > 0\)
(2) \(a^b\) is a nonzero integer OFFICIAL SOLUTION Let us start be examining the conditions necessary for \(ab > 0\). Since a cannot be negative, both a and b must be positive. However, since a is positive whether a is negative or positive, the only condition for a is that it must be nonzero. Hence, the question can be restated in terms of the necessary conditions for it to be answered "yes": “Do both of the following conditions exist: a is nonzero AND b is positive?” (1) INSUFFICIENT: In order for a = 0, \(a^b\) would have to equal 0 since 0 raised to any power is always 0. Therefore (1) implies that a is nonzero. However, given that a is nonzero, b can be anything for \(ab > 0\) so we cannot determine the sign of b. (2) INSUFFICIENT: If a = 0, a = 0, and \(a^b = 0\) for any b. Hence, a must be nonzero and the first condition (a is not equal to 0) of the restated question is met. We now need to test whether the second condition is met. (Note: If a had been zero, we would have been able to conclude right away that (2) is sufficient because we would answer "no" to the question is ab > 0?) Given that a is nonzero, a must be positive integer. At first glance, it seems that b must be positive because a positive integer raised to a negative integer is typically fractional (e.g., \(a^{2} = \frac{1}{{a^2}}\). Hence, it appears that b cannot be negative. However, there is a special case where this is not so: If a = 1, then b could be anything (positive, negative, or zero) since \(1^b\) is always equal to 1, which is a nonzero integer . In addition, there is also the possibility that b = 0. If b = 0, then \(a^0\) is always 1, which is a nonzero integer. Hence, based on (2) alone, we cannot determine whether b is positive and we cannot answer the question. An alternative way to analyze this (or to confirm the above) is to create a chart using simple numbers as follows: a b Is \(a^b\) a nonzero integer? Is \(ab > 0\)? 1 2 Yes Yes 1 2 Yes No 2 1 Yes Yes 2 0 Yes No We can quickly confirm that (2) alone does not provide enough information to answer the question. (1) AND (2) INSUFFICIENT: The analysis for (2) shows that (2) is insufficient because, while we can conclude that a is nonzero, we cannot determine whether b is positive. (1) also implies that a is nonzero, but does not provide any information about b other than that it could be anything. Consequently, (1) does not add any information to (2) regarding b to help answer the question and (1) and (2) together are still insufficient. (Note: As a quick check, the above chart can also be used to analyze (1) and (2) together since all of the values in column 1 are also consistent with (1)). The correct answer is E.
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If a and b are integers, and a not= b, is ab > 0? (1)
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