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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 non-zero 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.

If a and b are integers, and a not= b, is |a|b > 0?

(1) |a^b| > 0

(2) |a|^b is a non-zero 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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If a and b are integers, and a not= b, is |a|b > 0?

(1) |a^b| > 0

(2) |a|^b is a non-zero integer

Question is |a|b>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...

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?

>>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 non-negative: \(|some \ expression|\geq{0}\). Please check Walker's post on Absolute Value at: math-absolute-value-modulus-86462.html

As 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 non-zero 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 non-zero 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.

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 non-integer. However, b could be 0 since a number raised to the 0 is 1, which is a non-integer number. Also insufficient.

Using both statements still doesn't provide anything because b can still be equal to 0, in which case |a|b > 0 is false. However, b can also be any positive number which would make |a|b > 0 true. Thus E.

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

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04 Jun 2014, 19:35

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 non-zero integers.

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

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02 Sep 2014, 04:43

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 non-negative: \(|some \ expression|\geq{0}\). Please check Walker's post on Absolute Value at: math-absolute-value-modulus-86462.html

As 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 non-zero 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 non-zero 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.

>>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 non-negative: \(|some \ expression|\geq{0}\). Please check Walker's post on Absolute Value at: math-absolute-value-modulus-86462.html

As 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 non-zero 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 non-zero 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.

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

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20 Oct 2014, 23:23

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 non-zero 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 non-zero 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.

Re: If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

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15 Apr 2016, 07:36

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If a and b are integers, and a not= b, is |a|b > 0? (1) [#permalink]

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20 Mar 2017, 20:51

mm007 wrote:

If a and b are integers, and a not= b, is \(|a|b > 0\)?

(1) \(|a^b| > 0\)

(2) \(|a|^b\) is a non-zero integer

OFFICIAL SOLUTION

Let us start be examining the conditions necessary for \(|a|b > 0\). 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 non-zero.

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 non-zero 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 non-zero. However, given that a is non-zero, 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 non-zero 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 |a|b > 0?) Given that a is non-zero, |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 non-zero integer . In addition, there is also the possibility that b = 0. If |b| = 0, then \(|a|^0\) is always 1, which is a non-zero 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 non-zero integer? Is \(|a|b > 0\)? 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 non-zero, we cannot determine whether b is positive. (1) also implies that a is non-zero, 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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