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a^3b^4c^7>0
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18 Jul 2018, 17:00

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Question Stats:

\(a^3b^4c^7>0\)

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

_________________

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

_________________

Re: a^3b^4c^7>0
[#permalink]
18 Jul 2018, 19:53

2

Carcass wrote:

\(a^3b^4c^7>0\)

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

the above statement will be true if any of the following statement are true,

1. a , b , c are all positive numbers

2. if a is +ve, b is -ve and c is +ve

3. if a is -ve, b is +ve and c is -ve

Therefore only option C is always true

_________________

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Re: a^3b^4c^7>0
[#permalink]
29 Aug 2018, 07:38

4

Carcass wrote:

\(a^3b^4c^7>0\)

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

Key Concept: (any number)^(EVEN INTEGER) ≥ 0

First, since \(a^3b^4c^7>0\), we know that a ≠ 0, b ≠ 0, and c ≠ 0

Next, since \(b^4\) must be POSITIVE, we can safely divide both sides of the inequality by \(b^4\) to get: \(a^3c^7>0\)

Also, since \(c^6\) must be POSITIVE, we can safely divide both sides of the inequality by \(c^6\) to get: \(a^3c>0\)

Finally, since \(a^2\) must be POSITIVE, we can safely divide both sides of the inequality by \(a^2\) to get: \(ac>0\)

So, the ONLY relevant conclusion we can make is that \(ac>0\)

Answer: C

Cheers,

Brent

_________________

Re: a^3b^4c^7>0
[#permalink]
16 Nov 2018, 18:20

1

Answer: C

A: if ab <0 then:

a<0 and b>0 : then c should be negative to have a^3*b^4*c^7 >0

a>0 and b<0 : then it’s ok because b’s power is even.

So A is possible but not obligatory.

B: it’s possible, But it’s not obligatory.

C: ac is positive: True

Because power of a and c are odd, they both should have same sign, both negative or positibve to have the whole expression positive.

_________________

A: if ab <0 then:

a<0 and b>0 : then c should be negative to have a^3*b^4*c^7 >0

a>0 and b<0 : then it’s ok because b’s power is even.

So A is possible but not obligatory.

B: it’s possible, But it’s not obligatory.

C: ac is positive: True

Because power of a and c are odd, they both should have same sign, both negative or positibve to have the whole expression positive.

_________________

Follow your heart

Re: a^3b^4c^7>0
[#permalink]
15 Jul 2019, 08:13

1

the above statement will be true if any of the following statement are true,

1. a , b , c are all positive numbers

2. if a is +ve, b is -ve and c is +ve

3. if a is -ve, b is +ve and c is -ve

Therefore only option C is always true

1. a , b , c are all positive numbers

2. if a is +ve, b is -ve and c is +ve

3. if a is -ve, b is +ve and c is -ve

Therefore only option C is always true

Re: a^3b^4c^7>0
[#permalink]
15 Jul 2019, 08:15

GreenlightTestPrep wrote:

Carcass wrote:

\(a^3b^4c^7>0\)

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

Which of the following statements must be true?

Indicate all such statements.

A. \(ab\) is negative

B. \(abc\) is positive

C. \(ac\) is positive

Key Concept: (any number)^(EVEN INTEGER) ≥ 0

First, since \(a^3b^4c^7>0\), we know that a ≠ 0, b ≠ 0, and c ≠ 0

Next, since \(b^4\) must be POSITIVE, we can safely divide both sides of the inequality by \(b^4\) to get: \(a^3c^7>0\)

Also, since \(c^6\) must be POSITIVE, we can safely divide both sides of the inequality by \(c^6\) to get: \(a^3c>0\)

Finally, since \(a^2\) must be POSITIVE, we can safely divide both sides of the inequality by \(a^2\) to get: \(ac>0\)

So, the ONLY relevant conclusion we can make is that \(ac>0\)

Answer: C

Cheers,

Brent

Re: a^3b^4c^7>0
[#permalink]
01 Sep 2019, 18:56

Fatemeh wrote:

Answer: C

A: if ab <0 then:

a<0 and b>0 : then c should be negative to have a^3*b^4*c^7 >0

a>0 and b<0 : then it’s ok because b’s power is even.

So A is possible but not obligatory.

B: it’s possible, But it’s not obligatory.

C: ac is positive: True

Because power of a and c are odd, they both should have same sign, both negative or positibve to have the whole expression positive.

A: if ab <0 then:

a<0 and b>0 : then c should be negative to have a^3*b^4*c^7 >0

a>0 and b<0 : then it’s ok because b’s power is even.

So A is possible but not obligatory.

B: it’s possible, But it’s not obligatory.

C: ac is positive: True

Because power of a and c are odd, they both should have same sign, both negative or positibve to have the whole expression positive.

nvm got it, got tricked

abc: - - + -> +

347: - + + -> -

Re: a^3b^4c^7>0
[#permalink]
02 Sep 2019, 06:08

2

shadowmr20 wrote:

how come B isn't an answer?

We're told that \(a^3b^4c^7>0\)

So, it COULD be the case that \(a=1\), \(b=-1\) and \(c=1\)

Statement B says \(abc\) must be positive

However, if \(a=1\), \(b=-1\) and \(c=1\) then \(abc\) is negative

So, we can eliminate B

Cheers,

Brent

_________________

Re: a^3b^4c^7>0
[#permalink]
04 Sep 2019, 06:28

GreenlightTestPrep wrote:

shadowmr20 wrote:

how come B isn't an answer?

We're told that \(a^3b^4c^7>0\)

So, it COULD be the case that \(a=1\), \(b=-1\) and \(c=1\)

Statement B says \(abc\) must be positive

However, if \(a=1\), \(b=-1\) and \(c=1\) then \(abc\) is negative

So, we can eliminate B

Cheers,

Brent

if b is equal -1 then it must be positive as rules coz \(b^4\). If a or c is equal -1 not the b then we can easily eliminate the answer choice B.

_________________

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Re: a^3b^4c^7>0
[#permalink]
30 May 2020, 18:13

Brent's answer is a really clever one, and a reminder that when you see inequalities like this on the GRE, you should look to manipulate it so that it's still true. You'll likely find a cool shortcut.

a^3b^4c^7>0
[#permalink]
11 Jan 2024, 19:57

The concept being tested here is odd exponents preserve the sign of the base while even exponents do not.

For example

\((-2)^6 =+64\)

\((2)^6 = +64\)

\((-2)^6 =+64 = (2)^6 = +64\)

\((-2)^5 = -32\)

\((2)^5 = +32\)

\((-2)^5 = -32 \neq (2)^5 = +32\)

Now, if all three, \(a\),\(b\),\(c\) are positive, then the inequality is easily satisfied.

But it can also be satisfied if \(a\) and \(c\) are negative. Explanation below.

Now since \(a^3b^4c^7 > 0\), we can conclude that the sign of \(b\) is immaterial to satisfying the inequality. However, both \(a\) and \(c\) have to be negative so that \(a^3\) and \(c^7\) are negative and when multiplied together become positive to satisfy the inequality.

Therefore, \(a\) is negative, \(c\) is negative and \(b\) can be positive or negative.

A. ab : \(a=-ve\), \(b=+ve\) or \(b=-ve\), thus \(ab=+ve\) or \(-ve\), thus \(ab\) could be negative

B. abc : \(a=-ve\), \(b=+ve\) or \(-ve\),\(c=-ve\), thus \(abc = +ve\) or \(-ve\), thus \(abc\) could be positive

C. ac : \(a=-ve\) and \(c=-ve\), thus \(ac=+ve\), thus \(ac\) must be positive

Therefore, C is the correct answer.

_________________

For example

\((-2)^6 =+64\)

\((2)^6 = +64\)

\((-2)^6 =+64 = (2)^6 = +64\)

\((-2)^5 = -32\)

\((2)^5 = +32\)

\((-2)^5 = -32 \neq (2)^5 = +32\)

Now, if all three, \(a\),\(b\),\(c\) are positive, then the inequality is easily satisfied.

But it can also be satisfied if \(a\) and \(c\) are negative. Explanation below.

Now since \(a^3b^4c^7 > 0\), we can conclude that the sign of \(b\) is immaterial to satisfying the inequality. However, both \(a\) and \(c\) have to be negative so that \(a^3\) and \(c^7\) are negative and when multiplied together become positive to satisfy the inequality.

Therefore, \(a\) is negative, \(c\) is negative and \(b\) can be positive or negative.

A. ab : \(a=-ve\), \(b=+ve\) or \(b=-ve\), thus \(ab=+ve\) or \(-ve\), thus \(ab\) could be negative

B. abc : \(a=-ve\), \(b=+ve\) or \(-ve\),\(c=-ve\), thus \(abc = +ve\) or \(-ve\), thus \(abc\) could be positive

C. ac : \(a=-ve\) and \(c=-ve\), thus \(ac=+ve\), thus \(ac\) must be positive

Therefore, C is the correct answer.

_________________

gmatclubot

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