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If a, b, c, d, and x are nonzero numbers, which of the following condi

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Bunuel
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If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   26 Apr 2016, 00:55
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If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for \((ax)^{61}(bx)^{21}(cx)^{14}(dx)^6 > 0\)?

A. x > 0
B. a × b > 0
C. c × d > 0
D. a × d > 0
E. a × b < 0
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B
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raarun
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   26 Apr 2016, 06:38
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The question becomes a^(61) *b ^(21) *c^(14) *d^6*x^(102) >0
c^14 , d^6 , x^102 are positive no matter what the sign of c ,d and x respecively
=>a^61 *b ^21 must me positive
=> a*b should be positive


Ans B
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   06 Nov 2016, 20:57
Bunuel wrote:
If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for \((ax)^{61}(bx)^{21}(cx)^{14}(dx)^6 > 0\)?

A. x > 0
B. a × b > 0
C. c × d > 0
D. a × d > 0
E. a × b < 0


Can you please explain the answer for this question??
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JeffTargetTestPrep
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   14 Jun 2018, 10:27
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Bunuel wrote:
If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for \((ax)^{61}(bx)^{21}(cx)^{14}(dx)^6 > 0\)?

A. x > 0
B. a × b > 0
C. c × d > 0
D. a × d > 0
E. a × b < 0


To start, we can ignore any bases with even exponents because those quantities are positive. So we are left with:

a^61 * x^61 * b^21 * x^21 > 0

a^61 * b^21 * x^42 > 0

Dividing the inequality by a^60 * b^20 * x^42 (notice that this is a positive quantity), we have:

a * b > 0

Answer: B
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GyMrAT
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   14 Jun 2018, 11:02
Bunuel wrote:
If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for \((ax)^{61}(bx)^{21}(cx)^{14}(dx)^6 > 0\)?

A. x > 0
B. a × b > 0
C. c × d > 0
D. a × d > 0
E. a × b < 0


Given \((ax)^{61}(bx)^{21}(cx)^{14}(dx)^6 > 0\)

Since even power will always result in positive, irrespective of the sign of the base & odd power is dependent on the sign of the base.

We get, (+ve) * (+ve) * (+ve) * (+ve) > 0

or

(-ve) * (-ve) * (+ve) * (+ve) > 0

Now if ax > 0 & bx > 0, then it means a, x & b > 0 or a, x & b < 0

if ax < 0 & bx < 0, then it means a & b > 0 & x < 0 or a & b < 0 & x > 0

we can see that

a * b > 0 for any a, x & b combination.

Answer B.


Thanks,
GyM
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   14 Jun 2018, 11:40
a*b should be more than 0 as they have odd powers.
rest c and d have even powers so they will always be positive
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink] New post   14 Sep 2023, 16:11
This was super helpful. Thank you, Jeff!
JeffTargetTestPrep wrote:
Bunuel wrote:
If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for \((ax)^{61}(bx)^{21}(cx)^{14}(dx)^6 > 0\)?

A. x > 0
B. a × b > 0
C. c × d > 0
D. a × d > 0
E. a × b < 0


To start, we can ignore any bases with even exponents because those quantities are positive. So we are left with:

a^61 * x^61 * b^21 * x^21 > 0

a^61 * b^21 * x^42 > 0

Dividing the inequality by a^60 * b^20 * x^42 (notice that this is a positive quantity), we have:

a * b > 0

Answer: B
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Re: If a, b, c, d, and x are nonzero numbers, which of the following condi [#permalink]
14 Sep 2023, 16:11
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