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# If x^a*y^b*z^c equals the product of 154 and 56, z > y > x, and a > b

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Math Expert
Joined: 02 Sep 2009
Posts: 51095
If x^a*y^b*z^c equals the product of 154 and 56, z > y > x, and a > b  [#permalink]

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29 Jun 2018, 01:09
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Difficulty:

45% (medium)

Question Stats:

66% (02:17) correct 34% (02:32) wrong based on 93 sessions

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If $$x^ay^bz^c$$ equals the product of 154 and 56, z > y > x, and a > b > c, then what is the value of $$a^xb^yc^z$$?

A. 1,024

B. 2,048

C. 8,624

D. 22,528

E. It cannot be determined from the information given.

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Joined: 02 Aug 2009
Posts: 7099
Re: If x^a*y^b*z^c equals the product of 154 and 56, z > y > x, and a > b  [#permalink]

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29 Jun 2018, 01:35
1
Bunuel wrote:
If $$x^ay^bz^c$$ equals the product of 154 and 56, z > y > x, and a > b > c, then what is the value of $$a^xb^yc^z$$?

A. 1,024

B. 2,048

C. 8,624

D. 22,528

E. It cannot be determined from the information given.

Let's get 154*56 in lowest terms..
154*56=2*7*11*8*1= $$2^4*7^2*11$$...
since z>y>X and 11>7>2, we get X,y and z..
Also a>b>c and 4>2>1

$$a^xb^yc^z=4^2*2^7*1^11=2^11=2048$$

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Posts: 53
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If x^a*y^b*z^c equals the product of 154 and 56, z > y > x, and a > b  [#permalink]

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02 Jul 2018, 04:19
chetan2u wrote:
Bunuel wrote:
If $$x^ay^bz^c$$ equals the product of 154 and 56, z > y > x, and a > b > c, then what is the value of $$a^xb^yc^z$$?

A. 1,024

B. 2,048

C. 8,624

D. 22,528

E. It cannot be determined from the information given.

Let's get 154*56 in lowest terms..
154*56=2*7*11*8*1= $$2^4*7^2*11$$...
since z>y>X and 11>7>2, we get X,y and z..
Also a>b>c and 4>2>1

$$a^xb^yc^z=4^2*2^7*1^11=2^11=2048$$

B

It is nowhere mentioned that x,y and z are prime factors in the question, so why do we ignore the possibility that x=8 or 2^3 , Y=14 and Z=77

Then a can be 3 or 1 depending on weather x is considered as 2^3 or 8^1

Is there someting that i am missing here ?

I chose E only because we do not get a clarity in the question that x,y,z are prime factors.
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Dhruv
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Math Expert
Joined: 02 Aug 2009
Posts: 7099
Re: If x^a*y^b*z^c equals the product of 154 and 56, z > y > x, and a > b  [#permalink]

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02 Jul 2018, 04:39
DhruvPatelD10 wrote:
chetan2u wrote:
Bunuel wrote:
If $$x^ay^bz^c$$ equals the product of 154 and 56, z > y > x, and a > b > c, then what is the value of $$a^xb^yc^z$$?

A. 1,024

B. 2,048

C. 8,624

D. 22,528

E. It cannot be determined from the information given.

Let's get 154*56 in lowest terms..
154*56=2*7*11*8*1= $$2^4*7^2*11$$...
since z>y>X and 11>7>2, we get X,y and z..
Also a>b>c and 4>2>1

$$a^xb^yc^z=4^2*2^7*1^11=2^11=2048$$

B

It is nowhere mentioned that x,y and z are prime factors in the question, so why do we ignore the possibility that x=8 or 2^3 , Y=14 and Z=77

Then a can be 3 or 1 depending on weather x is considered as 2^3 or 8^1

Is there someting that i am missing here ?

I chose E only because we do not get a clarity in the question that x,y,z are prime factors.

Hi..
If you write $$x^ay^bz^c=2^3*14*77$$, a>b>c is not in place
There is no way you can place 2^4*7^2*11^1 in any way to fulfill the requirements of X>y>z and a>B>c
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x^a*y^b*z^c equals the product of 154 and 56, z > y > x, and a > b &nbs [#permalink] 02 Jul 2018, 04:39
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