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If xaybzc equals the product of 154 and 56, z > y > x, and a
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12 Nov 2016, 16:35
12 Nov 2016, 16:35
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Question Stats:
62% (02:19) correct
37% (01:24) wrong based on 45 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
It cannot be determined from the information given.
A. 1,024
B. 2,048
C. 8,624
D. 22,528
It cannot be determined from the information given.
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Question: 1
Page: 293
Question: 1
Page: 293
Re: If xaybzc equals the product of 154 and 56, z > y > x, and a
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12 Nov 2016, 16:40
12 Nov 2016, 16:40
Expert Reply
Explanation
To solve this question, find the prime factors: The prime factors of 154 are 2, 7, and 11, and the prime factors of 56 are 2, 2, 2, and 7. Thus, the product of 154 and 56 will have the prime factors 2, 2, 2, 2, 7, 7, and 11, or (\(2^4\))(\(7^2\))(\(11^1\)).
Line up your bases and exponents with the inequalities, and you get a = 4, b = 2, and c = 1 for the bases, and x = 2, y = 7, z = 11 for the exponents.
Now \(a^xb^yc^z\) = \((4^2)(2^7)(1^1^1)\), which equals 16 × 128 × 1, or 2,048. The correct answer is choice B.
To solve this question, find the prime factors: The prime factors of 154 are 2, 7, and 11, and the prime factors of 56 are 2, 2, 2, and 7. Thus, the product of 154 and 56 will have the prime factors 2, 2, 2, 2, 7, 7, and 11, or (\(2^4\))(\(7^2\))(\(11^1\)).
Line up your bases and exponents with the inequalities, and you get a = 4, b = 2, and c = 1 for the bases, and x = 2, y = 7, z = 11 for the exponents.
Now \(a^xb^yc^z\) = \((4^2)(2^7)(1^1^1)\), which equals 16 × 128 × 1, or 2,048. The correct answer is choice B.
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Re: If xaybzc equals the product of 154 and 56, z > y > x, and a
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17 Nov 2016, 12:49
17 Nov 2016, 12:49
sandy 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
It cannot be determined from the information given.
A. 1,024
B. 2,048
C. 8,624
D. 22,528
It cannot be determined from the information given.
Is this question missing some key information (like restricting the values to positive integers)??
If there are no such restriction, here's another set of values that work:
x = -1
y = 1
z = √8624 [aside: 8624 is the product of 154 and 56]
a = 4
b = 3
c = 2
In this case, \(a^xb^yc^z\) does not equal any of the answer choices (other than It cannot be determined from the information given)
