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Difficulty:
95%
(hard)
Question Stats:
41% (02:55) correct
59%
(03:02)
wrong
based on 438
sessions
History
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x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^(x-1)-5^x?
(1) z < 25 and w=7^x
(2) x = 4
OPEN DISCUSSION OF THIS QUESTION IS HERE: x-is-an-integer-and-x-raised-to-any-odd-integer-is-greater-95476.html
(1) z < 25 and w=7^x
(2) x = 4
OPEN DISCUSSION OF THIS QUESTION IS HERE: x-is-an-integer-and-x-raised-to-any-odd-integer-is-greater-95476.html
19 Jul 2012, 02:57
Kudos
Bookmarks
x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^(x-1)-5^x?
"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\).
Q: is \(w-z>5(7^{x-1}-5^x)\)?
(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.
(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.
Answer: A.
OPEN DISCUSSION OF THIS QUESTION IS HERE: x-is-an-integer-and-x-raised-to-any-odd-integer-is-greater-95476.html[/quote]
"x is an integer and x raised to any odd integer is greater than zero" means \(x=integer>0\).
Q: is \(w-z>5(7^{x-1}-5^x)\)?
(1) \(z<25\) and \(w=7^x\) --> is \(7^x-z>5(7^{x-1}-5^x)\)? --> is \(7^x-z>5*7^{x-1}-5^{x+1}\)? --> is \(7^x-5*7^{x-1}+5^{x+1}>z\)? --> as the lowest value of \(x\) is 1, then the lowest value of LHS is when \(x=1\): \(LHS_{min}=7^x-5*7^{x-1}+5^{x+1}=7-5+25=27\) --> so the lowest value of LHS is 27, which is more than \(z\) as \(z<25\) --> hence \(7^x-5*7^{x-1}+5^{x+1}>z\) is true. Sufficient.
(2) \(x = 4\). No info about \(w\) and \(z\). Not sufficient.
Answer: A.
OPEN DISCUSSION OF THIS QUESTION IS HERE: x-is-an-integer-and-x-raised-to-any-odd-integer-is-greater-95476.html[/quote]
General Discussion
05 Sep 2011, 06:21
Kudos
Bookmarks
Hey,
this is weird. The question states if w-z > 5(7x-1 - 5x), which is w-z > 10x - 5, right?
According to statement 1,
Is 7x - z > 10x - 5
When x = 2 and z = 1 then:
7(2) - 1 < 15
When x = 2 and z = -10 then:
7(2) + 10 > 15
Surely that's not enough.
The original info says that x to the power of any odd integer is greater than zero, which means x = positive
this is weird. The question states if w-z > 5(7x-1 - 5x), which is w-z > 10x - 5, right?
According to statement 1,
Is 7x - z > 10x - 5
When x = 2 and z = 1 then:
7(2) - 1 < 15
When x = 2 and z = -10 then:
7(2) + 10 > 15
Surely that's not enough.
The original info says that x to the power of any odd integer is greater than zero, which means x = positive
)
