In the Sequence P, is P11 P10?

Question

In the Sequence P, is  P_{11}>P_{10} ?

(1)  P_{k}=x^3k

(2)  P_{k}=y^6k

Tonkotsu · Accepted Answer

I agree with  Tamboz2   E

1)  10x^3  vs  11x^3 
even if x is negative, positive, or 0,  x^3  will also be negative, positive or zero. 
This makes the inequality uncertain.

2)  10y^6  vs  11y^6 
if y is negative, positive, or 0,  y^6  can only be zero or positive.
Still, the inequality is uncertain because of the zero.

1 & 2) Still won't work because both can be zero.

noobieTopro · Answer

is  P_{11}>P_{10} 
is  P_{11} (-) P_{10} > 0

(1)  P_{k}=x^3k 
P_{11} = 11x^3
P_{10} = 10x^3
P_{11} (-) P_{10} = 11x^3 (-) 10x^3 = x^3(1)
is x^3(1) > 0 
Maybe / maybe not - depending on the sign of x - of which, we have no information. 
 Therefore, statement (1) alone is insufficient.

(2)  P_{k}=y^6k  
P_{11} = 11y^6
P_{10} = 10y^6
P_{11} (-) P_{10} = 11y^6 (-) 10y^6 = y^6(1) 
is y^6(1) >0 
Yes - because y^6 cannot be -ve.
 Therefore, statement (2) alone is insufficient.

Answer is B.

mcmoorthy · Answer

P_{11} = 11y^6
P_{10} = 10y^6
P_{11} (-) P_{10} = 11y^6 (-) 10y^6 = y^6(1) 
is y^6(1) >0 
Yes - because y^6 cannot be -ve.
 Therefore, statement (2) alone is insufficient.

Answer is B.

Hi noobieTopro,

No info on x,y and k whether they are positive or negative integers or numbers.

I just had a question what if x,y or k is zero. Can you pls share your views?

Thanks

Posted from my mobile device

Tamboz2 · Answer

from statement 1
is insufficient since we do not know the sign of x whether its positive or negative or zero
 statement 2
we cant deduce whether y is zero or ( any other sign) despite the fact that squaring gives a positive value there is a fact that y can be zero so not sufficient

combining 1 & 2
 we get either y or x as 
zero or positive and we cant have a solid answer

Hence E

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In the Sequence P, is P11 > P10?

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