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# If integer x is greater than 0 but less than 10 and k = x^9, what is t

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Math Expert
Joined: 02 Sep 2009
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If integer x is greater than 0 but less than 10 and k = x^9, what is t  [#permalink]

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22 Aug 2017, 03:19
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Difficulty:

45% (medium)

Question Stats:

70% (01:40) correct 30% (01:43) wrong based on 140 sessions

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If integer x is greater than 0 but less than 10 and $$k = x^9$$, what is the value of integer k?

(1) x^2 has a units digit of 1.

(2) $$x^{(–2)} < \frac{1}{50}$$

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If integer x is greater than 0 but less than 10 and k = x^9, what is t  [#permalink]

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Updated on: 22 Aug 2017, 04:05
Bunuel wrote:
If integer x is greater than 0 but less than 10 and $$k = x^9$$, what is the value of integer k?

(1) x^2 has a units digit of 1.

(2) $$x^{(–2)} < \frac{1}{50}$$

Answer has to be C because from statement 1 we get x = 1, 9 while from statement 2 x can be 8 or 9 .
Hence statement C is sufficient to ans the question because combining we get x to be 9.

Originally posted by sandeep211986 on 22 Aug 2017, 04:01.
Last edited by sandeep211986 on 22 Aug 2017, 04:05, edited 1 time in total.
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Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t  [#permalink]

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22 Aug 2017, 04:02
1
Bunuel wrote:
If integer x is greater than 0 but less than 10 and $$k = x^9$$, what is the value of integer k?

(1) x^2 has a units digit of 1.

(2) $$x^{(–2)} < \frac{1}{50}$$

Statement 1
- Since $$0<x<10$$, we have 9 integer options for X.
- From that 9 options, we have two integers with 1 unit digit : $$1^2$$ and $$9^2$$.
- Therefore, INSUFFICIENT.

Statement 2
- $$\frac{1}{x^2} < \frac{1}{50}$$.
- Since X is a positive number, we can cross multiply without change the sign.
- $$50 < x^2$$, or $$X^2 > 50$$. We have different possibilities here. X can be 8 and 9.
- Therefore, INSUFFICIENT.

Statement 1&2
- We can conclude that X must be 9.
- SUFFICIENT.
C
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Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t  [#permalink]

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31 Aug 2017, 21:20
Another super careless mistake of mine,
I forgot 1, I only thought of 9^2= 8"1"
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Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t  [#permalink]

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26 Nov 2019, 06:30
1) 0<x<10 , Value of x = 1 or 9. NOT SUFFICIENT.

2) x^-2 < 1/50 => x^2>50, Value of x^2 can be 8^2 or 9^2 since x<10. Thus x = 8 or 9. INSUFFICIENT.

1+2, x = 9 SUFFICIENT.

Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t   [#permalink] 26 Nov 2019, 06:30
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