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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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Bunuel
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If integer x is greater than 0 but less than 10 and k = x^9, what is t [#permalink] New post   22 Aug 2017, 03:19
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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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sandeep211986
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If integer x is greater than 0 but less than 10 and k = x^9, what is t [#permalink] New post   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] New post   22 Aug 2017, 04:02
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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.
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Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t [#permalink] New post   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] New post   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.

Answer 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] New post   09 Jan 2021, 16:51
How can i choose that the correct answer would be 9 not 8? Can anyone explain me please?
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Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t [#permalink] New post   14 Jan 2021, 22:22
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.
This implies that x = 1 or 9
Insufficient.

(2) x(–2)<1/50
This implies that x^2 > 50 since a larger value in the denominator means a smaller fraction which is necessary if 1/50 > 1/x^2
x = 10, 9, or 8
Insufficient.

Combo pack: x = 9.
Sufficient.
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Re: If integer x is greater than 0 but less than 10 and k = x^9, what is t [#permalink]
14 Jan 2021, 22:22
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