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If b is a positive integer less than 10 and x = 1 + b/100, what is the

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Bunuel
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If b is a positive integer less than 10 and x = 1 + b/100, what is the [#permalink] New post   07 Apr 2021, 16:21
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If b is a positive integer less than 10 and \(x = 1 + \frac{b}{100}\), what is the value of b ?

(1) \(1 \leq b \leq 3\)

(2) The thousandths digit of \(10x^2\) is equal to the tens digit of \(10x^2\)


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If b is an integer and b<10, x=1+ b/100. b=?

1) 1<=b<=3

2) The thousandths digit of 10X^2 is equal to the tens digit of x^2
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C
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ramlala
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Re: If b is a positive integer less than 10 and x = 1 + b/100, what is the [#permalink] New post   07 Apr 2021, 19:11
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If b is a positive integer less than 10 and \(x = 1 + \frac{b}{100}\), what is the value of b ?

(1) \(1 \leq b \leq 3\)
b may be 1 or 2 or 3
Not sufficient

(2) The thousandths digit of \(10x^2\) is equal to the tens digit of \(10x^2\)
\(x = 1 + \frac{b}{100}\)

so \(x^2 = 1 + \frac{2b}{100} + \frac{b^2}{10000}\)

\(10x^2 = 10 + \frac{2b}{10} + \frac{b^2}{1000}\)

So 2b is tens digit and \(b^2\) is thousandths digit

2b = \(b^2\)

so b = 2

Sufficient

IMO B
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Re: If b is a positive integer less than 10 and x = 1 + b/100, what is the [#permalink] New post   20 Jul 2021, 03:46
Bunuel wrote:
If b is a positive integer less than 10 and \(x = 1 + \frac{b}{100}\), what is the value of b ?

(1) \(1 \leq b \leq 3\)

(2) The thousandths digit of \(10x^2\) is equal to the tens digit of \(10x^2\)


Hi Bunuel
Please check if the OA to this post is (B).
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Bunuel
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Re: If b is a positive integer less than 10 and x = 1 + b/100, what is the [#permalink] New post   20 Jul 2021, 09:12
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v12345 wrote:
Bunuel wrote:
If b is a positive integer less than 10 and \(x = 1 + \frac{b}{100}\), what is the value of b ?

(1) \(1 \leq b \leq 3\)

(2) The thousandths digit of \(10x^2\) is equal to the tens digit of \(10x^2\)


Hi Bunuel
Please check if the OA to this post is (B).


C is correct from (2) b can be 1 or 9:

10*1.01^2 = 10.201
10*1.09^2 = 11.881
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Re: If b is a positive integer less than 10 and x = 1 + b/100, what is the [#permalink] New post   12 Jun 2023, 23:31
Hi Bunuel

could you please give the solution for statement no 2? How did you get 1 or 9 as possible values of b?
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Re: If b is a positive integer less than 10 and x = 1 + b/100, what is the [#permalink]
12 Jun 2023, 23:31
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