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

Question

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

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

ramlala · Answer

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

v12345 · Answer

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

Bunuel · Answer

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

10*1.0 1 ^2 =  1 0.20 1 
10*1.0 9 ^2 =  1 1.88 1

Bonojit · Answer

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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