For integers a and b, If a/b = 12.12 then find the value of b? 1) 1/b

Question

For integers a and b, If \frac{a}{b} = 12.12 then find the value of b? 1) \frac{1}{b} is a terminating decimal 2) The odd integer b is less than 100 Source : https://www.GMATinsight.com

chetan2u · Answer

\frac{a}{b} = 12.12

a=12.12*b=12b+0.12b=12b+\frac{12b}{100}

Now   12b+\frac{12b}{100}=12b+\frac{3b}{25}

So b has to be 25 or a multiple of 25.

1)  \frac{1}{b}  is a terminating decimal

So b can be 2 and its powers or 5 and it’s powers or the product of their powers. 
b can be 25, 50, 200 and so on. 
Insufficient

2) The odd integer b is less than  100 
So b is odd and less than 100, so b can be 25 or 75.
Insufficient

Combined
b can not have any other factors other than 2s and 5s or their product and it is an odd integer less than 100.
Only 25 fits in. 
Sufficient

C

unraveled · Answer

For integers a and b, If  \frac{a}{b} = 12.12  then find the value of b?

\frac{a}{b} = 12.12= \frac{1212}{100} = \frac{909}{75} = \frac{606}{50} = \frac{303}{25} 
Hence b can be any multiple of 25.

1)  \frac{1}{b}  is a terminating decimal
Is it 25 or 50 or 100?

INSUFFICIENT.

2) The odd integer b is less than  100 
b = 25 or 75

INSUFFICIENT.

Together 1 and 2
b < 100 and  \frac{1}{b}  is terminating.
 \implies  b doesn't have any factor that leads to non-terminating answer e.g. 3 or 7 or 9

Since b can only be 25 and 75, where in the latter is not possible.

b = 25.

Answer C.

Archit3110 · Answer

note:
a ratio x/y will be terminating when its least form the only prime factors are in the form of (2^n*5^m i.e y)

target find if  \frac{a}{b} = 12.12  so find value of b 
12.12= 1212/100 ; 1212/2^2*5^2*x
value of b = 2^2*5^2*x possible values of b are many as least is 25 where a is 303 so on at b = 50,75 ,100

#1
 \frac{1}{b}  is a terminating decimal

value of b can be of the form 
2^n*5^m
many values of b are possible insufficient 
#2
The odd integer b is less than  100 
value of b <100 clearly insufficient as b = 25,75 
from 1 &2
we can conclude that value of b has to be factor of 2^m*5^n only and out of 25,75 ; 
25 is only possible
option C

OliveOyl2005 · Answer

Why is no one considering the fact that a and b can be negative as well? Because it is mentioned that they are integers. No one said anything about them being positive integers.

please correct me if I am wrong

bumpbot · Answer

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For integers a and b, If a/b = 12.12 then find the value of b? 1) 1/b

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