If a/b = 1/2, then the numerical value of which of the following

Question

If a/b = 1/2, then the numerical value of which of the following expressions cannot be determined?

A. 2a/b
B. (a + b)/a
C. (a + 1)/(b + 1)
D. (a - 3b)/(a + b)
E. 6a – 3b

Skywalker18 · Answer

a/b = 1/2
=> b = 2a

A. 2a/b
 = 2*(a/b)
 Can be determined
B. (a + b)/a
 Dividing numerator and denominator by a , 
 1+(b/a)
 Can be determined
C. (a + 1)/(b + 1)
 = (a + 1)/(2a+1)
 Numerical value can't be determined
D. (a - 3b)/(a + b)
 Dividing numerator and denominator by b,
 =(a/b - 3 )/ (a/b+ 1 )
 Can be determined
E. 6a – 3b 
 = 6a - 3*2a = 0
 
 Answer C

Abhishek009 · Answer

Plug in the value of a = 1 and b = 2

A. 2a/b => 2/1 = 1

B. (a + b)/a => 3/1 =3

C. (a + 1)/(b + 1) = 2/3

D. (a - 3b)/(a + b) => -5/3

E. 6a – 3b => 6 - 6 =0

I am getting both C and D , someone plz confirm where i am getting wrong....

Skywalker18 · Answer

Hi Abhishek009 I think the issue might be because we can't take values of a and b here . a=k b=2k k can any non zero number if we take a= 2 and b=4 then (a + 1)/(b + 1) = (2+1)/(4+1) = 3/5 But for other options we will get the same answer. In my opinion the issue is due to fact that except option C , either we take the ratio of a and b or are performing some operation on a and b ( in numerator or denominator) and then we take the ratio . A. 2a/b = 2* 2/4= 1 B. (a + b)/a = (2+4)/2 = 6/2=3 D.(a - 3b)/(a + b) = (2- 3*4)/(2+4) = (-10)/6 = -5/3 E. 6a- 3b = 6*2 - 3*4= 0 Hope it helps!!

Temurkhon · Answer

a/b=1/2, so b=2a and a=b/2.

A. 2a/b=b/b=1
B. a+b/a=a+2a/a=3
C. (a+1)/(b+1)=a+1/2a+1. No numbers
D. (a - 3b)/(a + b)=(a-3*2a)/(a+2a)=-5a/3a=(-5/3)
E. 6a – 3b=6a-3*2a=6a-6a=0

C

chetan2u · Answer

hi,
you cannot take numeric values of a and b....
it is but natural that you will get a numeric value for any expression if you have only a and b in it , and you substitute some value for them..
 how are you saying that you are getting C and D as answers.. afterall they are also giving you numeric values.. 
Therefore you have gone wrong in the first step itself " of taking numeric values"

Nunuboy1994 · Answer

In approaching this problem it's important to note patterns- the ratio of a to be is essentially 1:2 - so there are an infinite number of values "a" and "b" could take on as long as "b" is twice as a.

a=1/2b

A, b , d , e can all be solved using any set of variables for a and b - the explicit values of a and b aren't necessarily needed you just have to understand the ratio of a to b' for example, if we take out A

2 (a/b) = 2(1/2) 
2 (a/b) = 1
So no matter what set of numbers you choose for a and b the result will always be 1

Though for option C the explicit value actually does matter because if we take a number such as 1 and 2 the result is not same as say 2 and 4- in other words the result of this equation is various and not universally applicable to all values of a and b

(1 + 1 )/ ( 2 + 1) = 2/3
( 2 + 1)/ (4+1) = 3/5

Thus C

jfranciscocuencag · Answer

Just consider the -ve possibilities:

\frac{a}{b}=\frac{1}{2}

\frac{-a}{-b}=\frac{1}{2}

a = -1

So option C ( -1  + 1)/(b + 1) ... undifined

C

glagad · Answer

Why can't a or b be zero here?

Is it because a/b = 1/2, since b is the denominator, hence b can't be zero and subsequently a can't be zero too?

Bunuel · Answer

We are given that a/b = 1/2.

If a = 0, then a/b = 0/b = 0, not 1/2.
 If b = 0, then a/b = a/0, which is not defined, not 1/2.

If a/b = 1/2, then the numerical value of which of the following

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If a/b = 1/2, then the numerical value of which of the following

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