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

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Math Expert
Joined: 02 Sep 2009
Posts: 58358
If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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09 Nov 2015, 23:04
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45% (medium)

Question Stats:

62% (01:46) correct 38% (01:35) wrong based on 197 sessions

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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

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Re: If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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10 Nov 2015, 01:27
1
1
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

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Re: If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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10 Nov 2015, 02:13
Bunuel wrote:
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

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....
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Re: If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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10 Nov 2015, 03:00
Abhishek009 wrote:
Bunuel wrote:
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

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....

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!!
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Re: If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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10 Nov 2015, 23:39
1
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
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Joined: 02 Aug 2009
Posts: 7958
Re: If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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11 Nov 2015, 01:52
Abhishek009 wrote:
Bunuel wrote:
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

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....

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"
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If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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23 Apr 2017, 21:27
Bunuel wrote:
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

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
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If a/b = 1/2, then the numerical value of which of the following  [#permalink]

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29 Mar 2019, 15:15
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
If a/b = 1/2, then the numerical value of which of the following   [#permalink] 29 Mar 2019, 15:15
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