Problem Solving

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

The OA is C.

I get the solution as follows,

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

Then, the correct answer is C.

Has anyone another strategic approach to solve this PS question? Regards!

AAPL 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

An alternate approach is to plug into the five answer choices two cases such that a/b = 1/2:
Case 1: a=1 and b=2
Case 2: a=2 and b=4

Note:
When the question stem includes the phrase which of the following, the correct answer is likely to be D or E.
For this reason, we should start with answer choice E and work our way up.

E: 6a - 3b
Case 1 --> (6*1) - (3*2) = 0.
Case 2 --> (6*2) - (3*4) = 0.
Here, each case yields the same result, indicating that the value of 6a-3b can be determined.
Eliminate E.

D: (a-3b)/(a+b)
Case 1 --> (1 - 3*2)/(1+2) = -5/3.
Case 2 --> (2 - 3*4) - (2+4) = -10/6 = -5/3.
Here, each case yields the same result, indicating that the value of (a-3b)/(a+b) can be determined.
Eliminate D.

C: (a+1)/(b+1)
Case 1 --> (1+1)/(2+1) = 2/3.
Case 2 --> (2+1)/(4+1) = 3/5.
Here, each case yields a DIFFERENT RESULT, indicating that the value of (a+1)/(b+1) CANNOT be determined.

The correct answer is C.