If a/3 = 4/b , is a less than b?

Hi,

I have a question. Can we assume that b, a variable, will not be equal to zero by looking only at the question stem?

Hi ShristiK,

Of course you can deduce that b can't be Zero because 4/b won't be defined for b =0

Hence, b can't be zero for defining this question. Denominator can't be zero in any ratio of two variables

I hope this helps.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a/3 = 4/b , is a less than b?

(1) b ≥ 4
(2) b ≤ 5

There are 2 variables (a,b) and an equation (a/3=4/b), which means we need 1 more equation to be able to solve for 2 variables; the conditions provide us with 2 more equations, making (D) likely to be the answer.
Looking at condition 1, if b≥4, b=12/a≥4 and 12/4≥a, 3≥a. The answer is always ‘yes’ in this range, so it is sufficient.
For condition 2, the answer is ‘yes’ for b=4, a=3, but ‘no’ for b=-4, a=-3, so this condition is insufficient. Therefore, the answer becomes (A).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

a/3=4/b
=>ab=4/3~1.33

Statement 1: b≥ 4 Clearly for ab to have value 1.33, a must lie b/w 0<a<1

Sufficient

Statement 1: b≤ 5

For b > Sqrt(4/3) ,

a<b

for b≤sqrt(4/3)
a>b

Insufficient

Ans: A

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No This question asks: “Is a less than b?”

Given information from the question stem: a/3 = 4/b . If you cross-multiply this becomes ab = 12.

Statement 1: b is greater than or equal to 4. If this is the case then both a and b must be positive and a must be less than or equal to 3. This means that “yes, a is less than b.” This statement is sufficient. The correct answer is either A or D. Statement 2: b is less than or equal to 5. This statement is not as helpful as

Statement 1. First, you do not know if a and b are positive or negative. a could be -3 and b could be -4, which does work with the facts above and would yield a “no, a is not less than b.” Even if a and b are positive then a could equal 3 and b equal 4 in which case a would still be larger than b. Of course, b can be larger than a as well if b = 4 and a = 3. So Statement 2 allows for both a “yes” and a “no” and is not consistent and not sufficient. The correct answer is A.

If a/3 = 4/b , then ab=12, which means 1*12 or 6*2 or 4*3

(1) b ≥ 4
So be could be 4, 6, 12..In any case b>a ... Sufficient
(2) b ≤ 5
So B could be 5, 4, 3, 2 , 1, If B=4, b>a, but if B=3, b<a ....Insufficient..

Ans: 'A'.