AbeNeedsAnswers wrote:Is there a secret to these question types?
If 0 < a < b < c, which of the following statements must be true?
I. 2a > b + c
II. c - a > b - a
III. c/a < b/a
A) I only
B) II only
C) III only
D) I and II
E) II and III
B
There is no secret. BTG is a forum in which experts will introduce you to all the possible approaches to any question.
This one is a Must be True kind of question. In Must be True kind of questions, under all the circumstances, a statement under consideration must be true.
Let's take this one.
We have 0 < a < b < c. What do you make out of this information?
1. a, b and c all are positive numbers.
2. a, b and c are all not necessarily positive integers. One or none of them can be integers.
3. All can be less than 1. For example, a = 1/4; b = 1/3; c = 1/2.
Keeping these in mind, let's take the three statements.
I. 2a > b + c:
=> 2*SMALLEST number
> A SMALLER number + A SMALL number
This is not possible as the sum of a SMALLER number & a SMALL number would always be greater than twice the SMALLEST number.
For example, say a = 1, b = 2, and c = 3.
2*1 < 2 + 3 => 2 < 5. This statement is false.
II. c - a > b - a:
=> c > b; cancelling out '-a' from both the sides. This is a must be a true statement. it is given that 0 < a <
b < c
III. c/a < b/a:
=> c < b; cancelling 'a' from both the sides. Since 'a' is positive, we can cancel it without reversing the sign of inequality. Had it 'a' been negative, we would have to reverse the sign on the inequality. Had it been not known whether 'a' is positive or negative, we cannot cancel 'a.'
As seen in Statement II, this is false. We know that b < c.
The correct answer:
B
Hope this helps!
-Jay
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