Question

A is greater than C, C is greater than B then which is the smallest?
(a)A
(b)B
(c)C
(d)None

Answer 1

Hint: We have given the relation between A and C that A is greater than C. Also, we have given the relation between C and B that C is greater than B and we are asked to find who is the smallest. Now, the statement A is greater than C means that C is smaller than A. Then the statement C is greater than B means that B is smaller than C. Now, using these smaller inferences of the given statements we can find out from A, B, and C which is smaller.

Complete step-by-step solution:
We have given that A is greater than C meaning C is smaller than A. Now, we are going to write this statement in mathematical form:
$A > C or C < A$
In another statement, it is written that C is greater than B meaning B is smaller than C. Now, we are going to write this statement in mathematical form:
$C > B or B < C$
Combining the above two statements’ mathematical form we get,
$C < A$
$B < C$
In the above inequalities, you can see that C is smaller than A and C is greater than B so we can write B is lesser than C followed by C is lesser than A.
Writing the above two statements into one line we get,
$B < C < A$
From the above expression, you can see that B is the smallest among C and A.
Hence, the smallest among A, B, and C is “B”. Hence, the correct option is (c).

Note: In the above solution, you might mess around with inequality signs. So, to minimize such mistakes, always remember that in the inequality sign “<”, the number who is facing this inequality’s open mouth side will be a greater number and the number which is not facing its open mouth side is a smaller number. In this way, you can remember the trick.