Learn Mathematical Reasoning with Free Lessons & Tips

Three small snails are each at a vertex of an equilateral triangle of side 60 cm. The first sets out towards the second, the second towards the third and the third towards the first, with a uniform speed of 5 cm/min. During their motion, each of them always heads towards its respective target snail. How much time has passed, and what distance do the snails cover before they meet?

Answer: Resolve the velocity of snail 2 into a component pointing towards snail 1 and a component perpendicular to this. These two snails approach each other at a relative speed of v+V/2=3v/2=7.5cm/min, and therefore they meet after a time given by 60/7.5=8min.

They must all meet after this time and as they actually travel at a speed of 5 cm/min, they each cover a distance of 40 cm before doing so.

Syllogism Tricks 

Syllogism is a major part of reasoning in various competetive exams. It's simple but brain teaser too. Most of the students find it difficult to learn the concepts of venn diagram and apply accurately to questions.

I would try to help you all with some useful concepts and tricks that you may apply in competitive exams.

All of these tricks will surely help you in Banking, Railways, SSC, NDA, MBA and many other exams.

All + All = All

All + No = No

All + Some = No conclusion 

Some + All = Some

Some + No = Some not

Some + Some = No conclusion 

No + All = Some not (Reversed) 

No + Some = Some not (Reversed )

No + No = No conclusion 

Note:

Some not/ Some Not Reversed + Anything = No conclusion 

To solve syllogism questions you may take help of two types of cancellation :

• Cross Cancellation
• Vertical Cancellation 

Cross Cancellation

STATEMENTS

1.  All pens are Erasers
2. All Erasers are Books
3. No book is Table

CONCLUSIONS

1. No Eraser is table 

All + No = No

All Erasers are books

No book is a Table

If we will cross cancel books, we get

CONCLUSION:    No Eraser is table .

Hence conclusion follows

Vertical Cancellation 

STATEMENTS 

1. Some apples are fruits
2. All bananas are fruits

CONCLUSION

1. No banana is apple

All + Some = No conclusion 

Some apples are fruits

All bananas are fruits 

Here we can cancel fruits vertically but the direction of adding will get Reversed , i.e. Conclusion will be ALL + Some = No  conclusion 

Hence, Conclusion 1 doesn't follow.

There are more key points regarding Syllogism which I will post in next lesson.