Mahabir Singh Solutions for Chapter: SOF International Mathematics Olympiad, Exercise 1: LOGICAL REASONING

Starting from a point $P$, Aryan walked $40$ metres  towards North. He turned right and walked $60$ metres. He then turned right and walked $40$ metres. At last he turned right and walked $40$ metres and reached a point $Q$. How far and in which direction is he now from the starting point?

Which of the following Venn diagrams best represents the relationship amongst, 'Shirts, Trousers and Skirts'?

A family consists of five members $\mathrm{B}, \mathrm{C}, \mathrm{E},$ $\mathrm{F}$ and $G. C$ is the son of $G$ but $G$ is not the mother of $C. E$ and $G$ are married couple. $B$ is the brother of $G$. $F$ is the daughter of $E$. Who is the brother-in-law of $E$?

How many squares are there in the given figure?

Choose a box that is similar to the box formed when the given sheet of paper is folded to form a box.

Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations on numbers progress from left to right.

Rules:

(i) If a $2$-digit even number is followed by another even number, then the first one is to be divided by the second one.
(ii) If an even number is followed by a prime number, then the two are to be multiplied.
(iii) If an odd number is followed by another odd number, then the two are to be added.
(iv) If a $3$ -digit number is followed by a $2$-digit number which is a perfect square, then the second number is to be subtracted from the first number.
(v) If a $3$-digit number is followed by another $3$-digit number which is not a perfect square, then the first number is to be divided by the second one.

$$\begin{gathered} 150 81 43 \\ 336 m 39 \end{gathered}$$

If $m$ is the resultant of the first row, then what will be the resultant of the second row?

The question consists of a set of three figures $P, Q$ and $R$ showing a sequence of folding a piece of paper. Fig. $\left(R\right)$ shows the manner in which the folded paper has been cut. Select the figure from the options which would most closely resembles the unfolded form of Fig. $\left(R\right)$.

Select a figure from the options which will replace the '?' to complete the pattern in the given figure.