IMO Maths Olympiad Class 10 Chapter 16 Logical Reasoning MCQs with Answers

Answer: (b) 7

Explanation:
1. Letters of the first half (A to M) in the sequence: J, L, B, I, G, K, C, D, F, A.
2. Symbols or numbers next to them: @ (after J), $ (before L), δ (before G), 9 (before K), 3 (after D), 5 (before F), 7 (before A).
3. The other neighbours of these letters are letters (P, B, V, W, C, Y, R), so the count is 7.

Teacher's Note:
1. Mark the first-half letters, then check both neighbours of each.
2. Do not count letters, and count each symbol only once.

Answer: (d)

Explanation:
1. The water image is the reflection in a horizontal line below the figure, so the figure turns upside down but stays left-right the same.
2. In Fig. (X) the V-shaped notch is at the bottom left and the curved corner at the top right; in the water image the notch must be at the top left and the curved corner at the bottom right.
3. Only option (d) has the notch at the top left with the circle and the wavy curve below it: the answer is (d).

Teacher's Note:
1. Water image: top and bottom swap, left and right stay.
2. Follow one distinctive part (here the notch) to eliminate options.

Answer: (c)

Explanation:
1. One line is added in each figure: top line, then top and right lines, then three inner sides, then the full square, then the square plus an outer top line.
2. So the next figure has the square plus two outer lines, the top and the right, as in Figure 2.
3. The dots alternate between one and three; the single dot moves top, right, bottom, so the three-dot figures miss left, top and then right. Hence the sixth figure has dots at top, left and bottom, which matches (c).

Teacher's Note:
1. Study lines and dots separately.
2. Count how many parts are added at each step.

Answer: (c)

Explanation:
1. Look for the small curl with the vertical stem and the zigzag line of Fig. (X).
2. These appear together, with the same orientation and size, only in option (c).
3. In the other options the curls or lines are different or turned, so the answer is (c).

Teacher's Note:
1. Pick the most distinctive feature of Fig. (X) and search for it first.
2. The embedded figure must keep the same size and direction.

Answer: (c)

Explanation:
1. From (i) to (ii) the figure turns through 180° and its water image is joined to it along the horizontal line.
2. Turning (iii) through 180° puts the dot at the bottom, the line on top and the block on the left with its black part at the upper right.
3. Adding the water image above the line gives a left-pointing black triangle with dots at top and bottom on the right: (c).

Teacher's Note:
1. Find the transformation step by step: rotation first, then reflection.
2. Check the black part and the dots separately.

Answer: (b)

Explanation:
1. The pattern repeats after every quarter turn about the centre of the circle.
2. Turning the top-left part by 90° anticlockwise gives the missing bottom-left part, with the crossing bands and the small arc near the centre.
3. This matches option (b).

Teacher's Note:
1. Check the pattern in a quarter with rotation.
2. Compare bands, arcs and crossings, not just the outline.

Answer: (b)

Explanation:
1. Folding along the dotted line brings the right half onto the left half; the right half appears as a mirror image across the fold.
2. The right line with its circle at the top lands near the left edge as a line with a circle at the top, the left line with its circle stays at the bottom, and the circle on the fold stays on the edge.
3. This is option (b).

Teacher's Note:
1. Each point on the folded part moves to the same height, at the same distance on the other side of the fold.
2. Points on the fold line do not move.

Answer: (b)

Explanation:
1. With the mirror vertical, the image is the left-right reflection: the order reverses and every character is flipped sideways.
2. So 4Q2PR345Z appears as Z543RP2Q4 with each character reversed.
3. Option (b) is exactly this; (a) and (d) are turned upside down with the wrong letters, and (c) is unchanged. The answer is (b).

Teacher's Note:
1. Mirror image: reverse the order and flip each character sideways.
2. Upside-down text is a 180° turn, not a mirror image.

Answer: (b)

Explanation:
1. Unfold the paper step by step, reflecting the cuts in each fold line.
2. The small flat rectangle on the horizontal fold doubles in height into a square (left and right); the flat rectangle on the vertical fold doubles in width (top and bottom).
3. The quarter circle at the centre becomes a full circle, so the figure has a circle with squares at left and right and wide rectangles at top and bottom: (b).

Teacher's Note:
1. A cut on a fold line is doubled across that line.
2. A cut at the centre is repeated in all four quarters.

Answer: (a)

Explanation:
1. In Fig. (X), one dot is in the circle and the square only, one is in the square and the rectangle only, and one is in the square, the rectangle and the triangle together.
2. So the figure needs regions of exactly these three types.
3. Only option (a) has all three regions; (b) and (c) have no region common to square, rectangle and triangle only, and (d) has no triangle region inside the square, so the answer is (a).

Teacher's Note:
1. Name each dot by the set of shapes it lies in.
2. Then check that every option contains regions of those three types.