Arithmetic Reasoning Questions

• Relative ages (chain of differences): Determine how many years older C is than D. Relations: A is 3 years older than B and 3 years younger than C. B and D are twins (same age). Find C − D (years older). Choose the correct value.
• Heads and legs puzzle (systems with animals): Determine the count of peacocks. In a zoo there are deer and peacocks. Total heads = 80 (deer + peacocks). Total legs = 200 (deer have 4 legs; peacocks have 2 legs). Find the number of peacocks. Choose the correct value.
• Card distribution puzzle (simultaneous linear equations): Find the exact number of cards with C. Statements: If B gives A 3 cards, then B will have as many as A has now. If D takes 5 cards from B, D will have as many as E has now. A + C together equal twice E. B + D together equal A + C. Total cards with A, B, C, D, E is 150. Compute how many cards C has. Choose the correct value.
• People and horses (legs on the ground): Infer the number of horses from total legs counted. There are as many men as horses. Half of the owners (men) are mounted; the rest walk, leading their horses. Total legs on the ground counted = 70. Find how many horses there are. Choose the correct value.
• Finger-counting (back-and-forth on one hand): Determine the landing finger at a large count. Counting pattern on the left hand: thumb = 1, index = 2, middle = 3, ring = 4, little = 5; then reverse direction (ring = 6, middle = 7, index = 8), and continue similarly. The girl counts up to 1994 using this back-and-forth sequence. On which finger does she stop? Choose the correct finger.
• Mixed-category word puzzle (sparrows–pigeons–ducks): Compute the total birds from “all … but six” clues. A shooter says: “There were all sparrows but six, all pigeons but six, and all ducks but six in the bag.” Treat the birds as only three types: sparrows, pigeons, ducks. How many birds are there in total? Choose the correct number.
• Family ages at birth (multi-relation): Find the sister’s age when Rahul was born. At Rahul’s birth: Father was 32 years older than Rahul’s brother; Mother was 25 years older than Rahul’s sister. Given now (at birth context): Rahul’s brother is 6 years older than Rahul; Mother is 3 years younger than Father. How old was Rahul’s sister at Rahul’s birth? Choose the correct age.
• Minimum-count arrangement (ducks in line): Satisfy three positional descriptions simultaneously. Requirement: “Two ducks in front of a duck”, “two ducks behind a duck”, and “a duck between two ducks”. Find the smallest number of ducks that can satisfy all three statements at once. Choose the correct minimum.
• Knockout tournament (singles): Find the minimum matches to determine a winner among 30 players. Rules: One loss eliminates a player (single-elimination); no ties. How many matches are needed at minimum to produce a single champion? Choose the correct count.
• Arithmetic Word Problem — Remainders and the Chinese Remainder Idea After distributing sweets equally among 25 children, 8 sweets remain. If the number of children had been 28, then 22 sweets would have remained after equal distribution. Find the total number of sweets.
• Combinatorics — arranging 5 favorite books between two bookends: if you make a new arrangement every minute (one move per minute), how long to cycle through every possible ordering of the five books?
• Two banana bunches: the first has “one-quarter again as many” as the second, and the second has 3 fewer than the first. How many bananas are in the first bunch?
• Farm count — in a mixed group of cows and hens, the total legs are 14 more than twice the total heads. How many cows are there?
• Two-digit number puzzle — the digits sum to 11. Adding 27 reverses the digits. What is the original number?
• Handshake counting at a conference: if 10 people each shake hands with every other person exactly once, how many handshakes occur in total?
• Climbing monkey — climbs 30 ft at the start of each hour and then slips back 20 ft while resting. Starting at 8:00 a.m., when does it first reach a flag at 120 ft?
• Class attendance — 3/5 of the class are girls, rest boys. If 2/9 of girls and 1/4 of boys are absent, what fraction of the whole class is present?
• Captains and soldiers on a train — total people = 1200. For every 15 soldiers, there is 1 captain. How many captains are there?
• Clock chiming puzzle — if it takes 7 seconds to strike 7, how long will it take to strike 10?
• Cake pieces and weight — a cake is cut into two halves; one half is cut into equal small pieces of 20 g each. If she has 7 pieces total (including the uncut half), what was the weight of the original cake?