Math starts from the simple and goes a long way.
In this post, we will start from “pairing up” like 1 + 4 = 2 + 3 = 5 but there is a long way to go so that we learn the sets, working on the sets, pairing-up, observing and developing conditions for a perfect pair-up.
Pairing up for a Perfect Match
Questions chosen from previous Gauss contests
Gauss contests are organized by the Centre of Education for
Math and Computing, University of Waterloo
Problem 1
In the addition shown, P and Q each represent single digits, and the sum is 1PP7. What is P + Q?
(A) 9 (B) 12 (C) 14 (D) 15 (E) 13
Problem 2
In the right-angled triangle PQR, we have that PQ = QR. The three segments QS, TU and VW are perpendicular to PR, and the segments ST and UV are perpendicular to QR, as shown. What fraction of triangle PQR is shaded?
(A) 3 ⁄ 16 (B) 3 ⁄ 8 (C) 5 ⁄ 16 (D) 5 ⁄ 32 (E) 7 ⁄ 32
A box contains a total of 400 tickets that come in five colors: blue, green, red, yellow, and orange. The ratio of blue to green to red tickets is 1 : 2 : 4. The ratio of green to yellow to orange tickets is 1 : 3 : 6. What is the smallest number of tickets that must be drawn to ensure that at least 50 tickets of the same colour have been selected?
(A) 50 (B) 246 (C) 148 (D) 196 (E) 115
Problem 4
Greg, Charlize, and Azarah run at different but constant speeds. Each pair ran a race on a track that measured 100 m from start to finish. In the first race, when Azarah crossed the finish line, Charlize was 20 m behind. In the second race, when Charlize crossed the finish line, Greg was 10 m behind. In the third race, when Azarah crossed the finish line, how many metres was Greg behind?
(A) 20 (B) 25 (C) 28 (D) 32 (E) 40
Problem 5
In right-angled, isosceles triangle FGH, segment FH = √̅8. Arc FH is part of the circumference of a circle with centre G and radius GH. The area of the shaded region is
(A) π – 2; (B) 4 π – 2 (C) 4 π – (1 ⁄ 2) √̅8 ; (D) 4 π – 4 (E) π – √̅8
