2014 WMI Competition Grade 5 Part 1 Logical Reasoning Test

Size: px

Start display at page:

Download "2014 WMI Competition Grade 5 Part 1 Logical Reasoning Test"

Daniella Randall
5 years ago
Views:

014 WMI Competition Grade 5 Part 1 Logical Reasoning Test Five Points Each. Total 150 Points. Choose the best answer from (A) (D). 1. Compute (13579+35791+57913+79135+91357) 5.

014 10000 = A A, find A. (A) 014 (B) 0140 (C) 01400 (D) 10070 4. Consider a solid figure that is formed by 6 identical cubes of edge cm stacked together as shown in the figure on the right.

1 014 WMI Competition Grade 5 Part 1 Logical Reasoning Test Five Points Each. Total 150 Points. Choose the best answer from (A) (D). 1. Compute ( ) 5. (A) (B) (C) (D) If the product of three consecutive positive integers is 940, find the sum of these three numbers. (A) 60 (B) 63 (C) 69 (D) If = A A, find A. (A) 014 (B) 0140 (C) (D) Consider a solid figure that is formed by 6 identical cubes of edge cm stacked together as shown in the figure on the right. Find the total surface area (in cm 3 ) of this solid. (A) 96 (B) 104 (C) 4 (D) 6 5. As shown in the figure on the right, ABC is an equilateral triangle and DEFGH is a regular pentagon. If EDA is 40, find HGC in degrees. (A) 16 (B) 8 (C) 18 (D) Adam spent 6 hours and 6 minutes sdving a very difficult math problem, but Bill spent only 6 minutes and 6 seconds to solve it. How many times greater is Adam s time than Bill s time? (A) 100 (B) 66 (C) 60 (D) Compute (A) 0 (B) 1 (C) 014 (D) 015

2 8. A school is taking a survey on near sightedness of the four classes of their 5 th grade students with the results listed on the table below. What is the percentage of 5 th grade students who are near sighted? (Round your answer to nearest 1 percent) Class A Class B Class C Class D Near sighted Not Near sighted (A) 4% (B) 50% (C) 58% (D) 7% 9. If two decimal numbers with 3 decimal places are 1.85 and 3.70 after rounding, what is the smallest possible sum of these two numbers? (A) (B) (C) (D) Find the surface area of the hollowed solid shown on the right. (The figure is shown in perspective, but the solid is rectangular.) (A) 180 (B) 848 (C) 1344 (D) The figure on the right shows a parallelogram. Suppose its base is 10 cm, height is 6 cm, E is the intersection point of its two diagonals, and F is some point on BC. Find the area of quadrilateral AFDE in cm. (A) 60 (B) 30 (C) 15 (D) Insufficient data 1. Mike, Noah, and Ben are in a track competition and start running from the starting point at the same time. After a few seconds, Mike is out in front and Ben is behind the other two. The judge suddenly asks them to turn around. If their speeds have not changed, which of them will get back to the starting point first? (A) Mike (B) Noah (C) Ben (D) At the same time 13. Which one of the following expressions is not correct? (A) P (M+N)=P M+P N (B) (P Q) R=(R P) Q (C) (P+Q) R=P R+Q R (D) P R+Q R=(P+Q) R 14. There is a case of eggs. If 8 of them were sold, the remaining number of eggs is divisible by 8. If 9 of them were sold, the remaining number of eggs is divisible by 9. If 10 of them were sold, the remaining number of eggs is divisible by 10. What is the smallest capacity such a case could have? (A) 70 (B) 630 (C) 360 (D) 70

3 15. Susan had 100 chocolates. She ate 1 10 of them the 1st day, then ate 1 9 of the remainder during the nd day, 1 8 of the new remainder during the 3rd day,, and 1 of the remainder during the 9th day. After 9 days, how many chocolates are left? (A) 0 (B) 5 (C) 10 (D) Suppose a rectangular container m long, 1.5 m wide, and 0.8 m high is filled with 0.4 m 3 of water. If a metal rod of m long, 0.5 m wide, and 0.4 m high is placed in the bottom of this container, how much more water (in liters) must be added to fill the container? (1 m 3 = 1000 liters) (A) (B).8 (C) 000 (D) Three identical isosceles triangles are placed side by side as shown in the figure on the right. If the base angle of each triangle is 80, how many such triangles are needed altogether so that the last triangle will be tightly packed next to the first triangle if we continue packing the triangles the same way? (A) 6 (B) 1 (C) 18 (D) Anna s math teacher gave her some math problems to do during her school s winter break. If Anna does 30 problems in a day, she will complete the assignment 4 days behind schedule. However, if she can do 60 problems in a day, she can complete the assignment days ahead of schedule. How many problems does Anna have to do per day in order to finish exactly on schedule? (A) 36 (B) 40 (C) 45 (D) If =60, what is the number for? (A) (B) 6 (C) 41 (D) A subway train can go from Station A to Station B in 100 minutes. If its speed is increased by 5%, how many fewer minutes would it take to go from A to B? (A) 0 (B) 5 (C) 75 (D) Suppose there are 3 positive numbers A, B, and C such that 1 of A is equal to 3 of B and 3 4 of B is 4 5 of C. Which of these three numbers is the smallest? (A) C (B) B (C) A (D) All three are the same. A rectangular box that is 4 cm long and 15 cm wide holds water 0 cm deep. If two identical iron balls are placed inside this water container totally submerged, then the water would be 4 cm deep. Find the volume of each iron ball in cm 3. (A) 70 (B) 1440 (C) 3600 (D) 430

3. The figure at right represents a cube cut along its edges and spread flat. If it is refolded back into the form of a cube, which of the following pairs of points will touch?

Cathy writes 5 numbers 1, 3, 5, 7, and 9 on five pieces of paper and she writes the numbers, 4, 6, 8, and 10 respectively on the opposite sides of these 5 papers.

4 3. The figure at right represents a cube cut along its edges and spread flat. If it is refolded back into the form of a cube, which of the following pairs of points will touch? (A) L and A (C) J and C (B) A and I (D) B and F 4. Cathy writes 5 numbers 1, 3, 5, 7, and 9 on five pieces of paper and she writes the numbers, 4, 6, 8, and 10 respectively on the opposite sides of these 5 papers. If these papers are randomly placed, three of the numbers shown on the face up sides are odd and two of them are even. What is the sum of these 5 numbers? (A) 7 (B) 31 (C) 35 (D) If Sam had bought between 00 and 500 candies and he is sharing them evenly with 0 people. If number of candies each person can get is the same as the remaining number of candies. What is the total number of candies originally? (A) 480 (B) 41 (C) 399 (D) 5 6. A large watermelon originally weighed 50 kg with 90% of the weight as water content. Later, some of the water evaporated such that the water content now is only 80% of the current total weight. How much does this watermelon weigh (in kg) now? (A) 45 (B) 40 (C) 5 (D) 0 7. Two rectangles ABCD and EFGH overlapped as shown in the figure on the right. The area of the overlapped portion is of the area of 15 rectangle ABCD and 1 of the area of rectangle EFGH. How many 3 times is the area of the overlapped portion (the white region) as the non overlapped portion (the shaded region)? (A) 1 5 (B) 17 (C) 19 (D) Suppose A and B are two cylindrical containers on a leveled table. The base of A has an area of 80 cm and the base of B has an area of 100 cm with A totally filled with water and B empty. Pour all the water in A into B and the B s water level is 8 cm lower than the height of A. Find the volume of A in cm 3. (A) 180 (B) 560 (C) 300 (D) 4000

5 9. The figure on the right is a figure that is symmetrical along the dotted line AF. If A = 10 and B = 95, which one of the following statements is false? (A) BAF = 60 (B) CF = DF (C) C = 115 (D) AB = BC 30. A magician has 7 red and 7 black cards. After these 14 cards are shuffled fairly, they are placed face down into rows with a different number of cards in each row. The magician predicts the number of black cards in the long row is more than the number of red cards in the short row. The cards are then turned over and it revealed that the prediction is true. How many cards are in the short row and how many in the long row? (A) 6, 8 (B) 5, 9 (C) 4, 10 (D) 3, 11

Winter Quarter Competition

Winter Quarter Competition LA Math Circle (Advanced) March 13, 2016 Problem 1 Jeff rotates spinners P, Q, and R and adds the resulting numbers. What is the probability that his sum is an odd number? Problem