7/28/2019 Pragya Problems

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Problem 1 Problem 1 Problem 1 Problem 1 Five numbers are arranged in increasing order. As they get larger Five numbers are arranged in increasing order. As they get larger Five numbers are arranged in increasing order. As they get larger Five numbers are arranged in increasing order. As they get larger the difference between adjacent numbers doubles. The average of  the difference between adjacent numbers doubles. The average of  the difference between adjacent numbers doubles. The average of  the difference between adjacent numbers doubles. The average of  the five numbers is 11 more than the middle number. The s the five numbers is 11 more than the middle number. The s the five numbers is 11 more than the middle number. The s the five numbers is 11 more than the middle number. The sum of  um of  um of  um of  the second and the fourth numbers the second and the fourth numbers the second and the fourth numbers the second and the fourth numbers is equal to the largest number.is equal to the largest number.is equal to the largest number.is equal to the largest number.What is the largest number? What is the largest number? What is the largest number? What is the largest number?  

Problem 2 Problem 2 Problem 2 Problem 2 The houses and trees in the diagram are all in a straight line. InThe houses and trees in the diagram are all in a straight line. InThe houses and trees in the diagram are all in a straight line. InThe houses and trees in the diagram are all in a straight line. Ineach of the six houses lives a child. At which tree should theeach of the six houses lives a child. At which tree should theeach of the six houses lives a child. At which tree should theeach of the six houses lives a child. At which tree should thechildren meetchildren meetchildren meetchildren meet so that the sum of the distances they walk isso that the sum of the distances they walk isso that the sum of the distances they walk isso that the sum of the distances they walk isminimum?minimum?minimum?minimum?

Problem 3 Problem 3 Problem 3 Problem 3 If AB = BC = CD = DE = EF and angle AEF = 75°, what is theIf AB = BC = CD = DE = EF and angle AEF = 75°, what is theIf AB = BC = CD = DE = EF and angle AEF = 75°, what is theIf AB = BC = CD = DE = EF and angle AEF = 75°, what is thesize of angle EAF?size of angle EAF?size of angle EAF?size of angle EAF?

A B D F

C

E

Diagram not to scale

 

PROBLEMS OF THEPROBLEMS OF THEPROBLEMS OF THEPROBLEMS OF THE WEEK  WEEK  WEEK  WEEK 

7/28/2019 Pragya Problems

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Problem 4 Problem 4 Problem 4 Problem 4 Two identical squareTwo identical squareTwo identical squareTwo identical square----shaped holes have been drilled passing all theshaped holes have been drilled passing all theshaped holes have been drilled passing all theshaped holes have been drilled passing all theway through a solid cube, as shown. The holes are in the centres of way through a solid cube, as shown. The holes are in the centres of way through a solid cube, as shown. The holes are in the centres of way through a solid cube, as shown. The holes are in the centres of  the face the face the face the faces of the cube. What is the total surface area of thes of the cube. What is the total surface area of thes of the cube. What is the total surface area of thes of the cube. What is the total surface area of theresulting solid?resulting solid?resulting solid?resulting solid?

Problem 5 Problem 5 Problem 5 Problem 5 

Five men are crossing a rickety old bridge in the dark, strongFive men are crossing a rickety old bridge in the dark, strongFive men are crossing a rickety old bridge in the dark, strongFive men are crossing a rickety old bridge in the dark, strongenough toenough toenough toenough to hold only two men. They have only one flashlight. Eachhold only two men. They have only one flashlight. Eachhold only two men. They have only one flashlight. Eachhold only two men. They have only one flashlight. Eachman travels at a different speed. Anuj takes one minute to cross,man travels at a different speed. Anuj takes one minute to cross,man travels at a different speed. Anuj takes one minute to cross,man travels at a different speed. Anuj takes one minute to cross,Mohan takes two, Chetan takes 5, David takes 7, and EshanMohan takes two, Chetan takes 5, David takes 7, and EshanMohan takes two, Chetan takes 5, David takes 7, and EshanMohan takes two, Chetan takes 5, David takes 7, and Eshan

 takes 10. Traveling together, two men can only go as fast as the takes 10. Traveling together, two men can only go as fast as the takes 10. Traveling together, two men can only go as fast as the takes 10. Traveling together, two men can only go as fast as theslower man.slower man.slower man.slower man. What is the shortest amount of time all five men canWhat is the shortest amount of time all five men canWhat is the shortest amount of time all five men canWhat is the shortest amount of time all five men can take to reach the other side of the bridge? take to reach the other side of the bridge? take to reach the other side of the bridge? take to reach the other side of the bridge?