For prime numbers p and q, p + q = 102 and p > q. What is the least possible value of p − q

1. 2

2. 4

3. 8

4. 12

5. 16

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Amit has a total of n balls of which r, g, band w are red, green, blue and white respectively. His friend Sumit asks him about the balls he says,I have so many balls such that if I select four balls, probability of selecting four red balls is same as the probability of one ball of each kind and is same as probability of selecting one white and three red balls and is same as the probability of selecting two red, one white and one blue ball. Sumit asks him whether this is the minimum of such set of balls. Amit says yes. He tells him the value of r. What is it

1. 9

2. 10

3. 11

4. 12

5. 13

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Amit asks the total number of balls, sumit answers correctly what is his answer

1. 17

2. 19

3. 21

4. 23

5. 25

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Given that x2 + y2 = 14x + 6y + 6, what is the largest possible value that 3x + 4y can have

1. 72

2. 73

3. 74

4. 75

5. 76

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The director of a marching band wishes to place the members into a formation that includes all of them and has no unfilled positions. If they are arranged in a square formation, there are 5 members left over. The director realizes that if he arranges the group in a formation with 7 more rows than columns, there are no members left over. Find the maximum number of members this band can have

1. 172

2. 273

3. 374

4. 294

5. 476

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Correct Answer :

294

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Let n be a positive integer such that 1335 + 1105 + 845 + 275 = n5.Find n

1. 134

2. 144

3. 154

4. 164

5. 174

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Correct Answer :

144

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The perimeter of a right triangle is 60. The height to the hypotenuse is 12 what is the area

1. 75

2. 144

3. 150

4. 300

5. none of these

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Correct Answer :

150

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PQRST is a pentagon inscribed in a circle. U is a point outside the circle such that UP and UQ are tangents to the circle touching it at P and Q respectively. If ÐQST =:80° and ÐPQT = 10°, then ÐPUQ =

1. 30°

2. 40°

3. 50°

4. 60

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Correct Answer :

40°

Explanation :
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A ray is defined as a directed line segment (i.e., a line segment with a' specified direction), while a reversal is an operation defined as reversi ng the direction of a ray. If there are 100 I rays in a plane and all the rays were reversed after a total of R reversals were performed, which of the following is a possible value of R

1. 2002

2. 1008

3. 1024

4. 1007

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Correct Answer :

1007

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A, working alone, takes m times as much time as B and C, working together, to complete a piece of work. B, working alone, takes m times as much time as A and C, working together, to complete the same piece of work and C, working alone, takes m times as much time as A and B, working together. to complete the same piece of work. Find m.

1. 2

2. 3

3. 4

4. 5

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