## QBM029

Q1. If one and only one edge of a tetrahedron is greater than 1, then its volume is a. ≤ 1/8 b. ≤ 1/16 c.≥ 1/8 d.≥ 1/16 Q2. Find all integers n such that S(n) = S(2n) = ... = S(n*n), where S is the sum of the base-10 digits. Q3. A fly sits on the corner of a wooden cube. What is the shortest distance it must travel in order to reach the opposite corner of the cube? Q4. Find the integer N such that N and N2 together contain all 10 digits from 0 through 9 twice each, and also have the largest number of double digits (such as 11 or 66). Q5. If three integers x, y, and z satisfies the Pythagorean relation (x+y)2 + (x+z)2 = (y+z)2 Then which of the following is definitely true? a. there is no such set of odd positive integers b. there is only set of odd positive integers which satisfies the above condition. c. there are two sets of odd positive integers which satisfies the above condition. d. there are infinity sets of odd positive integers which satisfies the above condition. Q6. What is the smallest number divisible by three that is the sum of four distinct primes? (a)18 (b)21 (c)24 (d)27 (e) None of the above Q7. Using a rectangular area model, model the process and solution for finding the sum of 2/3 and 1/5. The answer must be clearly obtained from your model. Q8. If the diagonal and the area of a rectangle are 25 m and 168 m2, what is the length of the rectangle? A.17 m B.31m C.12m D.24 m Q9. 5^3 is 125, with 3 digits. 8^5 is 32768 with 5 digits. Find the largest N-digit number which is an N-th power. Q10. The sum of 5 numbers in AP is 75; and the product of the greatest and the lower is 161. What is the "greatest" number? a)7 (b)23 (c)36 (d)39 Q11.S and L are the smallest and the largest n-digit natural numbers respectively. a)9 b)10 c)9 and 10 d)none of these Q12. In a sport contest, there were m medals awarded on n successive days ( n >1). On the first day, one medal and 1/7 of the remaining m -1 medals were awarded. On the second day, two medals and 1/7 of the now remaining medals were awarded; and so on. On the n-th day and last day, the remaining n medals are awarded. How many days did the contest last, and how many medals were awarded altogether? Q13. Compute x if x = 1/1*2 + 1/2*3 + 1/3*4 + ....+ 1/(n-1)*n + 1/n*(n+1) a)n/(n-1) b) 2n/(n+1) c) n/(n+1) d) None of these Q14. SQRT(A) denotes the positive square root of (A) and MOD(A) denotes the largest integer less than A. Then: (MOD{SQRT[MOD(65)]} + 2] is equal to: Q15.If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1 : S4 = 1 : 10 then the ratio of first term to fourth term is: (A)1:3 (B)2:3 (C)1:4 (D)1:5 END