Problem of The day 06.08.09

1. Four digits of the number 29138576 are omitted so that the result is as large as possible. The largest omitted digit is (A) 9 (B) 8 (C) 7 (D) 6 (E) 5

Problem of the Day 30.07.09

Find the sum of the digits of the least natural number N, such that the sum of the cubes of the four smallest distinct divisors of N is 2N?

1)  9                                2) 8                             3) 7                    4) 6                      5) 10

Bonus QUestion 28.07.09

Suppose K be the number of integers n such that (2^n+1)/n^2 is also an integer.
Then K is
a) 0               b) 1               c) 2              d) 3              e) none of these

Problem of the day 28.07.09

if a<b and 12²+4²+5²+3²=a²+b² the find (a+b)?

Problem of the day 27.07.09

Find the number of quadratic polynomials ax² + bx + c such that:

a) a, b, c are distinct.

b) a, b, c ε {1, 2, 3, ...2008}

c) x + 1 divides ax² + bx + c
a) 2013018            b) 2013021            c) 2014024             d) 2018040       e) none of these

Bonus Question 16.07.09

Find the number of solutions in distinct positive  integers of x^4+y^4=z^4

A) 0                 B) 1                  C) 2                         D) 3                E) More than 3

Problem of the day 16.7.09

What is the sum of the digits of a two digit number which is 32 less than the square of the product of its digits?

A. 12                   B. 11                 C. 10 .                     D. 9                           E.      8

Problem of the day 14.7.09

Given that 1025/1024=1.0009765625, find the sum of the digits of 5¹⁰?



(a)  36       (b) 40    (c) 50   (d) 102   (e) 41

Problems 8.07.09

I could not post due to some engagements. Here are a bunch of problems to compensate :)

Question 1)

A + B + C + D = D + E + F + G = G + H + I = 17 where each letter represent a number from 1 to 9. Find out number of ordered pairs (D,G) if letter A = 4.
a) 0                       b) 1                 c)2                        d) 3                 e) none of these

Question 2)

The sequence 1, 3, 4, 9, 10, 12..... includes all numbers that are a sum of one or more distinct powers of 3. Then the 50th term of the sequence is
a. 252                    b. 283                     c. 327                      d. 360                  e) none of these

Question 3)


Given that g(h(x)) = 2x² + 3x and h(g(x)) = x² + 4x − 4 for all
real x. WHich of the following could be the value of g(-4)?
a)1                     b) -1                          c) 2                 d) -2                   e) -3

Question 4)


If a, x, b and y are real numbers and ax+by = 4 and ax² +by² = 2 and
ax³ + by³= −3 then find (2x − 1)(2y − 1)
a)4                      b) 3                    c) 5                 d) -3          e) cannot be determined.

Question 5)


K1,K2,K3...K30 are thirty toffees. A child places these toffees on a circle, such that there are exactly n ( n is a positive integer) toffees placed between Ki and Ki+1 and no two toffees overlap each other. Find n
a)4                        b) 5                     c) 9                 d) 12                       e) 13

Question 6)
For the n found in previous  question, which of the two toffees are adjacently
placed on the circle? ( All other conditions remaining same)
a) K11 and K13                    b) K6 and K23                   c) K2 and K10              d) K11 and K18
e) K20 and K28

Problem Of The Day 04.07.2009

Let aabb be a 4-digit number (a≠0). How many such numbers are perfect squares?

A) 0   B) 1   C)  2   D) 3  E) 4

Problem of the day 1.07.09

300! is divisible by (24!)^n. what is the max. possible integral value of n?

Problem of The Day (26.6.09)

Let S be the set of five-digit numbers formed by the digits 1, 2, 3, 4 and 5,
using each digit exactly once such that exactly two odd positions are occupied
by odd digits. What is the sum of the digits in the rightmost position
of the numbers in S?
a. 228 b. 216 c. 294 d. 192 e. None of these

Problem Of The Week 50

Find the number of unordered triplets (x,y,z) of positive integers such that x³+y³+z³=2008

1) 0

2) 1

3) 2

4) 3

5) None of these

Problem Of The Week 44

FInd the number of pairs (x,y) of integers 0<x<y such that sqrt(x)+sqrt(y)=sqrt(1984)

Problem Of The Week 41

Let s(p) be the sum of digits of a prime p. If p-s(p) is also a prime, then we call the prime a primal, how many primals below 100 are there ?

Problem Of The Week 40

When the mean, median and mode of the list 10,2,4,2,5,2,and x are arranged in increasing order, they form a non-constant arithmetic progression. FInd the sum of all such real x?

A)   3    B)  6  C) 9  D) 17   E) 20




Source : AMC 12

Problem Of The Week 39

A set of 2009 numbers from (1-2009) is written on the board. You are allowed to replace any two of these numbers by a new number which is either the sum or the absolute difference of these numbers, after 2008 such operations, Which of the following cannot be the last number left on the board?

A) 1  B) 3      C)  4     D) 5)    E) Cannot be determined

Problem Of The Week 38

My grandson, my son, and i share the same bday, this year all 3 of our ages have become prime numbers. i remarked to my son that For the last 17 years prior to this year, whenever your age was a prime number, so was mine and vice versa. "yes" he replied and said that 17 years from now, i will say to my son, for that last 18 years prior to this year, whenever your age was a prime number so was mine. How old are we?

Problem Of The Week 35

How many 3-d igit numbers are such that one of the digits is the average of the other two?

(A)   96   (B) 112   (C) 120   (D) 104   (E) 256

Problem Of The Week 33

The sum of base-10 logarithms of divisors of 10^n is 792. what is n?

(A) 11  (B) 12  (C) 10  (D) 13 (E) 14