Problem of the Day 12 Oct 2011

How many factors of  have last digit 2?

Problem of the Day 10 Oct 2011

Ten identical boxes of dimensions  are stacked flat on top of each other, with the orientation of each box being independent and random. If  is the probability that the height of the stack is  and , find . All units are in feet.

Problem of the Day 9th Oct 2011

In an increasing Arithmetic Progression, the product of the 5th term and the 6th term is 300. When
the 9th term of this A.P. is divided by the 5th term, the quotient is 5 and the remainder is 4. What is
the first term of the A.P.?
(a) 12                 (b) –40               (c) –16                     (d) –5

Problem of the day 8th oct 2011

Rohan is asked to figure out the marks scored by Sunil in three different subjects with the help of
certain clues. He is told that the product of the marks obtained by Sunil is 72 and the sum of the
marks obtained by Sunil is equal to the Rohan’s current age (in completed years). Rohan could not
answer the question with this information. When he was also told that Sunil got the highest marks
in Physics among the three subjects, he immediately answered the question correctly. What is the
sum of the marks scored by Sunil in the two subjects other than Physics?

(a) 6                  (b) 8                (c) 10               (d) Cannot be determined

Problem of the day 7th Oct 2011

Ten books are arranged in a row on a bookshelf. A student has to select three out of these ten books
in such a way that no two books selected by him must have been lying adjacently. In how many
ways can he make the selection?
(a) 56                                (b) 64                           (c) 72                    (d) None of these

Problem of the Day 6th Oct 2011

If xΔ(y +1) = yΔ(x +1), xΔ x = 1 and (x − y)Δ(x + y) = xΔ y, then what is the value of 1001Δ1?
(a) 1000                   (b) 100                    (c) 10                 (d) 1

Problem of the day 5th Oct 2011

The set S contains nine numbers. The mean of the numbers in S is 202. The mean of the five smallest of the numbers in S is 100. The mean of the five largest numbers in S is 300. What is the median of the numbers in S?

Problem of the Day 4th Oct 2011

Find  and , where the variables are natural numbers:

Problem of the Day 3rd Oct 2011

How many ordered pairs of positive integers  satisfy the system



where  and  denote the greatest common divisor and least common multiple of  and , respectively?


(A)   0        (B) 1         (C)  2            (3) More than 2

Problem of The day 2nd Oct 2011

Let [x] and {x} respectively denote the integer and fractional part of of a real number x. If {n} + {3n}=1.4, find the sum of all possible values of 100{n}.

(A) 180           (B) 145                (C) 85      (d) 102

Problem of the day 1 oct 2011

In 3-dimensional space, there are 3 rays leaving point . Any pair of 2 rays make a 60 degree angle with each other in their respective planes. Points , , and  are situated on the rays (one per ray) such that , , and  are all integers, and . if  and  is odd, then determine the value of  if .






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Problem of the day 30 Sept 2011

What is the largest number in the sequence ?




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Problem of the Day 29 Sept 2011

Let a, b, c be three distinct odd natural numbers. Which of the following can be the sum of the squares of a, b and c?

(a) 3333                            (b) 5555                                (c) 9999                        (d) 7777

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Problem of the Day 28 Sept 2011

A good approximation of π is 3.14. Find the least positive integer d such that if the area of a circle with

diameter d is calculated using the approximation 3.14, the error will exceed 1.

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Problem of the Day 27 Sept 2011

The diagram below shows some small squares each with area 3 enclosed inside a larger square. Squares that touch each other do so with the corner of one square coinciding with the midpoint of a side of the other square. Find integer n such that the area of the shaded region inside the larger square but outside the smaller squares is √n

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Problem of the Day 25 Sept 2011

Let P be the set of all the vertices of a regular polygon of 25 sides with its center at C. How many triangles have vertices in P and contain the point C in the interior of the triangles?


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Problem of the Day 24 Sept 2011

In triangles ABC and DEF, DE=4AB, EF=4BC, FD=4CA The area of triangle DEF is 360 units more than the area of triangle ABC. Compute the area of triangle ABC



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Problem of the Day 23 Sept 2011

Darryl has a six-sided die with faces 1; 2; 3; 4; 5; 6. He knows the die is weighted so that one face
comes up with probability 1/2 and the other five faces have equal probability of coming up. He
unfortunately does not know which side is weighted, but he knows each face is equally likely
to be the weighted one.

He rolls the die 5 times and gets a 1; 2; 3; 4 and 5 in some unspecified order. Compute the probability that his next roll is a 6.



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Problem of the Day 22 Sept 2011

Susan plays a game in which she rolls two fair standard six-sided dice with sides labeled one through six. She wins if the number on one of the dice is three times the number on the other die. If Susan plays this game three times, compute the probability that she wins at least once.

Problem of the Week 21 Sept 2011

The leftmost digit of an integer of length 2000 digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either a or b. What is the value of a+b?