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 34

Rakesh has the habit of always pouring his tea from the cup into the saucer before drinking it. He fills both the cup and the saucer to only 90% of their capacity (subject to the availability of tea). He also does not drink any tea which is below the 15% mark in the saucer. If he has to pour the tea from the cup into the saucer at least three times before emptying the cup (each time drinking from the saucer till it reaches the minimum level), then what is the maximum possible ratio of the volume of the cup to that of the saucer respectively? (1) 3 : 1 (2) 9 : 4 (3) 5 : 2 (4) 8 : 3  (5) None of these.

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

Problem Of The Week 32

Four Equilateral triangles are formed taking one of their sides as the sides of the square, the third vertices of equilateral triangles being inside the square. The ratio of the area of fig formed by the third vertices of the triangles to that of the square is nearly

Problem Of The Week 31

A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers chose spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires 2 adjacent spaces. What is the probability that she is able to park?

Problem Of The Week 30

Let b be an odd square and n be any natural number. Then b=n^3+2n^2. Find b?