Odessa Technologies Aptitude Test 2015
Numerical Reasoning
Problem 1 : Three typists A,B,C work in an office. They are given a handwritten document to type. Individually,
A, being the most experienced, can type the whole document in 40 minutes, B can do that in an hour, and C,
the fresher, can do it in 1 hr 20 minutes. They decided to split the document among themselves so that it can be done in minimal time. What would be the time taken to complete the task?
Problem 2 : Three chemists want to prepare a solution of HCl and HNO3. The solutions are labeled x/y to denote the concentrations x% and y% of the two acids (the rest being water). As individually they came up with labels 50/25, 40/40 and 30/40, what will be the ratio in which the three solutions need to be mixed, to get a desirable 37/37 solution?
Problem 3 : The price of a gemstone is proportional to the square of its weight. A piece of such a stone, valued at $1m is somehow broken in 5 different pieces, all equal in size. What would be the loss/profit incurred by the accident?
Problem 4 : Two trains are travelling in opposite direction between Am-sterdam and Paris. The AMS-PAR express is superfast, and travels 50% faster than the intercity PAR-AMS. Both of them started their journey at 9 am, and crossed each other at 12 noon. Where would that crossing take place, if the distance between PAR and AMS is 500 km.
Problem 5: Please refer to the question above.
Problem 6 : A bank gives an interest rate of k% annually to its account holders. The account is credited with interests on a daily basis. What would be the correct expression for the annual yield percentage of the customer
Problem 7 : A computer circuit has a million components, each of them can be either in ON or in OFF position. Initially, the circuit is entirely OFF. A tracer penetrates the system, and sends innite number of worms, who act sequentially. The k-th worm targets every k-th component (i.e. k,2k,3k, etc), for every k > 0, and alters its position (ON to OFF, and OFF to ON). How many components will remain in OFF position after the tracer attack.
Problem 8 : The intersection of a cone and a plane is
Problem 9 : A grocer has a common balance, and a single weight of 10 kg. He wishes to measure anything between 1 to 10 kg, with precision upto 1 kg, and decides to break the balance in minimum number of pieces. What would be the weights of the different pieces?
Problem 10 : A meter cube is standing on one of its vertices with its longest diagonal standing vertically. It is rotated using the same diagonal as the axis. What would be the radius of the circle made by its other extreme vertices during the rotation.
Problem 11 : During a dinner party with 5 sets of couples, it was announced during the cocktain dance that no one should dance with his/her partner. In how many ways this can be achieved?
Problem 12 : In a football tournament, the participating teams are divided in groups of four each. After the round-robin format in each group, the two top teams from each group progress to the next round, where they are divided in 4 groups of equal size, and again play in a round-robin format. The top two teams from these 4 groups then play in the quarter-
nals, then semi nals and then the nal. If there are 79 matches altogether, how many teams played in the tournament?
Problem 13 : In the k dimensional euclidean space, the following will be a plane.
Problem 14 : Find the missing term in the sequence 19, 51,........91,99 Problem 15 : A stick of certain length is broken (but not apart), and the right section is rotated at an angle of 90 degrees anticlockwise. The locus of the right end of the stick would be
Problem 16 : If x to the power of y= y to the power of x where both x,y are integers and x < y, then how many possible values of such (x,y) exist
Problem 17 : A circular disc of radius 50 cm is used as a dart- board. It is divided by 4 concentric circles with radii 10,20,30,40 cm respectively in 5 zones altogether - the smallest one in the center as red, and then orange, yellow, green and blue. For a stake of $1, the payouts are $ .25, .5, 1, 2 and 4 respectively, starting from the outermost to the innermost. If hitting any part of the dart-board is a random event, what would be the expected payout from the event,
after taking o the stake.
Problem 18 : The antipode of a place on earth is dened as the exactly opposite place on earth, so that a line joining the two places will traverse through the center. The antipode of Kolkata (22.5 degrees N, 88.4 degrees E) will therefore be located at
Problem 19 : Two friends A and B start a business with a 5:3 share partnership based on their agreement. After some time, a third friend C joins the company after paying $80000. A and B shared the money among them-selves, and then on, the business continued with a 1:1:1 partnership. How would A and B share the money?
Problem 20 : A person decides to invest money in a fixed rate interest (p%) instrument, and starts to invest $a
every month for 15 years continuously. His final takeout from the investment is $ A. Another person takes a loan
of $ B for the same 15 years with the same rate of interest (p %). His mortgage per month turns out to be the same $a. Then, A and B are related as follows.