Test Preparation on CAT paper 6

Consider 4 (dimensionless) flies, 2 males and 2 females. They are situated at the four corners of a
square of side 10 meters, the two males at diagonally opposite ends. At any time, each fly tries to
reach the male/female fly in front of her/him using the shortest possible route. Since the flies are
flying towards another, they will meet each other at a certain time at the center of the square. What
is the length of the path that each has traveled at the moment they reach each other?

A man is going to a car auction. All purchases must be paid for in cash. He goes to the bank and
draws out Rs. 25,000.
Since the man does not want to be seen carrying that much money, he places it in 15 envelopes
numbered 1 through 15 such that he could count any amount from 1 to 25000 using combinations of
some envelopes. Each envelope contains the least number of bills possible of any available
currency. (for example, no two tens instead of a twenty). The possible currency denominations are
1,2,5,10, 20, 50 and 100.
At the auction, he makes a successful bid of Rs. 8322 for a car. He hands the auctioneer envelopes 2,
8, and 14. After opening the envelopes the auctioneer finds exactly the right amount. How many
ones (one rupee notes) did the auctioneer find in the envelopes?

On Madagascar Island, there are x dodos in a particular year. 30 dodos in a thousand of the original
population dies every year and 25 dodos in a thousand of the original population are born every year.
In how many years will the population of dodos halve itself?

A cube is divided into 8 equal cubes. Each of these cubes is further sub-divided into 8 equal cubes.
If the original cube’s sides are painted blue, then what is the probability that exactly 2 sides of a
small cube is painted blue?

Balancing cards on one another where some are placed horizontally and others diagonally (slant
fashion) is a popular trick of all magicians. 30 playing cards of length 12 cm and breadth 6 cm are
used to build a pyramidal structure with 4 horizontal cards at the base. 8 cards are then put
diagonally on these cards to give four peaks. 3 cards are then put on the 4 peaks. The process
continues till the top is a peak made by 2 cards. Find the area covered by the front side of the
pyramid.

A man buys shares at a discount of Rs.x. Later he sells all but 10 of the shares he purchased at a
premium of Rs.x. If his investment was Rs.4500 and proceeds from the sale were Rs.6250, how
many shares did he buy originally? [Assume face value of shares as Rs.100.]

ABCD is a rectangle with AB = 6 cm and AD = 8 cm. QR is an arc which cuts the extension of the AD
at Q and AB at R. What is the length of the arc QR if C is a point on it?

The diameter of the smaller circle is equal to the side of the square and the diagonal of the square is
equal to the diameter of the bigger circle. If the circles are concentric, then their areas are in the
ratio.

An artist has a canvas of length 10 inches and breadth 7 inches. He divides the canvas into 70
squares of area 1 inch by drawing lines parallel to the edges. He paints a corner square with a green
color. He then paints the two adjacent squares that share the side with the existing green square
with blue color. He continues to paint the entire canvas in such a way that no green square is
adjacent (i.e. share the same side) to another green and no blue square adjacent to another blue.
What is the ratio of a number of blue squares on the canvas to the number of green squares?

If AB ^ BC and BD ^ AC, which of the following is true ?