91. Leon, who is always in a hurry, walked up an escalator, while it
was moving, at the rate of one step per second and reached the top in
20 steps. The next day he climbed two steps per second (skipping
none), also while it was moving, and reached the top in thirty-two
steps. If the escalator had been stopped, how many steps did the
escalator have from the bottom to the top?
92. A, B and C were asked to sell fun-fair tickets priced at $10
each. A sold 1/4 of them. B and C sold the remaining tickets in the
ratio 5:7. A received $90 less than C.
What fraction of tickets were sold by C? b) How many tickets did the
3 girls sell altogether?
93.If 500ml of popcorn and 1 box of potato chips cost $1.64, and
250ml of popcorn and 2 boxes of potato chips cost $1.99, and 250ml of
popcorn is half the price of 500ml of popcorn, then how much is one
box of popcorn?
94.There are three circles, they share a similar area. The similar
area is 1/10 of the biggest circle, 1/6 of the second biggest circle,
and half of the smallest circle. What is the ratio of the circles?(
biggest, second biggest, smallest)
95. Sally and Jeff took 37 hours to complete a whole project. If
Sally had worked 5 hours less and Jeff had worked 6 hours more, Jeff
would still have put in 2 more hours than Sally. How many hours did
Sally put in for the project? (Assume that Sally and Jeff worked
separately on their own project.)
96. Mrs Lee purchased 240 rings and some watches. The number of rings
was more than the number of watches by 20% of the total number of
both items bought. She sold all the watches at $36 each. From the
total sale of the rings and the watches, she earned $2240 from her
total sale. If each ring was sold at 25% less than the selling price
of each watch,
a) find the no. of watches purchased by Mrs Lee, and
b) find the total cost price of all the rings and watches
97. We play the following game with an equilateral triangle of
n(n+1)=2 pennies (with n pennies on each side). Initially, all of the
pennies are turned heads up. On each turn, we may turn over three
pennies which are mutually adjacent; the goal is to make all of the
pennies show tails. For which values of n can this be achieved? I. 17
II. 7 III. 8 IV. 6
A. all of the above B. none of the above
C. for more than 2 of the above including IV D. Exactly 2 of them.
98. In a certain town, the block are rectangular with stress running
East-West, the avenues North-South. A man wishes to go from one
corner to another m block East, n block North. In how many ways the
shortest path can be achieved.
99. Two players take turns drawing a card at random from a deck of
four cards labeled 1,2,3,4. The game stops as soon as the sum of the
numbers that have appeared since the start of the game is divisible
by 3, and the player who drew the last card is the winner. What is
the probability that the player who goes first wins?
100. We are given 1997 distinct positive integers, any 10 of which
have the same least common multiple. Find the maximum possible number
of pairwise coprime numbers among them.
Ans 9.
101. A rectangular strip of paper 3 centimeters wide and of infinite
length is folded exactly once. What is the least possible area of the
region where the paper covers itself?
A. 4.5 B. 4 C. 3.45 D. 5.4
102. A company has 50000 employees. For each employee, the sum of the
numbers of his immediate superiors and of his immediate inferiors is
7. On Monday, each worker issues an order and gives copies of it to
each of his immediate inferiors (if he has any). Each day thereafter,
each worker takes all of the orders he received on the previous day
and either gives copies of them to all of his immediate inferiors if
he has any, or otherwise carries them out himself. It turns out that
on Friday, no orders are given. The least employees who have no
immediate superiors are. A. 97 B. 518 C.216 D. none of these.
103.The numbers from 1 to 37 are written in a line so that each
number divides the sum of the previous numbers. If the first number
is 37 and the second number is 1, what is the third number?
104. The centre of the circumcircle of triangle ABC with angle C = 60
is O and its radius is 2 . Find the radius of the circle that touches
AO , BO and the minor arc AB.
105 . ABC is an equilateral triangle in which B is extended to K such
that CK = ½ BC. Find AK^2 * 1/ CK^2
A. 3 B. 7 C. 5 D. 6
106. Let S be the set of prime numbers bigger than 100 but smaller
than 150. Let n be the product of all the numbers in the set S .
Which of the following statement is FALSE?
A. 5 does not divide n B. 17 divide n. C. n is an odd number D. n is
a product of distinct primes.
107. A cube of side ‘a’ is converted into a sphere by adding clay
on all the faces of the cube. The minimum volume of clay required is
Ans. a^3( pie * sqrt(3)/2 - 1) .
108. The product of all integer from -129……….+130, ends
inclusive , then which of the following values is closet to the
result? A. 65^65 B. 9^2 C. -65^65 20^12.
109. Four people, A, B, C, and D, are on one side of a bridge, and
they all want to cross the bridge. However, it's late at night, so
you can't cross without a flashlight. They only have one flashlight.
Also, the bridge is only strong enough to support the weight of two
people at once. The four people all walk at different speeds: A takes
1 minute to cross the bridge, B takes 2 minutes, C takes 5 minutes,
and D takes 10 minutes. When two people cross together, sharing the
flashlight, they walk at the slower person's rate. How quickly can
the four cross the bridge?
110. A cube is divided into 27 pairwise congruent smaller cubes. Find
the maximum number of small cubes that can be stabbed by a straight
line.
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