A3
111
SECTION I
This section contains 25 questions
1. Consider the set S = {2, 3, 4, …., 2n+1}, where n is a positive integer larger than 2007. Define X as
the average of the odd integers in S and Y as the average of the even integers in S. What is the value of
X - Y ?
(1) 0
(2) 1
(3) n
2
1
(4)
n
n
2 1
+
(5) 2008
2. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years.
Three years later, one member died at the age of 60 years and a child was born during the same year.
After another three years, one more member died, again at 60, and a child was born during the same
year. The current average age of this eight-member joint family is nearest to
(1) 23 years
(2) 22 years
(3) 21 years
(4) 25 years
(5) 24 years
3. A function
)
(x
f
satisfies
)
1
(
f
= 3600, and
)
1
(
f
+
)
2
(
f
+ ... +
)
(n
f
=
)
(
2 n
f
n
, for all positive
integers n > 1. What is the value of
)
9
(
f
?
(1) 80
(2) 240
(3) 200
(4) 100
(5) 120
4. Suppose you have a currency, named Miso, in three denominations : 1 Miso, 10 Misos and 50
Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17
(2) 16
(3) 18
(4) 15
(5) 19
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja,
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5
6. How many pairs of positive integers m, n satisfy
12
1
4
1
=
+
n
m
,
where n is an odd integer less than 60?
(1) 6
(2) 4
(3) 7
(4) 5
(5)