SOF international mathematics olympiad (IMO) sample paper for performing best performance

PAPER 2
SECTION 01 LOGICAL REASONING
1. How many pairs of letters are there in the word "SACCHARINE" which have as many letters
between them in the word as in the alphabet in both directions?
(A) 2
(B) 6
(C) 4
(D) 3
Ans. [D]
These are AC, AE and AC.

GMHNHVFYTROPHGSRYWSZSVCXJLKG

2. In the given series which of the following alphabet will be seventh to the left of ninth from the
right alphabet?
(A) S
(B) T
(C) R
(D) H
Ans. [D]
It will be 7 + 9 = 16th from right end that is H.

Directions (Q. 3 to 5) : In each of the questions below statements are followed by four conclusions.
Read the conditions and decide which logically follows from the given statements :
3. Statement : (i) All doctors are fools.
(ii) All fools are illiterate.
Conclusions : I. All doctors are illiterate.
II. All illiterates are doctors.
III. All illiterates are fool.
IV. Some illiterates are doctors.
(A) Only I follows
(B) Only I and III follows
(C) Only I and IV follows
(D) II, III and IV follows

4. Statements : (i) Some alpha are beta.
(ii) All beta are gamma.
Conclusions : I. Some alpha are gamma.
II. No alpha is a gamma.
III. Some gamma are beta.
IV. No gamma is a beta.
(A) Only I follows

, (B) II and III follows
(C) Only III follows
(D) I and III follows
Ans. [D]
5. Statements : (i) Some blankets are pillows.
(ii) All pillows are bananas.
Conclusions : I. Some bananas are blankets.
II. Some bananas are pillow.
III. No banana is a pillow.
IV. Some blankets are not bananas.
(A) I and III follows
(B) I and II follows
(C) I and IV follows
(D) Only I follows
Ans. [B]
Directions (Q. 6-8) : In each of the questions below, a group of numerals is given followed by
four groups of symbol/letter combinations lettered (1), (2), (3) and (4). Numerals are to be coded
as per the codes and conditions given below. You have to find out which of the combinations (1),
(2), (3) and (4) is correct and indicate your answer accordingly.
Numerals: 3 5 7 4 2 6 8 1 0 9
Letter/Symbol Code: * B E A Ans. F K % R M
Following conditions apply:
(i) If the first digit as well as the last digit is odd, both are to be coded as ‘X’.
(ii) If the first digit as well as the last digit is even, both are to be coded as ‘$’
(iii) If the last digit is ‘0’, it is to be coded as ‘#’
6. 487692
(A) $KEFMAns.
(B) AKEFMAns.
(C) AKEFM$
(D) $KEFM$
Ans. [D]

7. 713540
(A) X%*BA#
(B) E%*BA#
(C) E%*BAR
(D) X%*BAR
Ans. [B]

8. 765082
(A) EFB#KAns.
(B) XFBRKAns.
(C) EFBRKAns.
(D) EFBR#K
Ans. [C]

, 9..Sunil remembers that his brother’s birthday is after 15th but before 18th of February whereas
his sister Kajol remembers that her brother’s birthday is after 16 th but before 19th of February.
When is Sunil’s brother’s birthday?
(A) 16th
(B) 17th
(C) 15th
th
(D) 9
Ans. [B]
According to Sunil, his brothers birthday fall on 16th or 17th February.
According to Kajol, Sunil’s brother’s birthday fall on 17th or 15th February.
So, common day is 17th February.
10. In a certain code, if STRONGER is written as TSSNOFFQ, then FREEDOM can be written as
(A) GFQRSNN
(B) GQFDENE
(C) GSFFEPN
(D) GQFDENN
Ans. [D]

S T R O N G E R
+1 –1 +1 –1 +1 –1 +1 –1
T S S N O F F Q
F R E E D O M
+1 –1 +1 –1 +1 –1 +1
G Q F D E N N


11. Some boys are sitting in a row. P is sitting fourteenth from the left and Q is seventh from the
right. If there are four boys between P and Q, then how many boys are there in the row?
(A) 19
(B) 21
(C) 25
(D) 28
Ans. [C]
14th 7th
P Q
13 4 6
13 + 1 + 4 + 1 + 6
= 25

12. In a company, out of 80 workers, 24 can read English and 64 can read Telugu. How many
workers can read both English and Telugu language?
(A) 2
(B) 24
(C) 28
(D) 8
Ans. [D]