Given:
x means greater than (>)
$ means equal to (=)
< means not less than (≥)
A means less than (<)
+ means not greater than (≤)
Find the expression equivalent to
a x b A c.
A. a $ c A b
B. b < a x c
C. c x b A a
D. c + b < a
Correct Answer: Option C — c x b A a
Step-by-Step Solution
Replace each coded symbol with its meaning.
The first comparison, a x b, means a > b.
The second comparison, b A c, means b < c.
Therefore, b is smaller than both a and c.
We can write the same relationship as c > b < a.
Converting it back into coded symbols gives c x b A a.
a > b < c = c > b < a
Final Answer: Option C.
Question 2: Factory Pipeline Distribution
A factory supplies goods to four cities through pipelines.
The cities consume exactly the amount they require.
If 300 units travel from City A to City B,
how many units travel from City D to City B?
A. 200 units
B. 600 units
C. 800 units
D. 1000 units
Correct Answer: Option C — 800 units
Step-by-Step Solution
City B requires 400 units for its own consumption.
City C requires another 700 units, supplied through City B.
So City B needs 400 + 700 = 1100 units.
City A already sends 300 units to City B.
The remaining units must arrive from City D.
1100 − 300 = 800 units
Therefore, the pipeline from D to B must carry
800 units.
Question 3: Letter-Number Substitution
Six letters A, B, C, P, Q and R represent
six different numbers from the set
{1, 2, 4, 5, 7, 9}.
Conditions:
A and C are consecutive and A > C.
P + Q = R and P > Q.
B is greater than both A and C.
The numbers 5A and 5B both have 5
in the tens position.
Therefore, A must be greater than B.
The number C9 is smaller than 5B.
Therefore, C cannot exceed 4.
Step 2: Use the largest C.
C = 4
A + B + 4 = 15
A + B = 11
Since A must be greater than B,
choose A = 6 and B = 5.
Step 3: Verify the numbers.
56 > 55 > 49
The condition is satisfied.
Step 4: Calculate the expression.
3B + 4C + 8
= 3(5) + 4(4) + 8
= 15 + 16 + 8
= 39
Smaller feasible values of C cannot produce
a result above 39 while satisfying all
the given conditions.
Final Answer: 39 (Option B).
Question 10: Calendar and Consecutive Multiples
In the given calendar, all marked dates
are consecutive multiples of a particular number.
The first marked date is the first Thursday.
Determine the last day of the month.
A. Monday
B. Sunday
C. Saturday
D. Friday
Correct Answer: Option B — Sunday
Step-by-Step Solution
The marked dates occur on Thursday,
Wednesday, Tuesday and Monday in successive weeks.
Moving from Thursday to Wednesday of the following
week represents a gap of 6 days.
The marked dates must therefore be:
6, 12, 18, 24
Since the 6th is Thursday,
the 1st is Saturday.
Calendar Illustration
Mon
Tue
Wed
Thu
Fri
Sat
Sun
1
2
3
4
5
6 X
7
8
9
10
11
12 X
13
14
15
16
17
18 X
19
20
21
22
23
24 X
25
26
27
28
29
30
The 29th is Saturday, so the 30th
falls on Sunday.
Last day of November = Sunday
Final Answer: Option B.
Final Answer Summary
Question
Correct Option
Answer
1
C
c x b A a
2
C
800
3
D
11
4
C
11 years
5
A
4
6
A
108
7
C
3
8
C
38
9
B
39
10
B
Sunday
Study Note:
These worked solutions are based on Chapter 4,
Expressions Using Letter-Numbers, questions 1 to 10.
The explanations are written to help students
understand the reasoning behind each correct answer.
