List of practice Questions

A delivery network allows routes from Start (S) to End (E) through intermediate hubs A, B, C.
Allowed edges:
S→A, S→B, A→C, A→E, B→C, C→E.
A route cannot visit more than 3 nodes including S and E.
How many valid routes from S to E are possible?

A, B, C, D, E, and F are seated around a circular table facing the center.
B sits third to the left of A.
Only one person sits between C and D.
E is not a neighbor of A or C.
F sits immediately to the right of D.
How many distinct seating arrangements satisfy all conditions?

Read the passage and answer:
Several historians argue that the decline of ancient civilizations was not solely due to environmental factors but also due to institutional rigidity. When rules and governance systems become resistant to change, societies lose flexibility and innovation capacity. Even mild environmental shocks can then trigger collapse because institutions cannot adapt quickly enough.
Question:
Which of the following can be inferred from the passage?

Arrange the sentences in a logical order:
A. This pursuit of conformity creates a dilemma: the more individuals try to blend in, the more homogeneous and predictable the group becomes.
B. Humans often conform to group norms to avoid social rejection.
C. Yet, creativity tends to flourish in environments that allow diversity of thought.
D. As a result, groups must balance the need for cohesion with the need for individual expression.
Question:
Arrange A, B, C, D in the most coherent order.

Identify the sentence that does not fit in the paragraph:
A. Urban planners increasingly recognize that walkable cities improve both physical and mental well-being.
B. Several studies indicate that green spaces in cities contribute to lower stress levels.
C. Public transportation systems are often designed to optimize fuel efficiency.
D. Compact city design reduces car dependency and encourages healthier lifestyles.
Question:
Which sentence is the odd one out?

Choose the option that best captures the central idea of the following paragraph:
Human memory is not a recording of the past but a reconstruction influenced by expectations, emotions, and present needs. People often recall events differently at different times, not because they are careless, but because memory adapts to serve current goals. Understanding this adaptive nature explains why eyewitness testimonies are unreliable and why personal narratives evolve over time.
Question:
Which option best summarizes the paragraph?

Argument:
A company claims its new productivity software significantly improves employee efficiency because workers using it complete tasks 30% faster.
Question:
Which of the following, if true, most seriously weakens the company’s claim?

Argument:
"Cities that invest in cycling infrastructure will see a long-term reduction in traffic congestion because people will shift from cars to bicycles."
Question:
Which of the following is an essential assumption in the argument?

Read the passage and answer the question that follows:
Modern behavioral economists argue that human decisions are not merely deviations from rationality but reflections of multiple competing goals: emotional satisfaction, social approval, cognitive ease, and fear avoidance. Traditional economic models assumed that people maximize utility through consistent preferences. However, empirical evidence shows that preferences fluctuate depending on framing, context, memory limits, and social cues. What we label as “irrationality” may simply be the mind optimizing for criteria that formal models fail to capture.
Question: Which of the following, if true, most strengthens the author’s argument?

A store sells four products — P, Q, R, and S — across four days (Mon–Thu), exactly one product per day.
P is not sold on Monday or Wednesday.
R is sold before Q.
S is not sold on Thursday.
Exactly one of P or Q is sold on Tuesday.
How many valid schedules are possible?

A group of 120 students attend at least one of three workshops: Data, Logic, and Verbal.
48 attend Data, 60 attend Logic, 50 attend Verbal.
20 attend both Data & Logic, 15 attend both Logic & Verbal, 12 attend both Data & Verbal, and 8 attend all three.
How many students attend exactly one workshop?

Four machines A, B, C, D produce items in a ratio.
A produces 40 more than B.
C produces 20% more than A.
D produces half of B.
If total production is 860 items,
how many items did Machine C produce?

Six people — P, Q, R, S, T, U — stand in a line.
P is somewhere ahead of Q.
Exactly two people stand between Q and R.
S is not adjacent to P or R.
T is not in the first or last position.
How many distinct valid arrangements are possible?

The number of non-negative values of n for which \(\log_{1/4}(n^2 - 7n + 14)>0\) is ____.

In a class there were more than 10 boys than a certain number of girls. After 40% of the girls and 60% of the boys left, the remaining number of girls were 8 more than the remaining boys. Find the possible number of students initially in the class.

Stocks A, B and C, at 120, 90 and 80 rs respectively. A trader holds a portfolio consisting 60 shares of A, 20 of B and C together. If total value is 33000 what is the number of shares he holds.

In a cafeteria, there are 5 breads. One can choose 1 bread from the available breads, either small or large sized, and can choose up to 2 sauces from 6 available sauces. What is the number of different ways one can place an order?

If the length of each side of a rhombus is 36 cm, and the area of the rhombus is 396 cm\(^2\), then what is the absolute value of the difference between the lengths of its diagonals?

A container contains only milk. 2/3 of the mixture is removed and replaced with water. This process is done once and then repeated another 3 times. What is the final ratio of milk and water?

A 200-litre container holds a solution that is 30% acid and the rest water. The solution undergoes the following three processes sequentially:
1. 20% of the water content is evaporated.
2. From the remaining mixture, 10% of the acid content is chemically extracted and removed.
3. Finally, 15% of the resulting solution is removed and replaced with water.
What is the volume of acid in the final solution?

Find the number of real values of x satisfying the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]

Find the number of integer pairs (x, y) that satisfy the following system of inequalities:
\[ \begin{cases} x \geq y \geq 3 \\ x + y \leq 14 \end{cases} \]

A shopkeeper offers a 22% discount on the marked price of chairs. He gives 13 chairs to a customer at the discounted price of 12 chairs. If he still makes a profit of 26%, what is the marked price (MP) of a single chair, assuming its cost price (CP) is Rupees 100?

Find the real value(s) of x that satisfy the equation:
\[ \log_{2}(x^2 - 5x + 6) + \log_{1/2}(x - 2) = 3 \]