List of top Data Interpretation & Logical Reasoning (DILR) Questions on Geometry

Two lines are given by the equations $ax + by = c$ and $dx + ey = f$. Do they intersect?
Statement A
A. $a, b, c, d, e, f$ are distinct \& real.
Statement B
B. $c \neq 0$ \& $f \neq 0$.
Ghosh flies to South Africa from Mumbai non-stop. His flight leaves Mumbai at 5 am on 10\textsuperscript{th} December 2000 as per Indian Standard Time. What is the local time in South Africa when Mr. Ghosh reaches there?
Statement A
A. The average speed of the plane during the flight is 700 km/h.
Statement B
B. The flight distance is 10,500 km.
Is $z$ the smallest of $x, y, z$?
Statement A
A. $x$ is greater than at least one of $y$ \& $z$.
Statement B
B. $y$ is greater than at least one of $x$ \& $z$.
Two concentric circles have the same centre O. A chord on the outer circle AE intersects the inner circle in points B and D. C is a point on the segment BD. What is the ratio of AC to CE?
Statement A
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.
What are the ages of X and Y?
Statement A
A. The difference in their ages is $6$.
Statement B
B. The product of their ages is divisible by $6$.
$x$ is a real number. Is $|x|<3$?
Statement A
A. $x(x+3)<0$
Statement B
B. $x(x-3)>0$
$a \oplus b = 1$ if $a,b>0$ or $a,b<0$; \quad $a \oplus b = -1$ otherwise.
What is $(2 \oplus 0) \oplus (-5 \oplus -6)$?
Statement A
A. $a \oplus b = 0$ if $a=0$
Statement B
B. $a \oplus b = b \oplus a$
Harshad bought shares of a certain company on one day and sold them the next day. He paid a brokerage of $1%$. What was Harshad’s profit per rupee?
Statement A
A. His selling price was $1.05$ times his purchase price.
Statement B
B. The number of shares he purchased was $100$.
How many people watch program P?
Statement A
A. The number watching Q is $1000$; the number watching both P and Q is $100$.
Statement B
B. The number of people watching either P or Q or both is $1500$.
In a triangle PQR, $\angle PRQ = 90^\circ$. What is $PR + RQ$?
Statement A
A. The diameter of the incircle is $10$.

Statement B
B. The diameter of the circumcircle is $18$.
If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$, then what is the value of $(\alpha^2 + \beta^2)$?
I. $\alpha + \beta = -\left(\frac{b}{a}\right)$.
II. $2\alpha\beta = \left(\frac{c}{a}\right)$.
What is the selling price of the article?
I. The profit on sales is 20%.
II. The profit on each unit is 25% and the cost price is Rs.\ 250.
How many different triangles can be formed?
I. There are 16 coplanar, straight lines.
II. No two lines are parallel.
What is the total worth of Lakhiram's assets?
I. A compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs.\ 1,500 this year.
II. The interest is compounded once every four months.
How old is Sachin in 1997?
I. Sachin is 11 years younger than Anil whose age will be a prime number in 1998.
II. Anil's age was a prime number in 1996.
What is the number of type-2 widgets produced, if the total number of widgets produced is 20,000?
I. If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.
II. The ratio in which type-1 and type-2 widgets are produced is 2 : 1.
A tractor travelled a distance 5 m. What is the radius of the rear wheel?
I. The front wheel rotates `N` times more than the rear wheel over this distance.
II. The circumference of the rear wheel is `r` times that of the front wheel.
What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)
I. The ratio of liquid A to liquid B in the first and second vessel is 3:5 and 2:3 respectively.
II. The ratio of liquid A to liquid B in vessel 3 is 4:3.
If $a, b, c$ are integers, is $(a-b+c)>(a+b-c)$?
I. $b$ is negative.
II. $c$ is positive.