Zahir and Raman are at the entrance of a dark cave. To enter this cave, they need to open a number lock. Raman sees a note on a rock: "... chest of pure diamonds kept for the smart one ... number has six digits ... second last digit is 2, third last is 4 ... divisible by all prime numbers less than 15 ...." Excited, Zahir and Raman seek your help: which of these can be the first digit of the six digit number that will help them open the lock?

Four friends, Ashish, Brian, Chaitra, and Dorothy, decide to jog for 30 minutes inside a stadium with a circular running track that is 200 metres long. The friends run at different speeds. Ashish completes a lap exactly every 60 seconds. Likewise, Brian, Chaitra and Dorothy compl…

Two circles P and Q, each of radius 2 cm, pass through each other's centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45…

From the passage: The following plot describes the height (in cm), weight (in kg), age (...

The BMI of the oldest person considered as normal weight is approximately [Figure: see page 18 of source PDF]

An encryption system operates as follows: Step 1. Fix a number k (k ≤ 26). Step 2. For each word, swap the first k letters from the front with the last k letters from the end in reverse order. If a word contains less than 2k letters, write the entire word in reverse order. Step 3…

Find z, if it is known that: a: −y² + x² = 20; b: y³ − 2x² − 4z ≥ −12; and c: x, y and z are all positive integers.

ABC is a triangle with integer-valued sides AB = 1, BC > 1, and CA > 1. If D is the mid-point of AB, then, which of the following options is the closest to the maximum possible value of the angle ACD (in degrees)?

The six faces of a wooden cube of side 6 cm are labelled A, B, C, D, E and F respectively. Three of these faces A, B, and C are each adjacent to the other two, and are painted red. The other three faces are not painted. Then, the wooden cube is neatly cut into 216 little cubes of…