Quant Aptitude
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| Item | Quick facts |
|---|---|
| Coins | coins → outcomes |
| Dice | dice → outcomes; for two dice, sum 7 is likeliest (6 ways) |
How many 4-letter words can be formed using the letters of the word "CODE" if repetition of letters is not allowed?
Two fair dice are thrown simultaneously. What is the probability of getting a sum of exactly 9?
In how many ways can a committee of 5 members be formed from 6 men and 4 women, consisting of exactly 3 men and 2 women?
A bag contains 5 red, 4 blue, and 3 green balls. If three balls are drawn at random without replacement, what is the probability that all three are red?
How many different words can be formed by arranging the letters of the word "SUCCESS" such that all the 'S's are always placed together?
Person A speaks the truth in 60% of cases, and Person B speaks the truth in 80% of cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?
In a corporate party, every person shakes hands exactly once with every other person. If there are a total of 105 handshakes, how many persons are there in the party?
Two cards are drawn simultaneously from a well-shuffled standard deck of 52 cards. What is the probability that both cards are either kings or diamonds?
| Cards | 52 cards, 4 suits of 13; 12 face cards |
How many 5-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition, such that the resulting number is strictly greater than 40,000?
Three persons A, B, and C take turns throwing a pair of dice, in that exact order, starting with A. The first person to throw a sum of 10 wins the game. What is the probability that C wins the game?
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if digits may repeat?
How many different arrangements can be made of the letters of the word BANANA?
In how many ways can 7 people be seated around a round table?
In how many ways can a team of 4 be chosen from 10 players?
In how many ways can a captain and a vice-captain be chosen from a squad of 15 players?
Three fair coins are tossed. What is the probability of getting exactly two heads?
In how many ways can the letters of the word LEADER be arranged?
In how many ways can 5 different books be arranged on a shelf if two particular books must always be together?
In how many ways can the letters of the word GARDEN be arranged so that the vowels are always together?
How many arrangements of the letters of the word MONDAY begin with a vowel?
How many different necklaces can be made using 8 distinct beads?
A committee of 5 is to be chosen from 6 men and 5 women so that it includes at least 3 women. In how many ways can this be done?
How many diagonals does a 12-sided polygon have?
Two dice are thrown together. What is the probability that the sum of the numbers is a prime number?
One card is drawn at random from a well-shuffled pack of 52 cards. What is the probability that it is a face card or a spade?
Two dice are thrown. What is the probability that the product of the numbers shown is even?
A bag contains 6 red and 4 green balls. Two balls are drawn at random without replacement. What is the probability that both are green?
A bag contains 5 white, 4 black and 3 blue balls. Two balls are drawn at random. What is the probability that both are of the same colour?
A and B independently try to solve a problem, with probabilities of success 1/4 and 2/5. What is the probability that the problem gets solved?
A die is thrown 3 times. What is the probability of getting at least one six?
From a group of 7 men and 6 women, 5 persons are to be selected to form a committee so that at least 3 men are included. In how many ways can this be done?
A box contains 2 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn from the box if at least one black ball is to be included?
Two cards are drawn together from a pack of 52 cards. What is the probability that one is a spade and one is a heart?
How many 4-digit even numbers can be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition?
In how many arrangements of the letters of the word ORANGE are no two vowels next to each other?
In how many ways can 7 people sit around a round table if two particular people must NOT sit next to each other?
A committee of 4 is to be formed from 8 people, including A and B. In how many ways can it be formed if A and B cannot both be on it?
There are 12 points in a plane, of which exactly 5 lie on one straight line and no other three are collinear. How many triangles can be formed using these points as vertices?
A and B take turns tossing a fair coin, A first. The first person to get a head wins. What is the probability that A wins?
In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?