### Counting Natural Numbers

Sum of three

*Natural*numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?- 45
- 36
- 54
- 28

**Correct Answer**Choice (B).

36 Correct answer- Explanatory Answer
- (n-1) C (r-1)
- Hard

### Counting Whole Numbers

Sum of three

*Whole*numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?- 66
- 78
- 72
- 56

**Correct Answer**Choice (A).

66 Correct answer- Explanatory Answer
- (n+r-1) C (r-1)
- Hard

### Counting - Toys and Boxes

In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?

- 72
- 54
- 45
- 36

**Correct Answer**Choice (C).

45 Correct answer- Explanatory Answer
- Counting
- Hard

### Permutation Combination Puzzle

a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?

- 8
- 6
- 2
- 4

**Correct Answer**Choice (D).

4 Correct answer- Explanatory Answer
- P&C Puzzle
- Medium

### Counting 7 Digit Numbers

A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12?

- 11
- 12
- 10
- 22

**Correct Answer**Choice (A).

11 Correct answer- Explanatory Answer
- Counting - Number Systems
- Medium

### Alphabetical Order

If all words with 2 distinct vowels and 3 distinct consonants were listed alphabetically, what would be the rank of “ACDEF’?

- 4716
- 4720
- 4718
- 1717

**Correct Answer**Choice (C).

4718 Correct answer- Explanatory Answer
- Word Rearrangements
- Hard

### Combinatorics Basics

If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?

- 3980
- 3700
- 3840
- 3780

**Correct Answer**Choice (A).

3980 Correct answer- Explanatory Answer
- Counting - Number Systems
- Medium

### Number Systems - Combinatorics

From the digits 2, 3, 4, 5, 6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?

- 36
- 60
- 84
- 72

**Correct Answer**Choice (B).

60 Correct answer- Explanatory Answer
- Counting - Number Systems
- Medium

### Numbers in Different Bases

All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?

- 143
- 200
- 157
- 122

**Correct Answer**Choice (A).

143 Correct answer- Explanatory Answer
- Base 6 and 7
- Hard

### Non-Zero Numbers

All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?

- 25
- 20
- 35
- 45

**Correct Answer**Choice (D).

45 Correct answer- Explanatory Answer
- Base 6
- Medium

### 5 Digit Numbers

How many numbers of up to 5 digits can be created using the digits 1, 2, 3 and 5 each at least once such that they are a multiple of 15?

- 24
- 18
- 15
- 12

**Correct Answer**Choice (D).

12 Correct answer- Explanatory Answer
- Counting - Number Systems
- Medium

### Numbers with Distinct Digits

How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?

- 975
- 960
- 978
- 986

**Correct Answer**Choice (C).

978 Correct answer- Explanatory Answer
- Counting 6 Digit Nos.
- Medium

### Alphabetical Order

All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"

- 36
- 74
- 42
- 86

**Correct Answer**Choice (B).

74 Correct answer- Explanatory Answer
- Word Rearrangements
- Medium

### Probability and GP

A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?

**Correct Answer**Choice (B).

Correct answer- Explanatory Answer
- Probability Duel
- Hard

### Probability Bayes Theorem

Doctors have devised a test for leptospirosis that has the following property: For any person suffering from lepto, there is a 90% chance of the test returning positive. For a person not suffering from lepto, there is an 80% chance of the test returning negative. It is known that 10% of people who go for testing have lepto. If a person who gets tested gets a +ve result for lepto (as in, the test result says they have got lepto), what is the probability that they actually have lepto?

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Bayes Theorem
- Hard

### Rearranging Letters

In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?

- 6720
- 2400
- 4320
- 1800

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Rearrangement
- Medium

### Possible Integer Solutions

2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b?

- 7
- 9
- 14
- 15

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- Integer Solutions
- Medium

### Rearrangement of Letters - Probability

If all the rearrangements of the word AMAZON are considered, what is the probability that M will feature between the 2As?

- 1/3
- 1/6
- 2/5
- 3/8

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- Probability
- Hard

### Probability and Number Theory

N is a 3-digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?

- 1/5
- 11/54
- 13/64
- 13/66

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Probability
- Medium

### Probability

A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?

- 2/5
- 1/2
- 1/3
- 2/3

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Probability
- Hard

### Rolling a Die

I roll a die four times. In how many outcomes do we have two throws have the same number and the other two something different?

- 720
- 480
- 360
- 350

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- Rolling a Die
- Medium

### Card Pack - Selection

In how many ways can be select 5 cards from a card pack such that all 4 suits appear.

- 52728
- 405646
- 685464
- 4056

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- Card Pack - Selection
- Medium

### Rolling a Die

I roll a die 4 times. In how many outcomes will each subsequent throw be greater that the previous one?.

- 30
- 48
- 54
- 60

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- Rolling a Die
- Medium

### 3 Digit Number

Find 3 digit numbers such that product of their digits is a natural number less than 5.

- 11
- 15
- 13
- 17

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- 3 Digit Number
- Medium

### 3 Digit Number - Sum of Digits

Find all 3 digit numbers such that sum of their digits is a whole number less than 5.

- 18
- 20
- 19
- 17

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- 3 Digit Number - Sum of Digits
- Medium

### Sum of Rearrangements

What is sum of all rearrangements of the 4-digit number 3214?

- 66660
- 55554
- 60048
- 65024

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- Sum of Rearrangements
- Medium

### Sum of Rearrangements

What is sum of all rearrangements of the 4-digit number 3321?

- 29999
- 27777
- 28888
- 29997

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Sum of Rearrangements
- Medium

### Forming Triangles

Of 22 points on a plane, 8 are on a straight line, 7 are on another straight line and 10 are on a third straight line. How many triangles can be drawn by connecting some three points from these 22?

^{22}C_{3}^{22}C_{3}- (^{8}C_{3}+^{7}C_{3}+^{10}C_{3})^{22}C_{3}+ (^{8}C_{3}+^{7}C_{3}+^{10}C_{3})^{8}C_{3}+^{7}C_{3}+^{10}C_{3}

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- Forming Triangles
- Medium

### Selection and Probability

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag one ball is drawn, then what is the probability that the ball drawn is red?

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Selection and Probability
- Medium

### MANANA Rearrangment

In how many ways can we rearrange the letters of the word MANANA such that no two A’s are adjacent to each other?

- 3 ! *
- 4 ! *
- 3 *
- 3 ! *

**Correct Answer**Choice (C) Correct answer- Explanatory Answer
- MANANA Rearrangment
- Medium

### I between 2 A's

How many ways are there for arranging letters of the word AMAZING such that the ‘I’ appears between the two ‘A’s?

- 5 ! ways
- 7 ! ways
- 8 ! ways
- 4 ! ways

**Correct Answer**Choice (A) Correct answer- Explanatory Answer
- I between 2 A's
- Medium

### Room Allocation

In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

- 6 * 5 ! ways
- 7 * 5 ! ways
- 3 * 3 ! ways
- 15 * 5 ! ways

**Correct Answer**Choice (D) Correct answer- Explanatory Answer
- Room Allocation
- Medium

### 3 Digit numbers > 500

How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?

- 191
- 176
- 153
- 189

**Correct Answer**Choice (B) Correct answer- Explanatory Answer
- 3 Digit numbers > 500
- Medium

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- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion