Mathematics · Quantitative Aptitude

Number Sums and Series

287 Questions

Number sums and series questions test the ability to find patterns and calculate the sum of number sequences. These problems are a staple in the quantitative aptitude sections of various competitive exams. Practice this collection to improve speed and accuracy in solving arithmetic and geometric series problems.

Sum of consecutive integersGeometric series sumsRatio and proportion sumsOdd and even number propertiesRoman numeral calculations

Number Sums and Series Questions

Multiple choice general knowledge math & puzzles

If a and b are both even numbers, which of the following could be and odd integer?

  1. a2 + b2

  2. (a + 1)^2 + (b + 1)^2

  3. (a + 1)*(b + 1) - 1

  4. (a + 1) / (b + 1)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $a, b$ are even, $a+1$ and $b+1$ are both odd. The ratio of two odd numbers can be an integer (e.g., $9/3 = 3$), and that integer will always be odd. The other options result in even numbers: (odd+odd=even), (odd*odd-1=even).

Multiple choice general knowledge math & puzzles

he sum of all the odd numbers from zero to 16 is an even number.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve this question, we need to find the sum of all the odd numbers from zero to 16 and determine if it is an even number or not.

The odd numbers from zero to 16 are: 1, 3, 5, 7, 9, 11, 13, 15.

To find the sum, we can add all these numbers together:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64.

Now, we need to determine if 64 is an even number or not.

An even number is any integer that is divisible by 2 without leaving a remainder.

To check if a number is even, we can divide it by 2.

If the remainder is 0, then the number is even.

If the remainder is not 0, then the number is odd.

Let's divide 64 by 2:

64 ÷ 2 = 32.

Since the remainder is 0, we can conclude that 64 is an even number.

Therefore, the correct answer is:

A. True

Multiple choice general knowledge math & puzzles

if a,b,c,d are 4 ditinct non zero positive integers such thatsum of cubes of first two nos. is equal to sum of cubes of last two nos. i.e.a^3+b^3=c^3+d^3then min. value of a+b+c+d is

  1. 30

  2. 32

  3. 31

  4. no such nos. possible
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The smallest solution to a^3 + b^3 = c^3 + d^3 with distinct positive integers is 1^3 + 12^3 = 9^3 + 10^3 = 1729. This is known as the Hardy-Ramanujan number or the smallest taxicab number. The sum is 1 + 12 + 9 + 10 = 32. Such numbers are possible and well-studied in number theory.