List of top Quantitative Ability and Data Interpretation Questions on Number Systems asked in XAT

Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4- digit number is divisible by a?

A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels.
How many rare jewels does the king have?

The roots of the polynomial are the radii of three concentric circles. \(P(x) = 2x^3-11x^2 +17x-6.\) The ratio of their area, when arranged from the largest to the smallest, is:

The least common multiple of a number and 990 is 6930. The greatest common divisor of that number and 550 is 110.
What is the sum of the digits of the least possible value of that number?

Read the following scenario and answer the questions that follow.
A T20 cricket match consists of two teams playing twenty overs each, numbered 1 to 20. The runs scored in any over is a non-negative integer. The run rate at the end of any over is the average runs scored up to and including that over, i.e., the run rate at the end of the k^th over is the average number of runs scored in overs numbered \(1, 2, …, k,\) where \(1 \leq k \leq 20, k\) a positive integer.
The following table indicates the run rate of a team at the end of some of the overs during a T20 cricket match (correct up to 2 decimal places), where \(1 \leq N – 2 < N + 6 \leq 20\), N a positive integer. It is also known that the team did not score less than 6 runs and more than 15 runs in any over.

Over Number	Run Rate
N-2	8.00
N	7.43
N+2	8.11
N+4	8.45
N+6	8.08

Consider an+1 = 1/1+1/an for n = 1,2,.......2008,2009. where a1 = 1. Find the value of a1a2 + a2a3 + a3a4+ .......+ a2008a2009.

The Madhura Fruits Company is packing four types of fruits into boxes. There are 126 oranges, 162 apples, 198 guavas and 306 pears. The fruits must be packed in such a way that a given box must have only one type of fruit and must contain the same number of fruit units as any other box. What is the minimum number of boxes that must be used?

Consider the real-valued function \(f(x) = \log \left( \frac{3x - 7}{\sqrt{2x \times 2x}} \right) - 7x + f\). Find the domain of f(x).

A supplier receives orders from 5 different buyers. Each buyer places their order only on a Monday. The first buyer places the order after every 2 weeks, the second buyer, after every 6 weeks, the third buyer, after every 8 weeks, the fourth buyer, every 4 weeks, and the fifth buyer, after every 3 weeks. It is known that on January 1st, which was a Monday, each of these five buyers placed an order with the supplier.
On how many occasions, in the same year, will these buyers place their orders together excluding the order placed on January 1st?

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is b. What is the product of the squares of the numbers?

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?

We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:
mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
m + n is a perfect square.
Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

An antique store has a collection of eight clocks. At a particular moment, the displayed times on seven of the eight clocks were as follows: 1:55 pm, 2:03 pm, 2:11 pm, 2:24 pm, 2:45 pm, 3:19 pm and 4:14 pm. If the displayed times of all eight clocks form a mathematical series, then what was the displayed time on the remaining clock?

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers (408X)63 and (789Y)85 are the same. What will be the possible value(s) of (X + Y)?
Example: If M = 3 then the digit at unit's place of the number (2M) is 3 (as the number is 23) and the digit at unit's place of the number (2M)2 is 9 (as 232 is 529).

In the final semester, an engineering college offers three elective courses and one mandatory course. A student has to register for exactly three courses: two electives and the mandatory course. The registration in three of the four courses is: 45, 55 and 70. What will be the number of students in the elective with the lowest registration?

If repetition of digits is allowed, how many five-digit numbers less than 13000 are possible such that the product of the digits of the number is 96?