**Number System Question 1.**A four-digit number has the sum of its digits in the odd positions equal to the sum of its digits in the even positions. If it is subtracted from the number formed by reversing it, the result will always be divisible by ______ ?

**Options -**

*A. 9*

*B. 11*

*C. 13*

*D. 9 and 11*

**Number System Solution 1.**

**Number System Question 2.**Find the sum of the remainders obtained when a number n is divided by 9 and 7 successively, if n is the smallest number that leaves respective remainders of 4, 6 and 9 when divided successively by 13, 11 and 15 ?

**Options**-

*A. 8*

*B. 7*

*C. 5*

*D. 6*

**Number System Solution 2.**

**Number System Question 3.**The sets Q(p) are defined as {p, p + 1, p + 2, p + 3, p + 4, p + 5, p + 6}, where p = 1, 2, 3 . . . . . 100. How many of these sets contain a multiple of 11 ?

**Options**-

*A. 63*

*B. 65*

*C. 61*

*D. 62*

**Number System Solution 3.**

**Number System Question 4.**How many four-digit perfect squares 'abcd' are possible such that 'dcba' is also a four-digit perfect square and is also a factor of 'abcd' ? (given a is not equal to d)

**Options**-

*A. 2*

*B. 1*

*C. 0*

*D. 3*

**Number System Solution 4.**

**Number System Question 5.**How many three-digit positive integers have their hundreds, tens and units digits in ascending order?

**Options**-

*A. 80*

*B. 70*

*C. 84*

*D. 77*

**Number System Solution 5.**

**Number System Question 6.**Rahul had some chocolates with him. He had just enough chocolates to distribute them among two groups of children A and B in the following manner. He distributed the chocolates among the children in group A such that each child got as many chocolates as the number of children in it. He distributed the chocolates among the children in group B such that each child got as many chocolates as the square of the number of children in it. He distributed 9 more chocolates to children in group A than in group B. If he had less than 600 chocolates, how many possibilities exist for the number of chocolates with him ?

**Options**-

*A. 2*

*B. 4*

*C. 3*

*D. 5*

**Number System Solution 6.**

**Number System Question 7.**How many natural numbers less than 100 when squared and then divided by 24 leave a remainder of 1 ?

**Options**-

*A. 32*

*B. 33*

*C. 34*

*D. 30*

**Number System Solution 7.**

**Number System Question 8.**A natural number has only two prime factors. It is 100 times the number of its factors. Find the sum of the digits of the least number satisfying these conditions ?

**Options**-

*A. 4*

*B. 3*

*C. 1*

*D. 2*

**Number System Solution 8.**

**Number System Question 9.**A certain number of chocolates which is a perfect square are distributed among 2156 students of a school equally. Find the minimum number of chocolates distributed given that it is greater than 90,000 ?

**Options**-

*A. 94864*

*B. 94874*

*C. 94894*

*D. 94884*

**Number System Solution 9.**

**Number System Question 10.**If p and q are prime and x^2 - px + q = 0 has distinct positive integral roots, find p - q ?

**Options**-

*A. 1*

*B. 3*

*C. 4*

*D. 2*

**Number System Solution 10.**

**Number System Question 11.**Three bells toll regularly at intervals of 8 minutes, 12 minutes and 18 minutes respectively. Find the time gap between two successive instances of all 3 bells tolling together ?

**Options**-

*A. 66 minutes*

*B. 72 minutes*

*C. 144 minutes*

*D. 78 minutes*

**Number System Solution 11.**

*The Solution this questions is super easy as we have to only take out the LCM of the 3 time intervals.*

*LCM (8,12,18) = 72 minutes.*

**Answer is Option B**
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