Arun Sharma Solutions for Exercise 3: XAT

In a cricket match, Team $A$scored $232$ runs without losing a wicket. The score consisted of byes, wides and runs scored by two opening batsmen: Ram and Shyam. The runs scored by two batsmen are $26$ times wides. There are $8$ more byes than wides. If the ratio of runs scored by Ram and Shyam is$6:7,$ Then runs scored by Ram is?

In the following question, one statement is followed by three conclusion. Select the appropriate answer from the option given below.

$A_0, A_1, A_2 ,....$ is a sequence of numbers with   $A_0=0, A_1=3$, and $A_t=\left(t+1\right) A_{t-1}-t A_{t-2}=2, 3, 4,....$

Conclusion $1:$ $A_8=77$.

Conclusion $2: A_{10}=121$.

Conclusion $3: A_{12}=145$.

$p$and $q$ are positive numbers such that $p^q=q^p$. And $q=9p.$The value of$p$ is:

Two numbers, ${297}_B$ and ${792}_B$  belong to base $B$number system. If the first number is a factor of the second number then the value of$B$ is:

Read the following instruction carefully and answer the question that follows: Expression $\sum _{n=1}^{13}\frac{1}{n}$ can also be written as $\frac{x}{13!}.$ What would be the remainder if $x$ is divided by $11?$

Amitabh picks a random integer between $1 to 999$, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds $50$ to the number and gives the result back to Amitabh, who doubles the number again. The first person whose result is more than $1000,$ losses the game. Let $\text{'}x\text{'}$be the smallest number that results in a win for Amitabh. The sum of the digits $\text{'}x\text{'}$ is :

Consider four natural numbers:$x, y, x+y,$ and $xy.$

Two statements are provided below - 

 $I.$All fours numbers are prime numbers.

$II.$ The arithmetic mean of the numbers is greater than$4.$

Which of the following statements would be sufficient to determine the sum of the four numbers? 

What is the sum of following series?

$-64, -66, -68,........, -100$.