A farmer divides his herd of $n$ cows amongst his four sons, so that the first son gets one-half of the entire herd, the second son gets one-fourth while the third son gets one-fifth and the fourth son gets only $7$ cows. The value of $n$ is: 

 

The least number which when divided by $48, 64, 90, 120$ will leave remainders $38, 54, 80, 110$ respectively, is:

(A) $2870$

(B) $2860$

(C) $2890$

(D) $2880$

The HCF and LCM of two positive integers are $35$ and $385$ respectively. If one of the integers is $77$, what is the other integer?

(A) $350$

(B) $210$

(C) $175$

(D) None of the above

There are four prime numbers written in ascending order. The product of the first three is $385$ and that of the last three is $1001$. The first prime number is:

(A) $5$

(B) $7$

(C) $11$

(D) $17$

If fractions $\frac{4}{5}, \frac{6}{7}, \frac{2}{9}, \frac{9}{11}$  and $\frac{3}{8}$are arranged in ascending order of their respective values, which one fraction will be the fourth?

(A) $\frac{9}{11}$

(B) $\frac{4}{5}$

(C) $\frac{3}{8}$

(D) $\frac{6}{7}$

If $12$ men or $18$ women can reap a field in$14$ days, then working at the same rate, $8$ men and $16$$$ women can reap the same field in how many days?

A jar contains a mixture of two liquids A and B in the ratio $4:1$. When $10$ litres of the mixture is replaced with liquid B the ratio now becomes $2:3$. The volume of liquid A present in the jar earlier was:

(A) $20$ litres 

(B) $10$ litres 

(C) $16$ litres 

(D) $15$ litres 

$A, B, C, D$ are four consecutive odd integers and their average is $42$. What is the product of $B$ and $D$?

(A) $1860$

(B) $1890$

(C) $1845$

(D) $1677$

Which one of the following numbers is exactly divisible by $99$?

(A) $42767$

(B) $31781$

(C) $21187$

(D) $53658$