Arihant Expert Team Solutions for Exercise 1: Practice Questions

The greatest number which on dividing $42, 49$ and  $56$ will leave $6, 7$ and $8$ respectively as remainder is_____.

The greatest number which on dividing $152, 277$ and $427$ leaves an equal remainder, is:

Find the smallest $4$-digit number, such that when divided by $12, 18, 21$ and $28$, it leaves remainder $3$ in each case.

Samantha, Jessica and Roseline begin to jog around a circular stadium. They complete their revolutions in $84 s, 56 s$ and $63 s$ respectively. After how many seconds will they be together at the starting point?

Four bells ring at intervals of $30$ $\min$, $1\mathrm{h}$, $1\frac{1}{2}\mathrm{h}$ and $1\mathrm{h} 45 \min$, respectively. They ring simultaneously at $12$ noon. All the bells will ring simultaneously again at:

Three rods of lengths $15 m$, $42 m$ and $39 m$ are to be cut into pieces of equal length. What is the greatest possible length of each piece?

Seven bells ring at intervals of $2, 3, 4, 6, 8, 9$ and $12$ minutes respectively. They started ringing simultaneously at $5:00$ a.m. in the morning. What will be the next time when they all right simultaneously?

Harish, Dilip and Asha start running around a circular stadium and complete one round in 27s, 9s and 36s, respectively. In how much time will they meet again at the starting point?