Quantitative Aptitude - Arithmetic Ability Questions

84% of a number is 105. The number is :

If tanA - cotA = x, then value of x is?

What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?

In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels always come together?

The average of marks of 17 students in an examination was calculated as 71. But it was later found that the mark of one student had been wronglyentered as 65 instead of 56 and another as 24 instead of 50. The correct average is

A train travels 40% faster than a car. Both start from point A at the same time and reach point B, 140 km away at the same time. On the way the train takes 25 minutes for stopping at the stations. What is the speed (in km/hr) of the train?

How many numbers are there from 2000 to 7000 which are both perfect squares and perfect cubes?

A, B and C can do a job working alone in 50, 75 and 20 days respectively. They all work together for 4 days, then C quits. How many days will A and B take to finish the rest of the job?