List of top Quantitative Aptitude Questions asked in CAT

Five-digit numbers are formed using only 0, 1, 2, 3, 4 exactly once. What is the difference between the maximum and minimum number that can be formed?

You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg and each emerald weighs 0.4 kg. Your bag can carry at most 12 kg. What should you collect to get the maximum wealth?

After what time will the two persons Tez and Gati meet while moving around the circular track? Both of them start at the same point and at the same time.
I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter.
II. Gati can complete one entire lap in exactly 10 s.

Three friends P, Q and R are wearing hats, either black or white. Each person can see the hats of the other two persons. What is the colour of P's hat?
I. P says that he can see one black hat and one white hat.
II. Q says that he can see one white hat and one black hat.

What is the value of x and y?
I. \( 3x + 2y = 45 \)
II. \( 10.5x + 7y = 157.5 \)

Is the number completely divisible by 99?
I. The number is divisible by 9 and 11 simultaneously.
II. If the digits of the number are reversed, the number is divisible by 9 and 11.

What is the value of \( a^3 + b^3 \)?
I. \( a^2 + b^2 = 22 \)
II. \( ab = 3 \)

In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF and AE = 22, BE = 6, CF = 16 and BF = 2. Find the length of the line joining the mid-points of the sides AB and BC.

Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.
What is X's average speed for the entire journey (to and fro)?

Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.
If X had started the return journey from India at 2.55 a.m. on the same day that he reached there, after how much time would he reach Frankfurt?

The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate.
Starting on February 25, 1996 (Sunday), if Raja had finished his job on April 2, 1996, when would T and S together likely to have completed the job, had they started on the same day as Raja?

The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate.
Raja starts working on February 25 (Sunday), 1996, and finishes the job on March 2, 1996. How much time would T and J take to finish the same job if both start on the same day as Raja?

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

A, B and C are defined as follows.
\( A = (2.000004) \div \big((2.000004)^2 + 4.000008\big) \);
\( B = (3.000003) \div \big((3.000003)^2 + 9.000009\big) \);
\( C = (4.000002) \div \big((4.000002)^2 + 8.000004\big) \).
Which of the following is true about the values of the above three expressions?

The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh squares, counting from the innermost square.

ABC is a three-digit number in which \( A > 0 \). The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?

For these questions the following functions have been defined.
\( la(x, y, z) = \min(x + y,\ y + z) \)
\( le(x, y, z) = \max(x - y,\ y - z) \)
\( ma(x, y, z) = \dfrac{1}{2}\big(le(x, y, z) + la(x, y, z)\big) \)
For \( x = 15,\ y = 10 \) and \( z = 9 \), find the value of \( le\big(x,\ \min(y,\ x - z),\ le(9,\ 8,\ ma(x, y, z))\big) \).

For these questions the following functions have been defined.
\( la(x, y, z) = \min(x + y,\ y + z) \)
\( le(x, y, z) = \max(x - y,\ y - z) \)
\( ma(x, y, z) = \dfrac{1}{2}\big(le(x, y, z) + la(x, y, z)\big) \)
Given that \( x > y > z > 0 \). Which of the following is necessarily true?

A man earns \( x\% \) on the first Rs. 2,000 and \( y\% \) on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from Rs. 5,000 of income, find \( x\% \).

Which of the following is true?

The sum of the areas of two circles, which touch each other externally, is \(153\pi\). If the sum of their radii is 15, find the ratio of the larger to the smaller radius.

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q?

A student instead of finding the value of \(\frac{7}{8}\) of a number, found the value of \(\frac{7}{18}\) of the number. If his answer differed from the actual one by 770, find the number.

An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?