List of top Quantitative Aptitude Questions asked in CAT

Find: \(\sum_{k=1}^{2007} \sqrt{1 + \frac{1}{k^2} + \frac{1}{(k+1)^2}}\)

Which of the following cannot be true?

Consider obtuse-angled triangles with sides \(8\) cm, \(15\) cm, and \(x\) cm, where \(x\) is integer. How many such triangles exist?

Square \(ABCD\) has midpoints \(E, F, G, H\) of sides \(AB, BC, CD, DA\) respectively. Let \(L\) be the line through \(F\) and \(H\). Points \(P, Q\) are on \(L\) inside \(ABCD\) such that \(\angle APD = \angle BQC = 120^\circ\). What is the ratio of area of \(ABQCDP\) to the remaining area?

What is the number of distinct terms in the expansion of \((a + b + c)^{20}\)?

Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

The seed of any positive integer \(n\) is defined as: \[ \text{seed}(n) = n, \ \text{if } n<10 \] \[ \text{seed}(n) = \text{seed}(s(n)), \ \text{otherwise} \] where \(s(n)\) is the sum of digits of \(n\). How many positive integers \(n\), such that \(n<500\), will have \(\text{seed}(n) = 9\)?

In \(\triangle ABC\), \(AB = 17.5\) cm, \(AC = 9\) cm. Let \(D\) be a point on \(BC\) such that \(AD \perp BC\) and \(AD = 3\) cm. What is the radius of the circumcircle of \(\triangle ABC\)?

Let \(f(x)\) be a function satisfying \(f(x) f(y) = f(xy)\) for all real \(x, y\). If \(f(2) = 4\), then what is the value of \(f\left( \frac12 \right)\)?

The number of common terms in the two sequences \(17, 21, 25, \ldots, 417\) and \(16, 21, 26, \ldots, 466\) is:

How many integers, greater than \(999\) but not greater than \(4000\), can be formed with the digits \(0, 1, 2, 3, 4\), if repetition of digits is allowed?

Neelam rides her bicycle from her house at \(A\) to her office at \(B\), taking the shortest path. The number of possible shortest paths that she can choose is:

Neelam rides her bicycle from her house at \(A\) to her club at \(C\), via \(B\) taking the shortest path. The number of possible shortest paths that she can choose is:

A shop stores \(x\) kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of \(x\)?

What are the last two digits of \(7^{2008}\)?

What is the other root of \(f(x) = 0\)?

If the roots of the equation \(x^3 - ax^2 + bx - c = 0\) are three consecutive integers, then what is the smallest possible value of \(b\)?

What is the value of \(a + b + c\) given the above conditions?

The integers \(1, 2, \ldots, 40\) are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say \(a\) and \(b\), currently on the blackboard are erased and a new number \(a + b - 1\) is written. What will be the number left on the board at the end?

Rahim plans to draw a square JKLM with point O on side JK but is not successful. Why?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.

ABC Corporation needs at least 400 kilolitres of water in its factory at all times. It considers a spherical tank with uniform wall thickness. The outer diameter of the tank is 10 m. Is the tank capacity adequate?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weighs 30,000 kg when empty, and is made of material with density 3 g/cc.

The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, \( W_I \), of Section I is smaller than the average weight \( W_{II} \) of Section II. If the heaviest student, Deepak, of Section II is moved to Section I, and the lightest student, Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched.
A: \( W_{II} - W_I = 1.0 \)
B: Moving Deepak from Section II to I (without any move to II) makes the average weights of the two sections equal.

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

A function \( f(x) \) satisfies \( f(1) = 3600 \) and \( f(1) + f(2) + \ldots + f(n) = n^2 f(n) \) for all positive integers \( n>1 \). What is the value of \( f(9) \)?

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to: