List of top Quantitative Aptitude Questions asked in CAT

Let \(S_n\) denote the sum of the squares of the first \(n\) odd natural numbers. If \(S_n = 533n\), find the value of \(n\).
Auto fare in Bombay is ₹2.40 for the first 1 km, ₹2.00 per km for the next 4 km, and ₹1.20 for each additional km thereafter. Find the fare in rupees for \(k\) km (\(k \geq 5\)).
If the concentration of petrol in the second tank is 75% and the cost price of kerosene is half that of petrol, then what is Govind Lal's net profit percentage on selling the contents of the second tank given that he claims to sell the petrol at a profit of 25%?
One morning, Govind Lal the owner of the local petrol bunk, was adulterating the petrol with kerosene. He had two identical tanks—the first was full of pure petrol while the second was empty. First, he transferred an arbitrary amount of petrol from the first tank into the second and then replaced the petrol removed from the first tank with kerosene. He then repeated this process one more time but this time he ensured that by the end of the process the second tank was exactly full.
Which of the following can be the concentration of petrol in the second tank?

In the figure, \(O\) is the centre of the circle and \(AC\) is the diameter. The line \(FEG\) is tangent to the circle at \(E\). If \(\angle GEC = 52^\circ\), find the value of \(\angle E + \angle C\).

On a plate in the shape of an equilateral triangle \(ABC\) with area \(16\sqrt{3}\) sq cm, a rod \(GD\), of height 8 cm, is fixed vertically at the centre of the triangle. \(G\) is a point on the plate. If the areas of the triangles \(AGD\) and \(BGD\) are both equal to \(4\sqrt{19}\) sq cm, find the area of the triangle \(CGD\) (in sq cm).
Two cars \(A\) and \(B\) start from two points \(P\) and \(Q\) respectively towards each other simultaneously. After travelling some distance, at a point \(R\), car \(A\) develops engine trouble. It continues to travel at \(2/3\)rd of its usual speed to meet car \(B\) at point \(S\) where \(PR = QS\). If the engine trouble had occurred after car \(A\) had travelled double the distance it would have met car \(B\) at a point \(T\) where \(ST = SQ/9\). Find the ratio of speeds of \(A\) and \(B\).
Let \( f_{n+1}(x) = f_n(x) + 1 \) if \( n \) is a multiple of 3; otherwise, \( f_{n+1}(x) = f_n(x) - 1 \).
If \( f_1(1) = 0 \), then what is \( f_{50}(1) \)?
Vaibhav wrote a certain number of positive prime numbers on a piece of paper. Vikram wrote down the product of all the possible triplets among those numbers. For every pair of numbers written by Vikram, Vishal wrote down the corresponding GCD. If 90 of the numbers written by Vishal were prime, how many numbers did Vaibhav write?
There are two water drums in my house whose volumes are in the ratio \(1 : 5\). Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by 1:30 pm the smaller drum would just be full. But today, I returned early and started drawing water manually. I poured one-third into the smaller drum and the rest into the bigger drum. I continued this till the smaller drum was full. Immediately after that, I shifted the pipe into the bigger drum. If today the bigger drum was filled 12 minutes earlier than the normal time, when was the smaller drum full?
Mohan’s fixed commission is ₹560 per assignment. Cost = ₹\(2n^2\), where \(n\) = number of chairs made. If average cost per chair ≤ ₹68, then minimum and maximum values of \(n\) are:
The values of the numbers \(2^{2004}\) and \(5^{2004}\) are written one after another. How many digits are there in all?
Rajat draws a \(10 \times 10\) grid with squares numbered 1 to 100. He places two identical stones on any two separate squares. How many distinct ways are possible?
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.
If \( r, s, t \) are consecutive odd integers with \( r<s<t \), which of the following must be true?
Let \( S \) be the set of rational numbers with the following properties:
[I.] \( \frac{1}{2} \in S \)
[II.] If \( x \in S \), then both \( \frac{1}{x+1} \in S \) and \( \frac{x}{x+1} \in S \) Which of the following is true?
\( P, Q, R \) are three consecutive odd numbers in ascending order. If the value of three times \( P \) is three less than two times \( R \), find the value of \( R \).
Consider the following statements: When two straight lines intersect, then:
[I.] Adjacent angles are complementary
[II.] Adjacent angles are supplementary
[III.] Opposite angles are equal
[IV.] Opposite angles are supplementary Which of these statements are correct?
A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates \( A \) and \( B \) on the boundary is 7 metres. The distance of the pole from one of the gates is:
From a square piece of cardboard measuring \( 2a \) on each side, a box with no top is to be formed by cutting out from each corner a square with sides \( b \) and bending up the flaps. The value of \( b \) for which the box has the greatest volume is:
Consider the following statements:
[I.] If \( a^x = b^x = c^x = abc \), then \( xyz = 1 \)
[II.] If \( a^p = b^q = c^r \) and \( a^q b^r c^p = 1 \), then \( xyz = 1 \)
[III.] If \( x^a = y^b = z^c \) and \( ab + bc + ca = 0 \), then \( xyz = 1 \)
If \( a, b, c \) are three real numbers, then which of the following is not true?
Let \( S \) denote the infinite sum: \[ S = 2 + 5x + 9x^2 + 14x^3 + 20x^4 + \ldots \quad \text{where } |x|<1 \] and the coefficient of \( x^n \) is \( \frac{1}{2}n(n+3) \). Then \( S \) equals:
ABCD is a rectangle. Points \( P \) and \( Q \) lie on \( AD \) and \( AB \) respectively. If triangles \( PAQ, QBC, \) and \( PCD \) all have the same areas and \( BQ = 2 \), then \( AQ = \) ?

For what value of \( k \) does the following pair of equations yield a unique solution for \( x \), such that the solution is positive?

\(x^2 - 3y^2 = 0 \)
\(x^2 - 6y^2 + k = 0 \)