List of top Quantitative Aptitude Questions asked in CAT

If \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} = r \), then \( r \) cannot take any value except.
A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?
If \(f(x) = x^3 - 4x + p\), and \(f(0)\) and \(f(1)\) are of opposite signs, then which of the following is necessarily true?
Two boats, traveling at 5 and 10 km per hour, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide?
A rectangular sheet of paper, when halved by folding it at the midpoint of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?
If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?
On January 1, 2004, two new societies \(S_1\) and \(S_2\) are formed, each with \(n\) numbers. On the first day of each subsequent month, \(S_1\) adds \(b\) members, while \(S_2\) multiplies its current numbers by a constant factor \(r\). Both the societies have the same number of members on July 2, 2004. If \(b = 10.5n\), what is the value of \(r\)?
If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?
Let $n(>1)$ be a composite integer such that $\sqrt{n}$ is not an integer. Consider the following statements: A: $n$ has a perfect integer-valued divisor which is greater than 1 and less than $\sqrt{n}$ B: $n$ has a perfect integer-valued divisor which is greater than $\sqrt{n}$ but less than $n$ Then:

Answer the questions on the basis of the information given below.
The seven basic symbols in a certain numeral system and their respective values are as follows:
• I =1, V=5, X=10, L=50, C=100, D=500, M=1000
In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols. For example,
XXVII = 10 +10+10+5+1+1+1=27.
An exception to the left-to-right reading occurs when a symbol is followed immediately by a symbol of greater value; then the smaller value is subtracted from the larger.
For example, XLVI = (50- 10) + 5 + 1 = 46. 

Consider three circular parks of equal size with centres at A1, A2, and A3, respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3, and C1C2C3, as shown. Three sprinters A, B, and C begin running from points A1, B1, and C1, respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.

Consider a cylinder of height h cm and radius \(r = \frac{2}{ π}\) cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns).

Two binary operations \( \oplus \) and \( \) are defined over the set \( \{ a, e, f, g, h \} \) as per the following tables:

Thus, according to the first table \( f \oplus g = a \), while according to the second table \( g h = f \), and so on. Also, let \( f^2 = f \oplus f \), \( g^3 = g g g \), and so on.

\( \oplus \)aefgha
aaaefgh
eeefgha
fffghae
ggghaef
hhhaefg
\( \)aefgh
aaaaaa
eaefgh
fafheg
gagehf
hahgfe

A string of three English letters is formed as per the following rules:
I. The first letter is any vowel.
II. The second letter is m, n or p.
III. If the second letter is m, then the third letter is any vowel which is different from the first letter.
IV. If the second letter is n, then the third letter is e or u.
V. If the second letter is p, then the third letter is the same as the first letter.

A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows were already installed. Following were the observation of the survey:
I. 15 had air conditioning
II. 2 had air conditioning and power windows but no radios
III. 12 had radio
IV. 6 had air conditioning and radio but no power windows
V. 11 had power windows
VI. 4 had radio and power windows
VII. 3 had all three options
What is the number of cars that had none of the options?
Let $x$ and $y$ be positive integers such that $x$ is prime and $y$ is composite. Then,
In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, the same number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years — 2001, 2002 and 2003. If floods are expected again in 2004, the number of huts expected to be destroyed is:
A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?
If $a$, $a+2$ and $a+4$ are prime numbers, then the number of possible solutions for $a$ is:
A square in sheet of side 12 inches is converted into a box with open top in the following steps. The sheet is placed horizontally. Then, equal-sized squares, each of side $x$ inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If $x$ is an integer, then what value of $x$ maximizes the volume of the box?
If $|b| \geq |a|$ and $x = |a| - b$, then which one of the following is necessarily true?
Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/hr. They continue walking for 4 hr along their respective roads and reach points B and C on R1 and R2 respectively. There is a straight line connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments BC and CA. Their speeds remain unchanged. The time interval (in hours) between Ram's and Shyam's return to the point A is:
Let $a$, $b$, $c$, and $d$ be integers such that $a = 6b$, $a = 12c$, and $2b = 9d = 12e$. Then which of the following pairs contains a number that is not an integer?
The number of roots common between the two equations $x^3 + 3x^2 + 4x + 5 = 0$ and $x^4 + 2x^3 + 7x + 3 = 0$ is:
If $n$ is such that $36 \leq n \leq 72$, then $x = \frac{n^2 + 2\sqrt{n(n+4)} + 16}{n + 4\sqrt{n + 4}}$ satisfies: