CAT 2003 Slot 2 — QA Questions with Solutions

QA

Similarity of TrianglesEasy

Q1.

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 a 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?

QA

VariationEasy

Q2.

In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years namely 2001, 2002 and 2003. If floods are again expected in 2004, the number of huts expected to be destroyed is:

QA

RatioEasy

Q3.

Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer?

QA

Prime and Composite NumbersEasy

Q4.

If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is:

QA

Basics of QuadrilateralsEasy

Q5.

A square tin 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?

QA

Basics of TSD/ProportinalityEasy

Q6.

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 hours along their respective roads and reach points B and C on R₁ and R₂, respectively. There is a straight line path 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 CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and Shyam’s return to the point A is:

QA

Prime and Composite NumbersEasy

Q7.

Let x and y be positive integers such that x is prime and y is composite. Then,

QA

Simple EquationsEasy

Q8.

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. The survey found

15 had air conditioning,
2 had air conditioning and power windows but no radios,
12 had radio,
6 had air conditioning and radio, but no power windows,
11 had power windows,
4 had radio and power windows and
3 had all three options.

What is the number of cars that had none of the options?

QA

Number TheoryEasy

Q9.

If n is such that 36 ≤ n ≤ 72, then x = $\frac{n^{2} + 2 \sqrt{n} (n + 4) + 16}{n + 4 \sqrt{n} + 4}$ satisfies

QA

Number TheoryEasy

Q10.

If 13x + 1 < 2z, and z + 3 = 5y², then

QA

Prime and Composite NumbersEasy

Q11.

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,

QA

ModulusEasy

Q12.

If |b| ≥ 1 and x = –|a|b, then which one of the following is necessarily true?

QA

Basics of Mensuration/PrismEasy

Passage / Data

Answer the following question based on the information given below.

Consider a cylinder of height h cms and radius r = 2/π cms 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.)

Q13.

What is the vertical spacing in cms between two consecutive turns?

QA

Basics of Mensuration/PrismEasy

Passage / Data

Answer the following question based on the information given below.

Consider a cylinder of height h cms and radius r = 2/π cms 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.)

Q14.

The same string, when wound on the exterior four walls of a cube of side n cms, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale).

The length of the string, in cms, is

QA

Basics of Mensuration/PrismEasy

Passage / Data

Answer the following question based on the information given below.

Consider a cylinder of height h cms and radius r = 2/π cms 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.)

Q15.

In the setup of the previous two questions, how is h related to n?

QA

2 CirclesEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q16.

Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a, b and c, respectively. Which of the following is true?

QA

2 CirclesEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q17.

Sprinter A traverses distances A₁A₂, A₂A₃, and A₃A₁ at average speeds of 20, 30 and 15 respectively. B traverses her entire path at a uniform speed of $(10 \sqrt{3} + 20) .$ C traverses distances C₁C₂, C₂C₃, and C₃C₁ at average speeds of $\frac{40}{3} (\sqrt{3} + 1), \frac{40}{3} (\sqrt{3} + 1),$ and 120 respectively. All speeds are in the same unit. Where would B and C be respectively when A finishes her sprint?

QA

2 CirclesEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q18.

Sprinters A, B and C traverse their respective paths at uniform speeds u, v and w respectively. It is known that u²: v² : w² is equal to Area A : Area B : Area C, where Area A, Area B and Area C are the areas of triangles A₁A₂A₃, B₁B₂B₃, and C₁C₂C₃ respectively.

Where would A and C be when B reaches point B₃?

QA

Infinite Geometric ProgressionEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q19.

The infinite sum $1 + \frac{4}{7} + \frac{9}{7^{2}} + \frac{16}{7^{3}} + \frac{25}{7^{4}} + . . . .$ equals

QA

SetsEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q20.

Consider the sets T_n = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3, … , 96.

How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?

QA

HexagonEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q21.

Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF?

QA

Higher Degree PolynomialsEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q22.

The number of roots common between the two equations x³+ 3x²+ 4x + 5 = 0 and x³+ 2x²+ 7x + 3 = 0 is:

QA

Solving InequalitiesEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q23.

A real number x satisfying $1 - \frac{1}{n} < x \leq 3 + \frac{1}{n},$ for every positive integer n, is best described by:

QA

LogarithmsEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q24.

If $\frac{1}{3} \log_{3} M + 3 \log_{3} N = 1 + \log_{0.008} 5,$ then

QA

Simple EquationsEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q25.

Using only 2, 5, 10, 25 and 50 paise coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs 1.01 to three different persons?

QA

PolygonsEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q26.

The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c, t, and s, respectively. Then,

QA

Number TheoryEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q27.

What is the remainder when 4⁹⁶ is divided by 6?

QA

Simple EquationsEasy

Passage / Data

Answer the following question based on the information given below.

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.

Q28.

If x and y are integers then the equation 5x + 19y = 64 has:

QA

MiscellaneousEasy

Passage / Data

Answer the following question based on the information given below.

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables:

âââââââ

Thus, according to the first table f ⊕ g = a, while according to the second table g * h = f, and so on.

Also, let f² = f * f, g³= g * g * g, and so on.

Q29.

What is the smallest positive integer n such that gⁿ = e?

QA

MiscellaneousEasy

Passage / Data

Answer the following question based on the information given below.

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables:

âââââââ

Thus, according to the first table f ⊕ g = a, while according to the second table g * h = f, and so on.

Also, let f² = f * f, g³= g * g * g, and so on.

Q30.

Upon simplification, f ⊕ [f * {f ⊕ (f * f)}] equals:

QA

MiscellaneousEasy

Passage / Data

Answer the following question based on the information given below.

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables:

âââââââ

Thus, according to the first table f ⊕ g = a, while according to the second table g * h = f, and so on.

Also, let f² = f * f, g³= g * g * g, and so on.

Q31.

Upon simplification, (a¹⁰ * (f¹⁰ ⊕ g⁹)} ⊕ e⁸ equals

QA

Simple EquationsEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q32.

How many strings of letters can possibly be formed using the above rules?

QA

Simple EquationsEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q33.

How many strings of letters can possibly be formed using the above rules such that the third letter of the string is e?

QA

Words (P&C)Easy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q34.

There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?

QA

Similarity of TrianglesEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q35.

In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC and QD is parallel to CP. In âARC, ∠ARC = 90°, and in ΔPQS, ∠PSQ = 90°. The length of QS is 6 cm. What is the ratio AP : PD?

QA

Height & DistanceEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q36.

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?

QA

Similarity of TrianglesEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q37.

In the figure (not drawn to scale) given below, if AD = CD = BC, and ∠BCE = 96°, how much is ∠DBC?

QA

Discriminant and Roots of Quadratic EquationEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q38.

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax² + bx + 1 = 0 having real roots is:

QA

Number TheoryEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q39.

If three positive real numbers x, y, z satisfy y – x = z – y and xyz = 4, then what is the minimum possible value of y?

QA

Words (P&C)Easy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q40.

An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, ... , 9 such that the first digit of the code is non-zero. The code, handwritten on a slip, can however potentially create confusion, when read upside down – for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?

QA

Basics of Mensuration/PrismEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q41.

Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps: the original square of side a is divided into n smaller squares, not necessarily of the same size; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is:

QA

Basics of CirclesEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q42.

In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with centre at O. The length of side AB is greater than that of side BC.

The ratio of the area of the circle to the area of the recrangle ABCD is π : $\sqrt{3}$ .

The line segment DE intersects AB at E such that ∠ODC = ∠ADE. What is the ratio AE : AD?

QA

LogarithmsEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q43.

If log₁₀ x - log₁₀ $\sqrt{x}$ = 2 log_x 10, then a possible value of x is given by:

QA

Number TheoryEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q44.

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

QA

Tangents & SecantsEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q45.

In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is:

QA

LogarithmsEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q46.

What is the sum of n terms in the series

$\log m + \log \frac{m^{2}}{n} + \log \frac{m^{3}}{n^{2}} + \log \frac{m^{4}}{n^{3}} + \dots + \log \frac{m^{n}}{n^{n - 1}} ?$

QA

Basics of QuadrilateralsEasy

Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

The first letter is any vowel.
The second letter is m, n or p.
If the second letter is m, then the third letter is any vowel which is different from the first letter.
If the second letter is n, then the third letter is e or u.
1. If the second letter is p, then the third letter is the same as the first letter.

Q47.

Let S₁be a square of side a. Another square S₂ is formed by joining the mid-points of the sides of S₁. The same process is applied to S₂ to form yet another square S₃, and so on. If A₁, A₂, A₃... are the areas and P₁, P₂, P₃... are the perimeters of S₁, S₂, S₃... respectively,

then the ratio $\frac{P_{1} + P_{2} + P_{3} + . . . . .}{A_{1} + A_{2} + A_{3} + . . .}$ equals:

QA

MiscellaneousEasy

Passage / Data

Answer the following question based on 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, and 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 + 5 + 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.

Q48.

The value of the numeral MDCCLXXXVII is:

QA

MiscellaneousEasy

Passage / Data

Answer the following question based on 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, and 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 + 5 + 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.

Q49.

The value of the numeral MCMXCIX is

QA

MiscellaneousEasy

Passage / Data

Answer the following question based on 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, and 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 + 5 + 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.

Q50.

Which of the following can represent the numeral for 1995?

a. MCMLXXV
b. MCMXCV
c. MVD
d. MVM

CAT 2003 Slot 2 — QA

CAT 2003 Slot 2 · QA