Recent questions tagged quantitative-aptitude / Aptitude Overflow

1 votes

1 answer

1441

CAT 2007 | Question: 10
Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? $3$ $2$ $4$ $0$ $1$

Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?$3$$2$$4$$0$$1$

go_editor

13.9k points

1.5k views

go_editor asked Dec 6, 2015

1 votes

0 answers

1442

CAT 2007 | Question: 08
Directions for the below question. Cities A and B are in different time zones. A is located $3000$ km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same ... difference between A and B? $1$ hour $30$ minutes $2$ hours $2$ hours $30$ minutes $1$ hour cannot be determined

Directions for the below question.Cities A and B are in different time zones. A is located $3000$ km east of B. The table below describes the schedule of an airline opera...

go_editor

13.9k points

801 views

go_editor asked Dec 6, 2015

0 votes

0 answers

1443

CAT 2007 | Question: 06
Directions for below question: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others. Option A: Invest in a ... guaranteed return to Shabnam is $0.25\%$ $0.10\%$ $0.20\%$ $0.15\%$ $0.30\%$

Directions for below question:Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. ...

go_editor

13.9k points

899 views

go_editor asked Dec 6, 2015

0 votes

1 answer

1444

CAT 2007 | Question: 04
Directions for the below question: Let $S$ be the set of all pairs $(i, j)$ where $ 1 \leq i \leq j < n$ and $n \geq 4$. Any two distinct number of $S$ are called friends' if they have one constituent of the pairs in common and enemies' otherwise. For example, if $n=4$ ... $2n-7$ $\frac{1}{2} (n^2 - 5n +6)$ $\frac{1}{2} (n^2 - 7n + 14)$

Directions for the below question:Let $S$ be the set of all pairs $(i, j)$ where $ 1 \leq i \leq j < n$ and $n \geq 4$. Any two distinct number of $S$ are called ‘frien...

go_editor

13.9k points

780 views

go_editor asked Dec 6, 2015

0 votes

0 answers

1445

CAT 2007 | Question: 03
Two circles with centres $\text{P}$ and $\text{Q}$ cut each other at two distinct points $\text{A}$ and $\text{B}.$ The circles have the same radii and neither $\text{P}$ nor $\text{Q}$ falls within the intersection of the circles. What is the smallest range that ... Between $0$ and $90$ Between $0$ and $30$ Between $0$ and $60$ Between $0$ and $75$ Between $0$ and $45$

Two circles with centres $\text{P}$ and $\text{Q}$ cut each other at two distinct points $\text{A}$ and $\text{B}.$ The circles have the same radii and neither $\text{P}$...

go_editor

13.9k points

389 views

go_editor asked Dec 6, 2015

2 votes

1 answer

1446

CAT 2007 | Question: 02
A quadratic function f(x) attains a maximum of $3$ at $x=1.$ The value of the function at $x=0$ is $1.$ What is the value of $f(x)$ at $x=10?$ $-119$ $-159$ $-110$ $-180$ $-105$

A quadratic function f(x) attains a maximum of $3$ at $x=1.$ The value of the function at $x=0$ is $1.$ What is the value of $f(x)$ at $x=10?$$-119$$-159$$-110$$-180$$-10...

go_editor

13.9k points

1.9k views

go_editor asked Dec 6, 2015

1 votes

1 answer

1447

CAT 2007 | Question: 01
The price of Darjeeling tea ( in rupees per kilogram) is $100 + 0.10 n,$ on $n$-th day of $2007\; (n=1, 2, 3, \dots,100),$ and then remains constant. On the other hand, the price of Ooty tea ( in rupees per kilogram) is $89 +0.15 n$ ... On which date in $2007$ will the prices of these two varieties of tea be equal? May $21$ April $11$ May $20$ April $10$ June $30$

The price of Darjeeling tea ( in rupees per kilogram) is $100 + 0.10 n,$ on $n$-th day of $2007\; (n=1, 2, 3, \dots,100),$ and then remains constant. On the other hand, t...

go_editor

13.9k points

796 views

go_editor asked Dec 5, 2015

2 votes

1 answer

1448

CAT 2008 | Question: 25
suppose, the seed of any positive integer $n$ is defined as follows: seed$(n) = n,$ if $n < 10$ $=$seed$(s(n)),$ otherwise where $s(n)$ indicates the sum of digits $n.$ For example, seed$(7)=7,$ seed$(248) =$ seed$(2+4+8) =$ seed$(14) =$ ... $(5) = 5$ etc. How many positive integers $n,$ such that $n <500,$ will have seed$(n) =9?$ $39$ $72$ $81$ $108$ $55$

suppose, the seed of any positive integer $n$ is defined as follows:seed$(n) = n,$ if $n < 10$ $=$seed$(s(n)),$ otherwisewhere $s(n)$ indicates the sum of d...

go_editor

13.9k points

1.0k views

go_editor asked Nov 29, 2015

0 votes

0 answers

1449

CAT 2008 | Question: 24
Rahim plans to Drive from city $\text{A}$ to station $\text{C}$, at the speed of $70$ km per hour, to catch a train arriving there from $\text{B}$. He must reach $\text{C}$ at least $15$ minutes before the arrival of the train. The train leaves $\text{B}$ ... leave $\text{A}$ and still catch the train is closet to $6:15$ am $6:30$ am $6:45$ am $7:00$ am $7:15$ am

Rahim plans to Drive from city $\text{A}$ to station $\text{C}$, at the speed of $70$ km per hour, to catch a train arriving there from $\text{B}$. He must reach $\text{C...

go_editor

13.9k points

626 views

go_editor asked Nov 29, 2015

0 votes

0 answers

1450

CAT 2008 | Question: 23
Two circles, both of radii $1$ cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecting region? $\frac{\pi}{3} - \frac{\sqrt{3}} {4} $ $\frac{2 \pi}{3} + \frac{\sqrt{3}} {2} $ ... $\frac{4 \pi}{3} + \frac{\sqrt{3}} {2} $ $\frac{2 \pi}{3} - \frac{\sqrt{3}} {2} $

Two circles, both of radii $1$ cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecti...

go_editor

13.9k points

439 views

go_editor asked Nov 29, 2015

0 votes

0 answers

1451

CAT 2008 | Question: 20
Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square root equals to the total of the three originals integers. Which of the following best describes the minimum, say m, of these three integers? ... $7 \leq m \leq 9$ $10 \leq m \leq 12$ $13 \leq m \leq 15$

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square root equals to t...

go_editor

13.9k points

481 views

go_editor asked Nov 28, 2015

1 votes

1 answer

1452

CAT 2008 | Question: 19
Consider obtuse-angled triangles with sides $8$ cm, $15$ cm and $x$ cm. If x is an integer, then how many such triangles exist? $5$ $21$ $10$ $15$ $14$

Consider obtuse-angled triangles with sides $8$ cm, $15$ cm and $x$ cm. If x is an integer, then how many such triangles exist?$5$$21$$10$$15$$14$

go_editor

13.9k points

983 views

go_editor asked Nov 28, 2015

1 votes

1 answer

1453

CAT 2008 | Question: 18
Consider a square $\text{ABCD}$ with midpoints $\text{E, F, G, H}$ of $\text{AB, BC, CD}$ and $\text{DA}$ respectively. Let $\text{L}$ denote the line passing through $\text{F}$ and $\text{H}.$ Consider points $\text{P}$ and $\text{Q},$ on $\text{L}$ and inside $\text{ABCD},$ ... $2 + \sqrt{3}$ $\frac{10-3 \sqrt{3} } {9} $ $1+ \frac{1}{\sqrt{3} }$ $2 \sqrt{3} -1$

Consider a square $\text{ABCD}$ with midpoints $\text{E, F, G, H}$ of $\text{AB, BC, CD}$ and $\text{DA}$ respectively. Let $\text{L}$ denote the line passing through $\t...

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13.9k points

3.1k views

go_editor asked Nov 28, 2015

0 votes

0 answers

1454

CAT 2008 | Question: 17
The integers $1, 2, \dots, 40$ 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? $820$ $821$ $781$ $819$ $780$

The integers $1, 2, \dots, 40$ are written on a blackboard. The following operation is then repeated $39$ times. In each repetition, any two numbers, say a and b, current...

go_editor

13.9k points

429 views

go_editor asked Nov 28, 2015

0 votes

1 answer

1455

CAT 2008 | Question: 14
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 $b?$ $-\frac{1}{\sqrt{3} }$ $-1$ $0$ $1$ $\frac{1}{\sqrt{3} }$

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?$$-\frac{1}{\sqrt{3} }$$-1$$0$$1$$\frac...

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13.9k points

725 views

go_editor asked Nov 28, 2015

2 votes

1 answer

1456

CAT 2008 | Question: 13
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 $f\left(\frac{1}{2}\right)$ $0$ $\frac{1}{4}$ $\frac{1}{2}$ $1$ cannot be determined

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(\frac{1}{2}\right)$$0$$\frac{1}{4}$$\frac{1}{2...

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13.9k points

715 views

go_editor asked Nov 28, 2015

0 votes

2 answers

1457

CAT 2008 | Question: 12
The number of common terms in the two sequences $17, 21, 25,\dots,417$ and $16, 21 26,\dots,466$ is $78$ $19$ $20$ $27$ $22$

The number of common terms in the two sequences $17, 21, 25,\dots,417$ and $16, 21 26,\dots,466$ is$78$$19$$20$$27$$22$

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13.9k points

1.1k views

go_editor asked Nov 28, 2015

2 votes

1 answer

1458

CAT 2008 | Question: 10
Let $f(x) = ax^2 + bx +c$, where $a$, $b$ and $c$ are certain constants and $a \neq 0$. It is known that $f(5) = -3 f(2) $ and that 3 is a root of $f(x)=0$. What is the other root of $f(x)=0?$ $-7$ $-4$ $2$ $6$ cannot be determined

Let $f(x) = ax^2 + bx +c$, where $a$, $b$ and $c$ are certain constants and $a \neq 0$. It is known that $f(5) = -3 f(2) $ and that 3 is a root of $f(x)=0$.What is the ot...

go_editor

13.9k points

895 views

go_editor asked Nov 28, 2015

0 votes

1 answer

1459

CAT 2008 | Question: 09
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. There after no rice left in the ... $5 \leq x \leq 8$ $9 \leq x \leq 12$ $11 \leq x \leq 14$ $13 \leq x \leq 18$

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. ...

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13.9k points

5.7k views

go_editor asked Nov 28, 2015

0 votes

0 answers

1460

CAT 2008 | Question: 08
Find the sum $\sqrt{1+ \frac{1}{1^2} + \frac{1}{2^2} } + \sqrt{1+ \frac{1}{2^2} + \frac{1}{3^2} } + \dots + \sqrt{1+ \frac{1}{2007^2} + \frac{1}{2008^2} }$ $2008 - \frac{1}{2008}$ $2007 - \frac{1}{2007}$ $2007 - \frac{1}{2008}$ $2008 - \frac{1}{2007}$ $2008 - \frac{1}{2009}$

Find the sum $\sqrt{1+ \frac{1}{1^2} + \frac{1}{2^2} } + \sqrt{1+ \frac{1}{2^2} + \frac{1}{3^2} } + \dots + \sqrt{1+ \frac{1}{2007^2} + \frac{1}{2008^2} }$$2008 - \frac{...

go_editor

13.9k points

563 views

go_editor asked Nov 28, 2015

0 votes

0 answers

1461

CAT 2008 | Question: 07
In a triangle $\text{ABC}$, the lengths of the sides $\text{AB}$ and $\text{AC}$ equal $17.5$ cm and $9$ cm respectively. Let $\text{D}$ be a point on the line segment $\text{BC}$ such that $\text{AD}$ is perpendicular to $\text{BC}.$ ... what is the radius (in cm) of the circle circumscribing the triangle $\text{ABC}?$ $17.05$ $27.85$ $22.45$ $32.25$ $26.25$

In a triangle $\text{ABC}$, the lengths of the sides $\text{AB}$ and $\text{AC}$ equal $17.5$ cm and $9$ cm respectively. Let $\text{D}$ be a point on the line segment $\...

go_editor

13.9k points

479 views

go_editor asked Nov 28, 2015

0 votes

0 answers

1462

CAT 2008 | Question: 05
Consider a right circular cone of base radius $4$ cm and height $10$ cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder. $\frac{100 \pi}{3}$ $\frac{80 \pi}{3}$ $\frac{120 \pi}{7}$ $\frac{130 \pi}{9}$ $\frac{110 \pi}{7}$

Consider a right circular cone of base radius $4$ cm and height $10$ cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of t...

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13.9k points

649 views

go_editor asked Nov 28, 2015

0 votes

2 answers

1463

CAT 2008 | Question: 06
What are the last two digits of $7^{2008}?$ $21$ $61$ $01$ $41$ $81$

What are the last two digits of $7^{2008}?$$21$$61$$01$$41$$81$

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13.9k points

950 views

go_editor asked Nov 26, 2015

0 votes

1 answer

1464

CAT 2008 | Question: 02
What is the number of distinct terms in the expansion of $(a + b + c)^{20}?$ $231$ $253$ $242$ $210$ $228$

What is the number of distinct terms in the expansion of $(a + b + c)^{20}?$$231$$253$$242$$210$$228$

go_editor

13.9k points

811 views

go_editor asked Nov 26, 2015

1 votes

1 answer

1465

CAT 2008 | Question: 01
How many integers, greater than $999$ but not greater than $4000,$ can be formed with the digits $0, 1, 2, 3$ and $4,$ if repetition of digits is allowed? $499$ $500$ $375$ $376$ $501$

How many integers, greater than $999$ but not greater than $4000,$ can be formed with the digits $0, 1, 2, 3$ and $4,$ if repetition of digits is allowed?$499$$500$$375$$...

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13.9k points

573 views

go_editor asked Nov 26, 2015

0 votes

1 answer

1466

arrangement-P and C
In how many ways 8 persons can be arranged on two round tables consisting of 4 chairs each? a)720 b)1260 c)2520 d)5040

In how many ways 8 persons can be arranged on two round tables consisting of 4 chairs each?a)720b)1260c)2520d)5040

Pooja Palod

1.8k points

996 views

Pooja Palod asked Sep 27, 2015

2 votes

2 answers

1467

In the given figure, ∠BAC = 120° and AD is the bisector of ∠BAC.

In the given figure, $∠BAC = 120º$ and $AD$ is the bisector of $∠BAC$. If $\frac{(AD)(AB)}{BD} = \frac{AE}{EC}( AE + EC )$ and $∠EDC = ∠ECD$, what is the ratio ...

makhdoom ghaya

8.0k points

1.6k views

makhdoom ghaya asked Aug 25, 2015

0 votes

2 answers

1468

In a section of a timber mill, cylindrical logs of wood, all of uniform dimensions, arrive as the input and are cut into smaller cylindrical pieces of the same radius using manual and mechanical saws.

In a section of a timber mill, cylindrical logs of wood, all of uniform dimensions, arrive as the input and are cut into smaller cylindrical pieces of the same radius usi...

makhdoom ghaya

8.0k points

1.6k views

makhdoom ghaya asked Aug 25, 2015

9 votes

2 answers

1469

Venn Diagram Question
There are $150$ students in a class. The number of students who play Cricket, Hockey, and Basketball are $125, 130, 135$ respectively. If $5$ students do not play any of the three games, the number of students playing all the three games must be at least $90$ $95$ $100$ $105$

There are $150$ students in a class. The number of students who play Cricket, Hockey, and Basketball are $125, 130, 135$ respectively. If $5$ students do not play any of ...

makhdoom ghaya

8.0k points

17.2k views

makhdoom ghaya asked Aug 25, 2015

1 votes

2 answers

1470

Rohan and Sohan start simultaneously from a point A on a circular track and run in the same direction.

Rohan and Sohan start simultaneously from a point A on a circular track and run in the same direction. The speed of Rohan is nine times the speed of Sohan. How many times...

makhdoom ghaya

8.0k points

4.9k views

makhdoom ghaya asked Aug 24, 2015

0 votes

2 answers

1471

If x1/5 > x1/3, then how many of the following statements are definitely true about x?

If x1/5 x1/3 , then how many of the following statements are definitely true about x?x2 x3x1/3 x41 x1/3 x-3x-1/3 x31234

makhdoom ghaya

8.0k points

990 views

makhdoom ghaya asked Aug 24, 2015

1 votes

1 answer

1472

Y is a subset of A such that the geometric mean of no two elements of Y is 350.

Given A = { 1, 3, 9, 27, 81,................................3100 }Y is a subset of A such that the geometric mean of no two elements of Y is 350. N is the maximum possib...

makhdoom ghaya

8.0k points

676 views

makhdoom ghaya asked Aug 24, 2015

0 votes

2 answers

1473

If f(x) = minimum of (3x + 5, 10 - 2x), what is the maximum possible value of f(x)?

If f (x) = minimum of (3x + 5, 10 - 2x), what is the maximum possible value of f (x)?1368

makhdoom ghaya

8.0k points

2.2k views

makhdoom ghaya asked Aug 24, 2015

1 votes

2 answers

1474

Let M be the set of all even numbers from 1 to 25 and all the odd numbers between 26 and 200.

Let M be the set of all even numbers from 1 to 25 and all the odd numbers between 26 and 200. If all the elements of M are multiplied, find the number of zeroes at the en...

makhdoom ghaya

8.0k points

2.8k views

makhdoom ghaya asked Aug 22, 2015

0 votes

2 answers

1475

A rectangle of the largest possible area is cut out from a semi-circle of perimeter 72 cm

A rectangle of the largest possible area is cut out from a semi-circle of perimeter 72 cm. What is the area of the rectangle cut out? ( Take n = 22 / 7 )196 cm 2156.8 cm ...

makhdoom ghaya

8.0k points

4.2k views

makhdoom ghaya asked Aug 22, 2015

1 votes

3 answers

1476

In a class of 51 students, the difference between the highest mark and the least mark is 70.

In a class of 51 students, the difference between the highest mark and the least mark is 70. If the average score is calculated without considering the student who got th...

makhdoom ghaya

8.0k points

5.5k views

makhdoom ghaya asked Aug 22, 2015

2 votes

2 answers

1477

What is the least number of cuts required to cut a cube into 84 identical pieces,

What is the least number of cuts required to cut a cube into 84 identical pieces, assuming all cuts are made parallel to the faces of the cube?11121310

makhdoom ghaya

8.0k points

22.5k views

makhdoom ghaya asked Aug 22, 2015

1 votes

2 answers

1478

Ganesh and Sarath were given a quadratic equation in x to solve.

Ganesh and Sarath were given a quadratic equation in x to solve. Ganesh made a mistake in copying the constant term of the equation and got a root as 12. Sarath made a mi...

makhdoom ghaya

8.0k points

1.5k views

makhdoom ghaya asked Aug 22, 2015

0 votes

1 answer

1479

Three friends - A, B and C - go boating in a stream and decide to play a game.

Three friends - A, B and C - go boating in a stream and decide to play a game. B and C are at a point X at time t =0 seconds. B is on a boat which is floating with the st...

makhdoom ghaya

8.0k points

2.8k views

makhdoom ghaya asked Aug 21, 2015

1 votes

3 answers

1480

A is a non-empty set having n elements. P and Q are two subsets of A, such that P is a subset of Q.

A is a non-empty set having n elements. P and Q are two subsets of A, such that P is a subset of Q. Find the number of ways of choosing the subsets P and Q.4 n3 n2 nn 2

makhdoom ghaya

8.0k points

2.4k views

makhdoom ghaya asked Aug 21, 2015

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