aimcat - equations

7/29/2019 Aimcat - Equations

1/31

AIMCAT 0917-15

1. If x1, x

2, x

3and x

4are real numbers, where x

1

and x2 are the roots of x2kx + 35 = 0, while

x3 and x4

are the roots of the equation

x2 7x + k = 0, then which of the following

can be the value of k?

(1) 11.8 (2) 12.4 (3) 13.2

(4) More than one of the above

(5) None of the above


2/31

AIMCAT 0917-16

The average age of a couple at the time of their

marriage was 27 years. After a few years, the couplehad a pair of twins. If the average age of the family of

four when each of the twins was five years old was

two-thirds of the average age of the couple just

before the birth of the twins, then find the average

age of the family of four when each of the twins is 10

years old.

1) 22 years 2) 25 years 3) 28 years4) 30 years 5) Cannot be determined


3/31

AIMCAT 0917-19

3. The cost prices of two varieties of rice differ byRs.12. Ram, the shopkeeper, mixed those twovarieties, in certain ratio and resultant mixturecosts Rs.18 per kg. If instead, Ram mixes the

two varieties in the inverse ratio, the cost priceof the resultant mixture will be Rs.26 per kg.find the cost price (in Rs.per kg) of the lessexpensive variety of rice.

1) 12 2)16 3) 14 4) 18 5)10


4/31

AIMCAT 0917-20

4. On a plane X, whose number system is to the

base n1, a quadratic equation is expressed as

x2 34 + 312 = 0. On another planet Y, whose

number system is to the base n2, the same

quadratic equation is expressed as x2 41x +420 = 0. Find the roots of this quadratic

equation, in the number system to the base 10.

1) 11 and 14 2) 11 and 13 3) 12 and 13

4) 13 and 14 5)None of the above.


5/31

AIMCAT 0917-20

5. A change dispensing machine contains 1rupee, 2 rupee and 5 rupee coins. Thetotal number of coins in the machine is200. The total amount in the machine adds

up to Rs.450. If the number of 1 rupee and2 rupee coins are interchanged, the totalamount comes down to Rs.325. Thenumber of 5 rupee coins in the machine is

1) 20 2) 25 3) 30 4)15 5) 28


6/31

AIMCAT 0910-3Answer the question:

1. An examination consists of 160 questions.

For each correct answer, as student earns 1

mark and for each wrong answer, a studentloses 1/4th of mark. Find the number of

distinct net scores that a student could earn

in the examination.

1) 790 2) 797 3) 795 4) 801


7/31

AIMCAT 0918-12

Answer the question:

1. Three cubical dice D1, D2 and D3each of which is

numbered 1,2,4,5,6 and 8 on its six faces, are rolled

simultaneously. Every time a die is rolled, the face thatturns up is referred to as the unfavourable faces. Also, a

function F(D) is defined for each die that is rolled, such

that F(D) = sum of the numbers on all the favourable

faces of the die. If S = F (D1) + F (D2) + F (D3), then howmany distinct values can S assume?

1)18 2) 21 3) 20 4) 22 5) 19


8/31

AIMCAT 0909-18

Answer the question:

1. Three cubical dice D1, D2 and D3each of which is

numbered 1,2,4,5,6 and 8 on its six faces, are rolled

simultaneously. Every time a die is rolled, the face thatturns up is referred to as the unfavourable faces. Also, a

function F(D) is defined for each die that is rolled, such

that F(D) = sum of the numbers on all the favourable

faces of the die. If S = F (D1) + F (D2) + F (D3), then howmany distinct values can S assume?

1)18 2) 21 3) 20 4) 22 5) 19


9/31

AIMCAT 0909-18

2. There is a cuboidal tank containing somemethyl alcohol which evaporates at aconstant rate (in litres per minute). If twelveidentical pipes start pumping methyl alcohol

into the tank, the tank will get filled in 96minutes. Instead, if 14 such pipes are used,the tank will get filled in 72 minutes. Howmany such pipes would be required, if thetank needs to be filled in 48 minutes?

(1) 15 (2) 16 (3) 18 (4) 20

(5) 21


10/31

AIMCAT 0920-5

1. The age of Mrs. Devi is such that if the digitof her age are reversed, the age of herhusband is obtained, Also, the age of herhusband exceeds her age by 1/11th of the

sum of their ages. Find the sum of the agesof Mrs. Devi and her husband. Consider allage in years.

1) 88 years 2) 121 years 3) 77 years

4) 143 years 5) None of these


11/31

AIMCAT 0920-6

2. If the cost of one mango, five apples and7 bananas if Rs.84 and the cost of onemango, seven apples and 10 bananas is

Rs.114, find the cost of nine mangoes,twenty three apples and thirty bananas?

1) Rs.428 2) Rs.423 3) Rs.434

4) Rs.426 5)Rs.436


12/31

AIMCAT0911

1.If p and q are the roots of ax2 + bx + c=0, then theequation whose roots are (p + q+ pq) and (pq p - q)

is

(1) a2x2-(c2-b2)x+2ac = 0

(2) a2x2-2bcx+(c2-b2) = 0

(3) a2x2 2acx +(c2-b2) = 0

(4) a2x2-2acx +(c2-a2) = 0

(5) ax2=bcx +c = 0


13/31

AIMCAT0912

1. In a theatre, there are 300 seats. The priceof each ticket, when the theatre is houseful,

is Rs.60. For every Rs.5 increase in the

price of the ticket, the number of ticketssold goes down by 10. Find the price of the

ticket (in Rs), for which the theatre owner

would earn the maximum possible revenue.

(1) 90 (2) 95 (3) 100 (4) 105 (5) 110


14/31

AIMCAT0912

2. Ram went to a shop to buy some syntheticand cotton sarees. Synthetic sarees costRs.300 each while cotton sarees costRs.400 each. Ram spent a total of Rs.3600on the sarees. If he had bought as manycotton sarees as the number of syntheticsarees he actually bought and vice versahe would have saved an amount equal tohalf the cost of one saree of one of the two

types. Find the total number of sarees hebought.

(1) 10 (2) 9 (3) 8 (4) 11 (5) 12


15/31

AIMCAT0912

3. The cost of 20 pens, 22 erasers and 25sharpeners is Rs.196. The cost of 23pens, 27 erasers and 30 sharpeners isRs.233. The cost of 109 pens, 125

erasers and 140 sharpeners is Rs.KWhat can be the value of K?

(1) 1089 (2) 1091 (3) 1093

(4) 1095 (5) More than one of these


16/31

AIMCAT09131. Mr. Vincents family consists of six

members, himself, his wife and their fourchildren. It is known that the average ageof the family immediately after the birth ofthe first, second, third and fourth child was16, 15, 16 and 15 years respectively. Find

the age of Mr. Vincents eldest son if thepresent average age of the entire family is16 years.

(1) 8 years (2) 15 years (3) 12 years

(4) 16 years (5) 14 years.


17/31

AIMCAT0913

2. If ax2 = by + cz, by2 = ax + cz and cz2 =ax + by, where x, y, z and a, b, c are all

positive, then find the value of the

expression 1/x+1 + 1/y+1 + 1/Z+1

(1) 1/3 (2) a + b + c (3) 1

(4) abc (5) Cannot be determined


18/31

AIMCAT09141. Consider the following set of equations:

3x + 5y + 2z =23

5x + 6y + 7z =44

Px + 28y + 25z + 178

If x,y and z are real, then which of the statementis/are not true?


19/31

AIMCAT0914

I. The set of equations will become

inconsistent (have no solution) for at leastone value of P.

II. There exists a unique solution for the setof equations for every real value of P

except 21.III. The set of equations will have more than

one solution for at least one real value ofP.

(1) I, II and III (2) Only II and III

(3) Only I (4) None of these


20/31

AIMCAT0914

2. If l, m, n, are eliminated from the equations

l/m = a3 + 1/b3,m/n = b3+1/c3, n/l = c3 + 1/a3then the relation between a, b and c is

(1) (a3 + b3 + c3) + (a3b3 + b3c3 + c3a3)=-1

(2) (a3 + b3 + c3)=1

(3) a3b3 + b3c3 + c3a3=a3b3c3

(4) a3 + b3 + c3+a3b3c3


21/31

AIMCAT0914

3. There are four baskets w, x, y and z, eachcontaining a particular variety of oranges. Thenumber of oranges in any basket is unknown. Theaverage weight of the oranges in the foyur basketsw, x, y, and z put together is 120 gm. The average

weights of the oranges in the baskets w, x, y and z,individually, are 90 gm, 100 gm, 144 gm, and 160gm respectively. If the average weight of theoranges in w and x put together is 96 gm and theaverage weight of the oranges in x and y put

together is 120 gm, what is the ratio of the numberof oranges in basket w to that in basket z?

(1) 9 : 1 (2) 2 : 1 (3) 4 : 3 (4) 5 : 4


22/31

AIMCAT0914

4. Two positive integers x and y are suchthat x2 + 12y2 7xy 4=0. How many

values can y assume?

(1) 2 (2) 1 (3) 3 (4) 4


23/31

AIMCAT0915

1. Qureshi bought four packets of chocolates

and distributed all the chocolates among hisdaughters. It is known that each daughtergot exactly one chocolate less than the totalnumber of daughters Qureshi has. If each

packet of chocolates that Qureshi boughtcontained at least 45 chocolates, find theminimum number of daughters that Qureshi

has.

(1) 16 (2) 14 (3) 13 (4) 12 (5) 15


24/31

AIMCAT0916

1. The average age of a family of seven members,

including Bunti and Babli, aged 70 years and 63years respectively, on January 1st 1986 was 33years. N years later, Bunti died on his birthdayand Mona was born on the same day. A fewyears after that Babli died on her birthday andRohan was born on the same day. N moreyears fter that, on January 1st 2007, Raj wasborn. What was the average age of the family ofeight members on January 1st 2008?

1) 28 years 2) 32 years 3) 33 years

4) 29 years 5) Depends on the years of death of

Bunti and Babli.


25/31

AIMCAT0919

1. If the boy purchased items worth Rs.47and Rs.29, what is the amount spent for

purchasing all the four items?

(1) Rs.190 (2) Rs.220 (3)Rs.271

(4) Cannot be determined


26/31

AIMCAT0919

2. A and B went to a market and found that

the only fruits available there were bananasand mangoes. A purchased 23 mangoesmore than the number of mangoespurchased by B. After that, both A and B

purchased certain number of bananas aswell. If A and B purchased a total of 30 and40 fruits respectively and spent an equalamount of money on the fruits, then find

the price of a mango, given that it is Rs.10more than that of a banana.

(1) 23 (2) 43 (3) 33 (4) 86


27/31

AIMCAT0919

3. If the length of a rectangle is increased by 5

units and the breadth is increased by 9units, the area of the rectangle triples. Instead, if the length is increased by 3 unitsand the breadth is decreased by 5 units, the

area of the rectangle becomes one third ofwhat it was. By what percent is the lengthof the rectangle more than the breadth?

(1) 133 1/3% (2) 120% (3) 108%

(4) 150%


28/31

AIMCAT0919

4. Two non-zero real numbers a and b

satisfy the following equations

4a + 6b + a2 + 37b, =0 and a/b + b/a = 24

If 2a + 3b 0, find the value of b,

(1) 1/5 (2) -6 (3) -1/6

(4) Cannot be determined


29/31

AIMCAT09195). P, Q, R and S are four books such that the cost of

is half that of S. Q costs twice as much as R,which in turn, is costlier than P. How many of thefollowing statements are either definitely true ordefinitely false?

I) S costs more than Q

II) P and S together cost less than Q and R together

III) Q and S together cost more than P and R together

IV) S costs more than R


30/31

AIMCAT0919Let , and be the roots of the equation,

x3 + ax2

+ bx + c =0. Let S1 denote the sumof the roots, S2, the sum of the squares ofthe roots, S3, the sum of the cubes of theroots and so on.

6. Find S4.

(1) a4 = b2 a2b

(2) a4 + 4ac

(3) a4 + 2b2 4a2b + 4ac

4 4a4 + b2 4a2 + 4ac


31/31

AIMCAT0919

7. There are four apples with A, four oranges

with B, Foyur bananas with C and fourmangoes with D. Any two persons amongA, B, C and D can exchange any numberand kind of fruits as long as they exchange

an equal number of fruits. Each suchexchange is termed as a transaction. Findthe minimum number of transactionsrequired so that every person possess onefruit of each variety.

(1) 6 (2) 3 (3) 4 (4) 8

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