AMCAT Previous Question Papers with answers – Quantitative Ability

Quantitative Ability AMCAT – Aspiring Minds CAT Compiled List of all Questions with answers

AMCAT Quantitative Ability Previous Papers-1
1) The probability of getting at least one tail in 5 throws of a coin is?
a)1/32                                   b)31/32                                                c)1/5                                      d)None of the above
Ans.  a coin throws 5 times is equal to the 5 coins throws  at one time.
So total no of choices are 25=32
Chances that not getting at least one tails is 1 i.e., (h,h,h,h,h)
So 1-(1/32)=31/32…option (b) is correct.
2) When a local train travels at a speed of 60kmph, it reaches the destination on time. When the same train travels at speed of 50kmph, it reaches its destination 15 minutes late. What is the length of journey?
a)75km                                 b)50km                                 c)60km                                 d)85km
Ans. let the time taken by a train to reach destination at 60kmph is x. Then it takes (x+15) at 50kmph.
So distance, 60x=50(x+15)
X=75…option (a) is correct.
3)Give the greatest pair of twin primes which are below 100?
a)71,73                                 b)93,95                                 c)97,99                                  d)87,89
Ans.  in the given options only 71 and 73 are primes.
So option (A) is correct.
4) In an examination involving quantitative aptitude and logical reasoning, 65% examinees cleared quantitative aptitude test while 70% cleared logical reasoning test. If 50% examinees passed both the tests, then how many failed in both tests?
a)35%                                    b)15%                                   c)30%                                    d)20%
Ans.  no of students who passed in at least one subject:
AUB=65+70-50=85
If total students are 100 .no of students who failed in both subjects = total students-students who passed in at least one subjective. 100-85=15
So option (b) is correct
5) A sum of money triples itself at compound interest in3 years. In 9 years it will be
a)6 times the principal                                   b)12 times the principal
c)18 times the principal                 d)27 times the principal
Ans. let the principal be x.
X(1+R/100)3=3x
(1+R/100)^3^3=3^3=27
So option (d) is correct.
6) Three friends Gerard, Runey and Ronaldo work together to dig a hole. Gerard alone can complete the work in 10 days and together all three can complete it in 4 days. They earn a total of Rs.1,200. Find the share of Runey  if the money that they receive is proportional to the work that they do?
a)Rs 480                                               b)Rs 165.51                         c)Rs 500                                d)Rs 600
7) The number which should be subtracted frm 5a2-3ab+7b2  to make it equal to a2+ab+b2 ,is:
a)4a2-4ab+6b2                   b)4a2-4ab+5b2                                   c)4a2+4ab+6b2                   d)4a2-3ab+6b2
e)None of the above
Ans..( 5a2-3ab+7b2 )-( a2+ab+b2)= 4a2+4ab+6b2
So option c is correct.
8)Given that the interest is only earned on principal, if an investment of Rs.1000.00 amount to Rs.1440.00 in two years, then what is the rate of interest earned?
a)20%                                    b)22%                                   c)21%                                    d)11%                   e)44%
Ans.  1000(1+r/100)2=1440
So the answer is 20%.
Option (A) is correct.
9)If nC5=nC0, then find the value of n.
a)n=0                                    b)n =1                                   c)n=5                                     d)n=10
Ans. nC5=nCn-5=nC0
n-5=0
n=5..so option (c) is correct
10)A bag contains 5 oranges, 4 bananas and 3 apples. Rohit wants to eat a banana or an apple.He draws a fruit from the bag randomly. What is the probability that he will get a fruit of this choice?
a)3.5/12                               b)7/12                                   c)5/12                                   d)None of the above
Ans. total fruits are 12.
Chances  to select banana or apple is: 4+3=7
Probability =7/12
So option (b) is correct.
AMCAT Quantitative Ability Previous Papers-2
11)A single letter is drawn at random from the word.”ASPIRATION”, the probability that it is a vowel is?
a)1/2                     b)1/3                                     c)3/5                                      d)2/5
Ans) A single letter drawn at random from the above given word is 5c1/10 = 1/2
12)The number of ways in which 15 students A1,A2,—A15 can be ranked, such that A4 is always above A8 is:
a)15!                      b)13!                                     c)15!/2                                  d)13!/2
13)Suparna needs to browse through 75pages of a novel before she gives her review to the class. She has 2.5 hrs before the lecture. What should be her reading speed in pages/hour?
a) 16    b)30   c) 20  d) 22
Ans) speed=distance/time
S=75/2.5
S=30
14) The value of log100.1 is :
a) 0  b) -1   c) -10  d) -100
Ans)log100.1 = log1010-1 = -1 log 1010 = -1     (log 1010 =1)
15) A written exam consists of 6 questions with the answer options as yes/no/none. In how many ways can the examinees select the answers?
a) 6  ways   b) 6  ways  c) 3 .3 .3 .3 .3    d) (3 6
Ans) In 36 ways the examiners select the answers.
16) What is the sum of the two consecutive numbers, If the difference of whose squares is 19?
a. 9                         b. 10                      c. 18                       d. 19
Ans) (n+1)2-n2=19
We get 2n=18, n=9
17) P is an integer. P>883. If (p-7) is a multiple of 11, then the largest number that will divide (p+4) (p+15) is :
11           121         242         None of the above
18) Find the least number which when divided by 5, 7 and 13 leaves the same remainder 3 in each case
398         453         458         463
Ans) By trial method we get the answer as 458.Why because if we divide the number with 5,7,13 it leaves the        remainder as 3 in all the three cases.
19)Which number should be subtracted from 321 so that it becomes prime?
2              4              6              9
Ans) If we apply trial method 2 is the answer.If we subtract 321 from 2 the result will be 319 hence this is the prime number
20)  28X22 =
410                210                216                416
Ans) By the formula am*an=am+n
28 *22 =28+2 =210
21) What will be the value of the expression a8/3  *  a-6/9  ?
a-2                     a-1                                   a0                                          a1                                          a2
ans:    if bases are equal we have to add powers
a8/3-6/9
a18/2=a2  .
22) What is the square root of 576/9?
1.4          2.8          3.12        4.16
Ans:   2
=24/3
=8
23) Which number is the fourth power of 7?
1. 2401                  2. 2421                  3. 2601                  4. 2621
ans:  72*72
=49*49
=2401
24) HCF of two numbers is 11 and their LCM is 693. If one number is 77, find the other number?
1. 7         2. 9         3. 63       4. 99
ans:   product of two numbers = product of HCF and LCM
77*x =11*693
X=11*693/77
X=99
25) Recycling 900 kg of paper saves 17 trees . How many trees are saved when 1200 kg of paper are recycled?
1. 19       2. 25       3. 20       4. 22
ans:   900kg papers=17 trees
1200kg papers=?
The trees to find is=X
X= 1200*17/900
=68/3
=22
26) How many different four letter words can be formed ( the words need not to be meaningful ) using the letters of the word PACIFIC such that the first letter is p and the last letter is F?
1. 8         2. 3         3. 6         4. 7!/5!
Ans:  PACIFIC
Total number of letters n=7
R=2
Npr =n!/(n-r)!
=7!/(7-2)!
=7!/5!
27) Mauli purchased a designer saree from Mumbai at 8/9th of its MRP. When she came back to Delhi, her neighbour coaxed mauli to sell the saree to her. She was even ready to pay 9% more than its MRP. What would Mauli’s gain percentage be, if she decides to sell the saree to her neighbour?
1. 15.59%             2. 16.61%             3. 20.36%             4. 22.65%
ans:   assume that MRP rate =100
cost prize = 800/9
selling prize=(100*9/100)+100 =109
sp=(100+gain%/100)cp
109 =((100+gain%)/100)800/9
By solving above equation we get  gain=181/8
=22.65%
28) A goods carriage of length 2km, headed to Srinagar from Punjab was running at a speed of 30 km/hr. It crosses a tunnel which is 58 km long with that speed. Find the time taken by the goods carriage to cross the tunnel?
1. 4 hours            2. 3 hours            3. 2 hours            4. 1 hour
ans:    in this we have to add the distances. The goods carriage 2km and to cross tunnel distance 58km.
time =?   Speed=30km/hr
Time =distance /speed
=(2+56) /30
Time=60/30
=2hours
29) A lucky draw is organized as part of the first anniversary celebration of new Age Company. There are 25 chits in a bowl one for each employee and the chits are marked from 1-25. Sarika and Rajesh have chits marked with numbers that are multiples of 3 or 7. They want to know if there are chances of them being awarded the trip to Goa which is the first prize of the lucky draw. When one chit is drawn at random, what is the probability that the chit has a number which is a multiple of 3 or 7?
1. 3/25                  2. 2/11                  3. 11/25                4. 10/25
ans:     no of chits =25
sarika and ragesh chits aremultiples of 3 and 7
3 multiples up to 25 =8
7multiples up to 25 =2
Total multiples= 8+2 =10
=total multiples / total no of chits
=10/25
30) What is the loss percentage incurred by a company when it buys an asset for Rs. 1,50,000 and sells it for Rs. 75,500?
1. 49.67%             2. 49.34%             3. 98.68%             4. 98.34%
ans:   loss = cost prize – selling prize
=1,50,000-75000
=74,500
Loss%  = (loss/cp)*100
=(74000/150000)*100
31) If Ruparno is expected to spend Rs. 2,300 on electricity bill in the first 3 months of the year, what amount can he be expected to spend on electricity bill for the rest of the year?
1. Rs. 5,400          2. Rs. 5,700          3. Rs. 6,200          4. Rs. 6,900
Ans: 6,900 ( 2,300 * 3)
32) Out of every 100 people in police department, 10 are women. Out of every 100 people in military forces, 3 are women. In a batch of 180 police personnel and 200 army personnel, how many of them would be women?
1. 24                       2. 30                       3. 18                       4. 6
Ans: 18+ 6 = 24
33) Probability of one of the power plants over heating is 0.15 per day and the probability of failure of the backup cooling system is 0.11. if these events are independent, what is the probability of ‘big trouble’ (i.e., both evnets taking place)?                 1. 0.35                   2. 0.0185                              3. 0.0165                              4. 0.26
Ans: 0.0165
34) There are 5 clients and 5 consultants in a round table meeting. In how many ways can the clients be seated such that no consultant is next to the other consultant?
1. 5!6!                   2. 4! 4!                  3. 4! 5!                  4. 9!                       5. 10  5! 4!
Ans:  consultants can be arranged in 4! ways  and clients in 5! ways.
So 4! 5! is the answer
35) A person forgets two digits of user ID for a website. He remembers that two digits are odd. What is the probability of him typing the correct last digits by randomly typing 2 odd digits?
(1/25)                    (1/5)                      (1/2)                      (2/5)
36) Give the greatest pair of twin prime which are below 100?
71,73                     93,96                     97,99                     87,89
Solution:
Twin primes are pairs of primes which differ by two. The first twin primes are {3,5}, {5,7}, {11,13} and {17,19}.
Ans: 87,89
37) In how many ways a panel of 5 students be selected from 8 kids if a particular student be included?
36                           51                           71                           210
Solution:
as one student is to be included left is 7 from 8 and need to make choice from 4,i.e 7c4 =35
38) A woman sold 15 bead sheets for Rs 15,000. Hence gaining the cost of 5 bed sheets. The cost per sheet is.
960         775         1000       800         750
Solution:
b) 750
If CP of 1 bedsheet=x,then CP of 15 bedsheet=15x
15000-5x=15x, 20x=15000,x=750
39) Gitu and rashmi were playing ludo. Game and starts when one gets 6 in two consecutive throws of dice. What is the probability that gitu can start the game in first chance?
1/6         1/36       5/6         5/36
Solution: Getting 6 is 1/6
getting two 6’s is (1/6) * (1/6) = 1/36
40) A vendor bought 15 oranges at Rs. 36 for 5 oranges and sold all of them at four oranges for Rs. 45. How much did the vendor earn or loose in this transaction?
Loses Rs.4.05 per orange              gains Rs.4.05 per orange               gains Rs.60 overall
Loses Rs.5.06 per orange              gains Rs.75.90 overall
Solution:
vender bought 15 oranges,5 oranges are rs.36 so 15 oranges cost rs.108.
then now the vender selling it at rs.45 for 4 oranges.
so each orange cost 11.25.
the selling price of 15 oranges is rs.168.75
hence the difference between the cost price and selling price is 60.75
hence 15 oranges he gained 60.75 rupees.
so for one orange he got 4.05 gain.
ANS:(b)
41) The length of the rectangle varies inversely with its width. If the length of the rectangle is 60 feet and width is 24 feet find the length of the rectangle when its width is 40 feet?
36 feet                  100 feet               25 feet                  20feet
42) Sum of money triples itself at compound interest in 2 years. In 9 years it will be.
6 times the principle       12 times the principle     18 times the principle     27 times the principle
Solution:
3p=p(1+r/100)
now as per ques 3p^3=(p(1+r/100))^3
thus (1+r/100)=27,,,, hence ans is 27 times the pricipal.
43) Nitish sold his watch and sun glassesat a loss of 4% and gain of 4% respectively for 2600 to Kamal. Kamal sold the same sun glasses and watch at a loss of 4% and gain of 4% respectively for 2700. The price of watch and sun glasses to Nitish were.
(Rs.1960, Rs.700)              (Rs.2000, Rs.1000)            (Rs.1500, Rs.700)              (Rs.800, Rs.2000)
Solution:
Let the CP of watch be Rs x and sunglasses be Rs y.
2600=96x/100 + 104y/100
2700= 104x/100 + 96y/100
On solving,
y=700
x=1960
44) Problem question: What is the 5thnumber?
Statements: 1) 1st and 2nd numbers are 1 and 2 respectively.
2) 3rd and 4th numbers are 3 and 4 respectively.
Statement 1 alone is sufficient                   Statement 2 alone is sufficient
Both statements put together is sufficient           Both statements even put together is not sufficient
Either of 2 statements are individually is sufficient
45)  EK : VP :: GM :
TN          NT          UN         VN
46) In a certain code REINFORCE is written as ENOCRIFRE. How is ATTEMPT written in that code?
ATMTTEPS          TEPSATMT          TEMPSATT          ATTTEMPS
47) In a certain code, ASSUMPTION is written as 1113472065. How is KNOWLEDGE written in that code?
254545475           256565675           256535475           256565475
48) A tourist has strayed from his path while on his way to his hotel. He moves 28km towards south, then he moves 20km towards west, then 4km north and then 2km towards east to reach his hotel. What is the distance of shortest possible route?
45 km                    20km                     18km                     30km
Solution:
AB=28km toward south
BC=20km toward west from B
CD=4km toward north from C
DE=2km toward east from D
EF=BC-DE=18km
AF=AB-CD=24km
in Triangle,AFE
AE=sqrt(24^2+18^2)=sqrt(900)=30km
49) Two friend Raman and Rajan starts a race and run together for 20km towards east. From there Raman runs 10km towards north east and Rajan continues in the east for 8km. How far are the two friends now from each other?
6km                       20km     18km     30km
50) 8,8,6,2,..
-4            -3            3              4
51. If the logx 16 = 0.8, then what is the value of x?
A. 4    B. 2     C. 32         D. 16
Solution:
x^0.8=16
x=(2^4)^(10/8)
x=2^5
x=32
52. If f(x) = ex and g(x) = loge x, then what is the value of {f of g(x)}?
A. X      B. ex       C. logex                 D. cannot be determined
53. The value of log864 –log644096 is
A. -1      B. 0       C.  1              D. 2
Ans:  0
54. What is the relationship between the fractions 14/15 and 37/40?
A.14/15=37/40            B.14/15>37/40            C.14/15<37/40            D. Cannot be determined
Option c)
Take LCM of both 15, 40 we get 120
(14*8)/(15*8) = 112/120
(37*3)/(40*3) = 111/120
So 14/15>37/40
55. If LCM and HCF of two numbers are equal and product of two numbers is 2916, find their LCM?
A. 54      B. 56      C.64        D. 66
LCM and HCF will be equal if and only if both the numbers are equal.
therefore, 2916=54*54
so LCM of both number =54
56. If the sum of squares of two numbers is 2754 and their HCF and LCM are 9 and 135 respectively, then the numbers are
A.27, 36          B. 27, 35         C. 28, 45         D. 27, 45
As we know product of two nos.=their H.C.F*L.C.M
So,x*y=135*9=1215
and x^2+y^2=2754
So,(x+y)^2=x^2+y^2+2*x*y
=2754+2*1215=5184
So,x+y=72
Now on solving,the nos. are 45 and 27
57. The number of ways in the letters of the word “RESULT” can be arranged without repetition is
A.720       B. 120    C. 60    D. 840
58. The HCF of two numbers is 4 and LCM is 48. If one of the numbers is 12, then one of the divisions of the numbers is:    A.3    B.   6    C.  8    D. 12
59. Which number should be added to 113257 so that it can be divided by 9?
A. 4   B. 6   C. 8   D. 10
60. ABCD is a square PQRS is a rhombus lying inside the square such that P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. A point is selected at random in the square. Find the probability that lies in the rhombus   A.1/3   B.   2/3    C.  1/2       D. 1/4
61. 4.28 and -3.28 are two numbers on a real number line. If 1 is added to the numbers, then which of the following is true?
A. Distance between the two new numbers is 2 more than distance between 4.28 and -3.28
B. Distance between the two new numbers is 2 less than distance between 4.28 and -3.28
C. Distance between the two new numbers is 2 equal distance between 4.28 and -3.28
D. None of these
62. When a local train travels at a speed of 60 kmph. It reaches the destination on time .  when the same train travels at speed of 50kmph. It reaches its destination15 minutes late. What is the length of journey?
A. 75km   B.50km    C. 60km   D.85km
Solution:
distance is constant.
so let time taken be t when it travels with 60kmph
let time be t’ when it travels with 50kmph
d=s*t
therfore
s*t=s’*t’
60*t=50*(t+15/60)(in hrs)
on solving
t=5/4 hrs
d=60*5/4
75km
63. In ashooting competition, the probability of hitting the target by P is 3/5. By Q is 1/3 and by R is 2/5. If all they fire independently at the same target calculate the probability that only one of them will hit the target.
A. 25/75           B. 32/75               C. 39/75                  D. 43/75
Solution:
ans .32/75.
P(p)=3/5 P(p’)=2/5 same way for rest and by using formula
P(p)*P(q’)*P(r’)+P(p’)*P(q)*P(r’)+P(p’)*P(q’)*P(r)
64. For what value of M is the number 7M42876M divisible by 11?
A. 0    B. 8    C.4     D. 9
Solution:
Here an easy way to test for divisibility by 11. Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.
So, for instance, 2728 has alternating sum of digits 2-7+2-8 = -11. Since -11 is divisible by 11, so is 2728.
Similarly, for 31415, the alternating sum of digits is 3-1+4-1+5 = 10. This is not divisible by 11, so neither is 31415.
Coming to the given question,
7-M+4-2+8-7+6-M
16-2M
so if M=8 then 16-16=0 so total number is divisible by 11.
65. A group of women can finish a piece of work in 50 days. In how many days will one-third the number of women be able to finish two-third of the work?
A.        150 days       B.        75 days        C.        50 days         D.        100 days
Solution:
x women takes 50 days to complete a piece of work.
1/3 x women takes 150 days to complete a piece of work.
1/3 x women takes 100 days to complete 2/3 rd work.
66. What is the value of log512 8?
A.        3          B.        1/3                 C.        -3        D.        -1/3
Solution:
log512 8
= log512 (512)1/3
=1/3
67.      If log10 3 = 0.477, then the value of log10 9 is:
A.        1          B.        0.477             C.        0.954             D.        0.523
Solution:
log10 9= 2 log 10 3 = 2 * 0.477 = 0.954
68.      When the price of a pair of shoes is decreased by 10%, the number of pairs sold increased by 20%. What is the net effect on scales?
A.        8% decrease                        B.10% decrease      C.10% increase       D.        8% increase
ans: let cp be 100, when price decreased by 10% then sp=90. Now sales increased by 20%, ie, 90+20%of90=108.
so cp=100, sp=108, gain=8, gain%=gain*100/cp=8%increase
69.      Replace the symbols * and # in 9586*4# so that it is divisible by both 8 and 5.
A.        0,0      B.        1,0      C.        0,5      D.        1,5
Solution:
Rule for Divisible by 5 : number should end with either 0 or 5
Rule for divisible by 8: Last 3 digits should be divisible by 8
Solve from options: If option (A) is correct then number becomes 9586040
It is divisible with both 5 and 8 so Option(A) is correct.
70.      If a coin with both heads is tossed, then the probability of obtaining a tail is:
A.        0          B.        ½         C.        1/3     D.        1
Solution: If a coin contains both heads then no way we get tail so probablity is 0.
71.      Find the remainder when 221 is divided by 6.
A.        0          B.        1          c.         2          D.        3
72.      Which of the following numbers is the smallest number?
A.        1/12   B.        1/6     C.        ¼         D.        1/3
Ans: (A)
73.      A phone company offers 5 phone plan options: call waiting, call forwarding, voice mail, conferencing, and caller ID. A customer can   choose 3 options. The number of ways one can avail the plan options        is:
A.        5          B.        10       C.        3          D.        20
Solution:
5c3 =10 is correct answer
74.      If log32 x + log32 (1/8) = 1/5, then the value of x is equal to:
A.        8          B.        5          C.        16       D.        32
Solution:
log b x+ log b y = log b xy
so log32 x + log32 (1/8) = 1/5
log 32 x(1/8) = 1/5
x/8 = 321/5
x/8 = 2
x= 16
75.      Length and breadth of a rectangle are directly proportional. If length increases from 6 cm to 21 cm and if breadth now is 14 cm, then what    was the breadth before any change in length occurred?
A.        4 cm   B.        1.5 cm           C.        2 cm               D.        3 cm
Solution:
since they are directly proportional
6/21=x/14
x=(14*6)/21=4
76.      At an election there are 5 candidates among which 3 members are to be elected and a voter may vote for any number of candidates not greater than the number to be elected. Then the number of ways in     which a voter may vote are ?
A.        25       B.        30       C.        32       D.        None of the above
Solution:
77.      One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is ‘9’ of hearts.
A.        1/13               B.        1/26               C.        1/52               D.        3/52
Solution:
78.      If 2x * 3y = 18 and 22x * 3y =36, the value of x is:
A.        0          B.        1          C.        2          D.        3          E.         None of the above
Solution:
second equation can be written as,
2^x*2^x*3^y=36. substituting the first equation value,
2^x*18=36.
2^x=2^1;
a^m=a^n, then m=n, so we get x=1
79.      An unbiased coin is tossed 5 times. If tail appears on first 4 tosses,        then probability of tail appearing on the fifth toss is:     A.        ½         B.        1          C.        0          D.        4/5
Solution: (A) Appearing tail on fifth toss is independent of first 4 tosses.
80.      In a single throw of dice, what is the probability to get a number greater than or equal to 4?                        A.        1/3                 B.        2/3                 C.        ½         D.        None of the above
Solution: Getting number greater than or equal to 4 means 4,5 and 6 are possibilities.
Total case for a dice is 6.
ans: 3/6 = 1/2
81.      For irrigational purposes, a farmer uses a tank of water. He uses a pipe during night to fill the tank, so that he could use the tank of water in the morning to irrigate his farm. The pipe fills the tank in 3 hours but on the particular day,because of a leak in the tank, the pipe takes 4.5 hours to fill it. In how many hours can the tank be completely emptied by the leak alone?
A.        6          B.        9          C.        1.5      D.        Data insufficient
Solution:  pipe one hour capacity is 1/3
1/3 + x = 2/9
x=9
Answer is 9 hours.
82.      The printed price on a book is RS. 400, a bookseller offers a 10% discount on it. If he still earns a profit of 12%, then the cost price of  the book is:
A.        RS. 280                      B.        RS. 352          C.        RS.360           D.        RS.300
S.P= 360 Rs.
If Profit = 12% then 1.12*C.P = S.P
1.12*C.P = 360
C.P= 321.43 Rs.
And If Profit=12 Rs. then C.P= 348 RS.
As there is ambiguity in question.
83.      If r = at2 and s = 2at, then the relation among s, r and a is:
A.        s2 = 4ar          B.        s = ar              C.        s2 = ar                        D.        None of the above
Solution:
r=at2
s=2at
therefore t=s/2a
r=as^2/4a^2
s^2=4ar
84. Amit bought 10 cycles for Rs1750 each. He sold four cycles for Rs8400, three for 1900 each. At what price he should sell remaining cycles so as to earn an average profit of Rs320 per cycle?
1900       2000       1800       2050       2200
Solution: 10 cycles cost price + 10 cycles profit = 10 cycles selling price
10(1750) + 10 (320) = 8400 + 3(1900) + 3 (x)
solve above equation then x = 2200
85. Out of 26, 13, and 34, which two numbers are co-primes?
26 and 14             13 and 34             26 and 34             None of the pairs are co primes
Ans:  Two numbers are said to be co-prime when their GCD is 1.
GCD( 26,13) = 13
GCD ( 26,34) = 2
GCD (13, 34) = 1
SO answer is 13 and 34.
86. A man earns 24,000 per month. He spends one-third of his income on personal expenditure. Half of the remaining income is invested in a scheme for 15% interest per annum. After investing half of the remaining income is invested in a scheme which gives 10% income per annum. The remaining lies in a bank where it earns an interest of 4% per annum. The effective rate of interest earned by the man on his investments by the end of the year is?
19%                        10%                        11%                        29%                        12.33%
Solution:
amount remaining= 24000-24000/3=16000
1. 16000/2=8000 SI=PRT/100=8000*15*1/100=1200
2. 8000/2=4000 SI=4000*10*1/100=400
3. 4000 SI=4000*4*1/100=160
SI=PRT/100 1760=16000*R*1/100
Solving this R=11% Ans……
87)A person forgets the last two digits of user ID for a website. He remember that both digits are odd. what is the probability of him typing the correct last digits by randomly typing 2 odd digits?
A)1/25                  B)1/5     C)1/2                     D)2/5
Ans: guessing one odd digit is 1/5
guessing  two odd digits is (1/5) * (1/5) = 1/25
88)Every number of housing socity contributed as much as there are numbers f members in the socity. The president added Rs.150 extra from to take the total of Rs. 2,650. How many members are there in the housing society?
A)25                       B)50       c)60        d)35
Ans: 2650 – 150 = 2500
50*50 = 2500
ans is 50.
89)Given that the interest is only earned on principal, if an investment of Rs 1000.00 amounts to Rs 1440.00 in two years, then what is the rate of interest earned?
A)20%   B)22%   c)21%    D)11%   e)44%
Solution: Interest for two years is 440
Interest for one year is 220
Apply Simple interest formula. (1000 * 1 * r )/ 100 = 220
r =22%
90)Gitu and Rashmi were playing ludo. Game starts when one gets 6 in two consecutive throws of dice. What is the probability that gitu can start the game in first chance?
A)1/6     B)1/36                   C)5/36   D)5/6
Solution: Getting 6 is 1/6
getting two 6’s is (1/6) * (1/6) = 1/36
91)Ritu has 3 shirts in shades of red , 4 in yellow shades  and 5 in green shades .Three shirts are  picked at random. The probability that all of those are in red shades is:
A)1/12                  B)1/660                                c)1/66                   D)1/4
Solution: Given  3red,  4yellow, 5green shirts
Total shirts = 3+4+5 = 12
Probability of getting Red = 3/12 = 1/4
92)(1.0816)1/2=?
A)0.14                   B)1.4      c)1.004                  D)1.04
Solution:  It written as square root of 1.0816
By trail method, check all options
Like   1.04 * 1.04
1.0816
93)An intern can a job in 15 days . The manager and senior manager are busy with other priorities and thus take 25 and 40 days respectively to complete the task. How long will they task to finish the task if all of them work together?
A)7         b)722/29               c)8          D)821/29
Solution:  It can be written as …
Work together =  1/15 + 1/25 +1/40
= 1/5[1/3 + 1/5 + 1/8]
= 1/5[40+24+15/120]
=[79/5*120]
It can be written..
ð  600/79 = 7.59    (Answer is in fractions..in this options solution is not present)
94)if a + b =6, ab = 5, then the value of a-b is:
A)4         B)5         C)6         D)7         E)9
Solutions : By using formulae…..
(a+b)2  –  (a-b)2  = 4ab
36 – (a-b)2  = 20
=> (a-b)2 = 16
=> (a-b) = 4
95)At  a certain party ratio the ratio of gents and ladies was 1:2 . But when  2 gents and 2 ladies left the party . The ratio became 1:3. How many people were initially present in the party?
A)12       B)15      C)18       D)24
Solutions:  Ratio of G & L =1:2 => x : 2x
Two G & Two L are left i.e  =>x-2 : 2x-2
=> x-2 : 2x-2 = 1 : 3
=> x-2/2x-2 = 1/3
=>3x-6 = 2x-2
=> X=4 (Gents)
:. Total people = 12
96)The SI on Rs 10 for 4 months at the rate of 3 paise per rupee per month is :
A)Rs 1.20             B)Rs 1.60             C)Rs 2.40              D)rs.3.60/-
Solution : By using Formulae…
SI = P * T* R/100
=>10*4*3/100
=>120/100 => Rs  1.20
97)In a miniature wonderland,three countries Austria,America and Germany are on display.If Austria and America occupied 3/7 and 4/9 of the display area respectively,what is the display area occupied by Germany?
a.3/21   b.5/63   c.8/63    d.1/21
Solution:  Let  3/7 + 4/9  + G =1
ð  27+28/63 + G = 1
ð  G  = 1 – 55/63
ð  G = 8/63
98)Find the value of p which satisfies the relation log2(p-1) + 2 =log2(3p+1).
a.1          b.3          c.5          d.7
Solution:  log2(p-1) + 2 =  log2(3p+1)
ð   log2(p-1) + log2(22) = log2(3p+1)     (:. Log2 2 2= 2 )
ð  log2 22 (p-1) = log2 (3p+1)   (:. Log a+ log b = logab )
ð  4p-4 = 3p+1
ð  P = 5
99)          28 * 22  =
a.410          b.210          c.216           d.416
Solution : am  * an = am+n
Using this formulae = 28 * 22 = 210
100)Mauli purchased a designer saree from mumbai at 8/9th  of its MRP.When she came back to Delhi,her neighbour coaxed Mauli to sell the saree to her.She was even ready to pay 9% more than its MRP.What would Mauli’sgain percentage be,if she decides to sell the saree to her neighbour?
a.15.59%                              b.16.61%                              c.20.36%                              d.22.625%
Solution: cost price = 8/9 x
Selling price = 9% more =>  x + 9/100 x
=>109x/100
Formulae  = ( s.p-c.p/c.p) * 100
ð  {[(109x/100 )– (8x/9) ]/(8/9)}x100
ð  By Solving we get :22.625%
101)Deepak sells 50 shirts at the cost price of 60 shirts.His gain percent is:
a.0.15      b.0.1        c.0.25      d.0.2
sol:    Let cost of each shirt is 100
60*100=50*x  ==>    x=120(new cost)
20%  is the profit. i.e.,    20/100 = 0.2
102)The LCM of 26 * 32 * 5 * 7, 23 * 35 * 7 and 2 * 34 * 5 is:
a.26  * 35                           b.26 * 35 * 5            c.26 * 35 * 7             d. 26 * 35 * 5 * 7
Sol:    26*35*5*7
Hint: Product of all primes with highest powers.
103)Find the greatest number that divides 125,218,280 and 342 so as to leave the same remainder in each case.
a.37         b.35         c.33         d.31
Sol:  Trail method.
(Or)
218-125=93,                           280-218=62,
280-125=155,                         324-218=124,
342-125=217,                         342-125=217
H.C.F of  93,155,217,62,124,217 is 31
104)The sum of squares of 3 numbers is 170, while the sum of their products taken two at a time is 157.What is the sum of the numbers?   a.20     b.22    c.24    d.28
Sol:  a2+b2+c2=170,                ab+bc+ca=157
(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
=170+2(157)
=484
(a+b+c)=22
105)Eight teams are playing in a cricket match.If a team loses,it is out of the tournament.How many games are needed to determine the winner?    a.7     b.6              c.8           d.9
Sol:   7 games are needed.
1 1           1 1           1 1           1 1           —    4 games
1            1              1              1            —    2 games
1                              1                    —    1 game
1                                Total =7 games
106)What will be the value of x in the expression[ 722-282 = 50x]?
a.44         b.46         c.86         d.88
Sol: 722-282=50x     ==>     (72-28)(72+28)=50x   ==>     44*100=50x    ==>     x=88
107)There are 3 main steps of completion of a project-Development,Review and Roll out.After development, there are 4 people who can independently work and lead the process to the process to the next step i.e. Review.Further ahead,there are 5 people who can work independently and lead to the next step i.e.Roll-out.In how many ways can a project manager complete the project?
a.20         b.9           c.15         d.25         e.18
Sol:       4c1*5c1=4*5=  20                     (Combinations)
108)Find a number that can replace y in the expression (x4)0= x2/3 * xy
a. -2/3     b. 2/3      c. 1          d. 0          e.-4
Sol:   (x4)0=x2/3 *xy       ==>        x0=x(2/3)+y        ==>          0=(2/3)+y      ==>     y=-2/3
109)A group of 4 students is to be chosen from 3 boys and 5 girls.Find the probability that the group contains exactly 3 girls.                                a.3/7       b.4/7       c.5/7        d.6/7
Sol:     (5C3*3C1)/8C4    ==>  3/7
110.A cistern can be filled by two pipes A and B in 10 and 15 hours respectively and is then emptied by a tap in 8 hours.If all the taps are opened,the cistern will be fill in:
a. 21 hours              b. 22 hours              c.23 hours               d.24 hours               e.None of the above
Sol:          Time takes to fill the tank, if all pipes are opened = (1/10 )+(1/15) -(1/8)
=(5/120)
=1/24
i.e., 24 hrs to fill the tank
111)Evaluate:log(a2bc3)5
a. 32log a + 5log b + 243log c                        b. (10log a + 5log b + 15log c)                       c. 15(log a + log b + log c)              d. 5log (a2bc3)
Ans: (B)
112) if p varies directly as the square of q and inversely as the square root of r,which of the following would be true if k represents constant of variation?
a.p(q)2 = √k        b.k= r2* p *q-2     c.p/k(q)2 =√r      d. √p =1/k(q)2
113) what is the loss percentage incurred by a company when it buys an asset for Rs 1,50,000 and sells it for Rs 75,500?
a.49.67%                              b.49.34%                              c.98.68%                              d.98.34%
A) c.p = 1,50,000rs
s.p= 75,500
loss = c.p – s.p
= 1,50,000 – 75,500
= 74,500
Loss% = (loss/c.p)*100
= (74,500/1,50,000)*100
= 49.67%
114)If a positive integer n is divided by 5 then the remainder is 3. Which of the following numbers gives remainder 0,when it is divided by 5?                              a.  n + 3                 b.  n – 2                                c.  n + 2                 d. n + 1
Ans: n+2;
115) Find the greatest 5 digit number that is exactly divisible by 3, 4, 5 and 7?
a.99940                 b.99960                                c.99970                 d.99990
Ans: 99999 / LCM(3,4,5,7)  = 99999 / 420 = 238 ( quotient)
238 * 420 = 99960
116)Probability of one of the power plants over heating is 0.15 per day and the probability of failure of the backup cooling system is 0.11 .If these events are independent.What is the probability of ‘big trouble’(i.e . both events taking place)?                  a.0.35                    b.0.0185                               c. 0.0165                               d.0.26
Ans:  big trouble occur when overheating and failure of cooling system happens at the same time.
0.15 * 0.11 = 0.0165
117)If the selling price of a watch is halved,the profit becomes quartered.Find the profit percentage of the watch?
a.50%                    b.66.67%                              c.100%                  d.200%
let c.p=x
s.p=y
((y/2)-x)/x=((y-x)/x)*(1/4)
y=3x
profit%=((3x-x)/x)*100
=200%
118)Simplify the expression 7log5 p + √3 /2 log5 q – ½ log5 2r
a.log5 p7 + q(√3)/2 – (√2)( √r)                        b.log5(p7 + q(√3)/2)/r        c.log  p7 .q(√3/2)/(( √2)( √r))         d. log5 p7 . q(√3/2 )– ((√2)( √r))
7logp+((3)^(1/2))/2logq-(1/2)log2r
=logp^(7)+logq^((3^(1/2))/2)-log2r^(1/2)
=log((p^(7)*q^((3^(1/2))/2))/(2r^(1/2))
119)There are 5 clients and 5 consultants in a round table meeting.In how many ways can the clients be seated such that no consultant is next to the other consultant?
a. 5! 6!                  b.4! 4!                   c.4! 5!                    d.9!                        e.c5 5! 4!
Ans:  5 clients can be arranged in 4! Ways as it is a circular arrangement.
Now 5 places left in between 5 clients. So 5 consultants can be arranged in 5! Ways.
Total: 4! * 5!
120)A company decides to reorganise its financial transaction files and put all such files into various drawers. In how many ways can 7 files be put into 3 drawers ,if any number of files can be put in each drawer?
a.73                                     b.7p3                     c.7!/4!                   d.37                                    e.7c3
121)In  AMY company,the probability that an employee takes a sick leave as well as a casual leave in a month is 0.15. The probability that an employee takes a sick leave in a month is 0.45. What is the probability that the employee would take a casual leave given that he would take a sick leave?
a.0.33                    b.0.42                    c.0.66                    d.0.7
122) When a local train travels at a speed of 60kmph, it reaches the destination on time. When the same train travels at speed of 50kmph, it reaches its destination 15mnts late. What is the length of journey?
a.       75kms                           b. 50kms                              c. 60kms                               d. 85kms
Ans. let the time taken by a train when it  takes 60kmph is x.when it takes 50kmph will be (x+15)
So distance , 60x=50(x+15)
X=75 mins
Distance= Speed * Time = (60* 75)/60  ( Convert minutes to hours by dividing with 60)
option (a) is correct.
123) Give the greatest pair of twin primes which are below 100?
a.       71, 73                            b. 93, 95                               c. 97, 99                                d. 87, 89
Ans: 71,73
124) In an examination involving quantitative aptitude and logical reasoning, 65% examinees cleared quantitative aptitude test while 70% cleared logical reasoning test. If 50% examinees passed both the tests, then how many failed in both tests?   a. 35%                                   b. 15%                                   c. 30%                                   d. 20%
Ans.  no of students who passed in atleast one subject:
AUB=65+70-50=85
If total students are 100 .no of students who failed in both subjects = total students-students who passed in atleast one subject.i.e.,100-85=15
So option (b) is correct.
125) A sum of money triples itself at compound interest in 3 years. In 9 years it will be
a. 6 times the principle  b. 12 times the principle                c. 18 times the principle                   d. 27 times the principle
Ans: d
126) 3 friends Gerard, Rooney and Ronaldson work together to dig a hole. Gerard alone can complete the work in 10 days, Rooney in 8 days and together all three can complete it in 4 days. They earn a total of Rs. 1,200. Find the share of Rooney if the money that they receive is proportional to the work that they do?
a.       Rs.480           b. Rs.165.51        c. Rs.500   d.Rs.600
Ans: Ronaldson can complete work in 40 days ( ¼ – 1/10 -1/8)
Rooney share is 1200/2 = 600
127) The number which should be subtracted from 5a^2-3ab+7b^2 to make it equal to a^2+ab+b^2 is
a.       4a2-4ab+6b2               b. 4a2-4ab+5b2                            c. 4a2+4ab+6b2                           d. 4a2-3ab+6b2    e.None of the above
Ans..( 5a2-3ab+7b2 )-( a2+ab+b2)= 4a2+4ab+6b2
So option c is correct.
128) Given that the interest is only earned on principle, if an investment of Rs.1000.00 amounts to Rs.1440.00 in 2 years, then what is the rate of interest earned?
a.       20%                b. 22%                   c. 21%                   d.11%                    e. 44%
Ans.  1000(1+r/100)2=1440
So the answer is 20%.
Option (A) is correct.
129)If nc5=nC0, then find the value of n.
a.  n=0                   B. n=1                   C. n=5                   D. n=10
Ans: Ans. nC5=nCn-5=nC0
n-5=0
n=5 so option (c) is correct
130) A bag contains 5 oranges, 4 bananas, a apples. Rohit wants to eat a banana or an apple. He draws a fruit from the bag randomly. What is the probability that he will get a fruit of his choice?
A.      3.5/12           B. 7/12                  C.5/12                   D.None of the above
Ans. total fruits are 12.
Chances  to select banana or apple is: 4+3=7
Probability =7/12
So option (b) is correct.
131)A single letter is drawn at random from the word. “ASPIRATION”, the probability that it is a vowel is?
A. ½       B. 1/3    C. 3/5   D. 2/5
132): The number of ways in which 15 students A1, A2…………..A15 can be ranked, such that A4 is always above A8 is
A. 15!                    B. 13!                     C. 15!/2                                D. 13!/2
133) solve : 0.001210*0.00011
A. 0.000000133  B. 0.00001331     C.0.001331          D.0.000000001331            E.0.1331

Ques. The unit’s digit in the product (771 x 659 x 365) is
Op 1: 1
Op 2: 2
Op 3: 4
Op 4: 6
Correct Op :
Solution:

7^1=unit digit=7

7^2=unit digit=9(7*7=49)last unit digit

7^3=unit digit=3(9*7=63)last unit digit

7^4=unit digit=1(3*7=21)last unit digit

7^5=unit digit=7(1*7=7)last unit digit

it repeats for every 4 cycle

so 71/4=remainder=3 it points 3rd cycle whose unit digit is=3

in same vise 6^anything will be resultant 6;

3^1=3
3^2=9(3*3)
3^3=7(9*3)
3^4=1(7*1)
3^5=3(1*3)
same like 7^71 term thus remainder is 1
multiply 3*6*3=24 .
unit digit is 4
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Ques. 1.52 * 0.02251/2 = ?
Op 1: 0.0375
Op 2: 0.3375
Op 3: 3.275
Op 4: 32.75
Op 5:
Correct Op : 2
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Ques. If x1/2 / 4411/2 = 0.02, the value of x is:
Op 1: 0.1764
Op 2: 1.764
Op 3: 1.64
Op 4: 2.64
Op 5:
Correct Op : 1

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Ques. The value of 21/2 upto three places of decimal is

Op 1: 1.41
Op 2: 1.412
Op 3: 1.413
Op 4: 1.414
Op 5:
Correct Op : 4
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Ques. The value of (8-25- 8-26) is:
Op 1: 7 x 8-25
Op 2: 7 x 8-26
Op 3: 8 x 8-26
Op 4: None of these
Op 5:
Correct Op : 2
Solution;
8^-25-8^-26=[(1/8^25)-(1/8^26)]= 7*8^-26
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Ques. If 22n-1 = (1 / 8n-3) then the value of n is:
Op 1: 3
Op 2: 2
Op 3: 0
Op 4: -2
Correct Op : 2
SOLUTION:
Simple put  n=2 in both side so in one side

2^2n-1=2^2*2-1=2^3=8—-(1)
.
Another Side 1/8^n-3= 1/8^-1= 1/8^-1=8 —-(2)
.
So compare both equation both are equal than value 2 should be satisfied to equation

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Ques. If 2x = 3y = 6-z, then (1/x + 1/y + 1/z) is equal to:
Op 1: 0
Op 2: 1
Op 3: 3/2
Op 4: -0.5
Op 5:
Correct Op : 1
Solution:
2x = 6 -z Þ 2 = 6-z/x ————-(i)
3y = 6 -z Þ 3 = 6-z/y ————-(ii)
Multiplying (i)and(ii)
2×3 = 6-z/x x 6-z/y
6 = 6(1-z/x) *6(1-z/y)
1 = (-z/x) +(-z/y)
1= -z(1/x +1/y)
1/-z = 1/x +1/y
1/x + 1/y + 1/z = 0

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Ques. What is the remainder when 1723 is divided by 16?

Op 1: 0
Op 2: 1
Op 3: 2
Op 4: 3
Op 5:
Correct Op : 2
————————————————————————————————————————-
Ques. What will be the remainder when 1336 is divided by 2196?
Op 1: 0
Op 2: 1
Op 3: 12
Op 4: 2195
Op 5:
Correct Op : 2
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Ques. The roots of the equation 4x-3*2x+2+32=0 would include
-Op 1: 2, 3
Op 2: 1, 2, 3
Op 3: 1, 2
Op 4: 4, 8
Op 5:
Correct Op : 1
Solution:
Split the second term and rewrite 4^(x) as 2^(2x):

2^(2x) – 3 * [2^(x) * 2^2] + 32 = 0

2^(2x) – 12 * 2^(x) + 32 = 0

Let’s give 2^x a value of y:

y^2 – 12y + 32 = 0

Factor it out:

(y – 8)(y – 4) = 0

y = 4, 8

Now substitute 2^x back for y and solve for each:

2^x = 4
x = 2

2^x = 8
x = 3
Overall:

x = 2, 3

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Ques. If ax =b, by=c and cz =a, then the value of xyz is:
Op 1: 0
Op 2: 1
Op 3: 2
Op 4: 3
Op 5:
Correct Op : 2
Solution:
ax=b
by=c
cz=a
=> ax * by * cz = bca
=> xyz = bca/abc=1
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Ques. If x = 1+21/2 and y=1-21/2, then x2+y2 is –
Op 1: 2

Op 2: 3
Op 3: 6
Op 4: 0
Op 5:
Correct Op : 3
Solution:
x2+y2= (1+2^1/2)^2+ (1-2^1/2)^2

= (a+b)^2+(a-b)^2

so, we get
1+2+2*2^1/2+1+2-2^1/2
1+2+1+2=6 ans.

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Ques. If 4x+3 = 2x+7, then the value of x is:
Op 1: 3
Op 2: 2
Op 3: 1
Op 4: None of these Op 5:
Correct Op : 3
Ques. 2x+y = 2*(2)1/2 and 2x-y = 21/2,the value of x is:
Op 1: 1
Op 2: 2
Op 3: 3
Op 4: 4
Op 5: None of these Correct Op : 1
————————————————————————————————————————-
Ques. If x = 8, y = 27, the value of (x4/3+y2/3)1/2 is:
Op 1: 5
Op 2: 6
Op 3: 7
Op 4: 8
Op 5: None of these Correct Op : 1
————————————————————————————————————————-
Ques. If xy = yx and x = 2y, the value of y is:
Op 1: 1
Op 2: 2

Op 3: 3
Op 4: 4
Op 5: None of these
Correct Op : 2
Solution:
put x=2y

> (2y)^y = y^2y

> 2^y * y^y =y^y * y^y

>2^y = y^y

y=2
————————————————————————————————————————-
Ques. If 2x * 3y = 18 and 22x * 3y= 36, the value of x is:
Op 1: 0
Op 2: 1
Op 3: 2
Op 4: 3
Op 5: None of these Correct Op : 2
Ques. What is the value of 50^0 ?
Op 1: 0
Op 2: 1
Op 3: 50
Op 4: None of these
Op 5:
Correct Op : 2
Solution:

anything power zero is zero
50^0=1
————————————————————————————————————————-
Ques. What is the value of 6-2 ?
Op 1: 1/36
Op 2: 36
Op 3: -36
Op 4: None of these
Op 5:
Correct Op : 1
Solution:
answer is 1/6 *1/6 = 1/36
————————————————————————————————————————-
Ques. What is the value of 0-10 ?
Op 1: 0
Op 2: 1
Op 3: -10

Op 4: None of these
Op 5:
Correct Op : 4

Solution:

0^-10= 1/(0^10)=1/0= not defined
————————————————————————————————————————-
Ques. What is the value of 251.5 ?
Op 1: 325
Op 2: 32.5
Op 3: 125
Op 4: None of these
Op 5:
Correct Op : 3

Solution:

25^3/2=(5^2)^3/2 then 5^3=125
————————————————————————————————————————-
Ques. What is the value of (0.027)1/3?
Op 1: 0.3
Op 2: 0.03
Op 3: 0.003
Op 4: None of these
Op 5:
Correct Op : 1
————————————————————————————————————————-
Ques. What is the value of (0.016)1/4?
Op 1: 0.2
Op 2: 0.02
Op 3: 0.002
Op 4: None of these
Op 5:
Correct Op : 4

Solution;