divelab/Sys2Bench huggingface dataset:
Question: Present ages of X and Y are in the ratio 2:3 respectively. Four years hence this ratio will become 3:4 respectively. What is X's present age in years?
Options:
A)8
B)36
C)37
D)39
E)40
Rationale: Let the present ages of X and Y be 2x and 3x years respectively.
Then, (2x + 4)/(3x + 4) = 3/4
4(2x + 4) = 3(3x + 4) =>8x+16=9x+12 => x=4
X's present age = 2x = 2*4 = 8
ANSWER:A
Answer: A
Question: A tree increases annually by 1/8th of its height. By how much will it increse after 2 years, if it stands today 64 cm high?
Options:
A)72 cm
B)74 cm
C)75 cm
D)81 cm
E)83 cm
Rationale: Increase % = (1/8 x 100)%
= 12 1/2 % = 25/2 %
height after 2 years =(64 x(1+(25/2x100)power of 2)) cm
= (64 x 9/8 x 9/8 ) cm= 81 cm
Answer is D
Answer: D
Question: If 32455 × 3145208 × m^100 is divisible by 5, which of the following could be the value of m?
Options:
A)6000209
B)5644564
C)2345678
D)1000000
E)2355232
Rationale: The first two terms are not divisible by 5, so we need the third term to be divisible by %. The only way that (m^10) is going to be a multiple of 5 is if m is a multiple of 5. Therefore, we need the single answer that is a multiple of 5.
Answer =(D)
Answer: D
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,45) and (-5,15). Which can be the coordinate of fourth vertex?
Options:
A)(-5,-5)
B)(5,45)
C)(-5,-25)
D)(-5,10)
E)(15,25)
Rationale: A(-5, 15)
B(5, 15)
C(5, 45)
X(-5, 45): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 45): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:B
Answer: B
Question: {3, 5, 8, y}
For the above mentioned Set, Mean of the set is equal to Range of the set then find out possible values of y
Options:
A)16/5, 28/3
B)4, 16/5
C)4, 16/5, 28/3
D)4, 28/3
E)3, 4, 5
Rationale: The set can have the following forms:
1. {3,5,8,y} , range = y-3 and mean = 4+y/4, y= 28/3
2. {3,5,y,8} , range = 5 and mean = 4+y/4, y=4
3. {3,y,5,8} , range = 5 and mean = 4+y/4, y=4
4. {y,3,5,8} , range = 8-yand mean = 4+y/4, y=16/5. But as y<3 (assumed here), y=3.2 can not be true. Hence reject this case.
Thus the possible values are 4 and 28/3.
D is the correct answer.
Answer: D
Question: A small college reduced its faculty by approximately 23 percent to 195 professors. What was the original number of faculty members?
Options:
A)253
B)208
C)224
D)254
E)302
Rationale: If x is the original number of faculty members, then after 23% reduction in faculty members number is .77x
but we are given .77x = 195
x = 253
So the original number of faculty members is 253
Correct Answer - A
Answer: A
Question: A book is bought for $32 and sold for $56. What is the profit in percentage?
Options:
A)15
B)35
C)75
D)25
E)85
Rationale: 56/32 = 1.75
The answer is C.
Answer: C
Question: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
Options:
A)Rs. 21,000
B)Rs. 22,500
C)Rs. 25,300
D)Rs. 25,800
E)Rs. 28,800
Rationale: 85 : 18700 = 115 : x
x = (18700 x 115)/85 = 25300.
Hence, S.P. = Rs. 25,300.
Answer: Option C
Answer: C
Question: There are many numbers that can be expressed as the sum of three squares in three different ways.
Can you find out the smallest of such number?
Options:
A)87
B)54
C)29
D)30
E)70
Rationale: B
54
7^2 + 2^2 + 1^1
6^2 + 3^2 + 3^2
2^2 + 5^2 + 5^2
Answer: B
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 3/4 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?
Options:
A)30
B)45
C)60
D)120
E)135
Rationale: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (3/4) of total igneous rocks.
(2/3)*Total igneous rocks = 30
Total igneous rocks = 30 * (4/3) = 40
Total sedimentary rocks = 2*Total igneous rocks = 2*40 = 80
Total number of rocks = 40 + 80 = 120
Answer (D)
Answer: D
Question: Tough and Tricky questions: Probability.
Medical analysts predict that half of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?
Options:
A)16/81
B)7/8
C)2/3
D)19/27
E)65/81
Rationale: At the end of each day we will have 1/2 alive. So after 3 days we will have (1/2)^3 people alive. Therefore, fraction of dead people will be 1-(1/2)^3=7/8.
The correct answer is B.
Answer: B
Question: If the mean of numbers 28, x, 50, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?
Options:
A)76.5
B)58
C)39.8
D)90.3
E)66.67
Rationale: Mean = (Sum of all no. in series)/(no. in series)
M1 = 62 = (X+28+50+78+104)/(5)
62 x 5 = 260 + X
X = 50
Therefore mean of 2nd series
M2 = (X+48+62+98+124)/5
M2 = 76.5
Answer = A
Answer: A
Question: 10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day?
Options:
A)4 days
B)10 days
C)20 days
D)25 days
E)26 days
Rationale: Explanation:
10*12*15/20 = 24*20*x/32
X=4
Answer: Option A
Answer: A
Question: Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 8, and 9. seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 3:01 pm (i.e. three hours and one minute later)?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: The least common multiple is 2*2*2*3*3*5=360.
10860 seconds / 120 = 30 + remainder.
The answer is B.
Answer: B
Question: The curved surface of a sphere is 64 pi cm2. Find its radius?
Options:
A)1 cm
B)4 cm
C)2 cm
D)3 cm
E)5 cm
Rationale: 4 Ï€r2 = 64 => r = 4
ANSWER B
Answer: B
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is :
Options:
A)15
B)30
C)45
D)60
E)65
Rationale: Sol.
Let the three integers be x, x + 2 and x + 4. Then, 3x = 2(x + 4) + 3 = ⇔ x = 11.
∴ Third integer = x + 4 =15.
Answer A
Answer: A
Question: In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)3 sec
C)8.9 sec
D)6.9 sec
E)2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 120/40
= 3 sec.
Answer: B
Answer: B
Question: The average score of a cricketer in 2 matches is 27 and in other 3 matches is 32. Then find the average score in all the 5 matches?
Options:
A)25
B)27
C)30
D)35
E)42
Rationale: Average in 5 matches = (2*27 + 3*32)/2+3 = 54+96 / 5 = 30
Answer is C
Answer: C
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)84%
B)94%
C)65%
D)64%
E)34%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer:D
Answer: D
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.07. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fifth day it is overdue?
Options:
A)$0.60
B)$0.70
C)$0.86
D)$0.90
E)$1.00
Rationale: 1st day fine - 0.07
2nd day fine - 0.07*2 = 0.14 (as doubling gives lower value)
3rd day fine - 0.14*2 = 0.28 (as doubling gives lower value)
4rd day fine - 0.28*2 = 0.56 (as doubling gives lower value)
5th day fine - 0.56 + 0.3 = 0.86 (as doubling gives higher value we add 0.3 this time)
Answer: C.
Answer: C
Question: (2^2+4^2+6^2+.....+20^2)=?
Options:
A)770
B)1155
C)1540
D)385x385
E)None of them
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x10)^2
=2^2 x (1^2+2^2+3^2+.......+10^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x10x11x21)
=(4x5x77)=1540
Answer is C
Answer: C
Question: If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:3
Webs 3:1
1 x 3 x x = 3 x 1 x 3
=> x= 3
Answer is E
Answer: E
Question: How many three digits numbers can be formed by using the digits 1,2,3,4,5.
Options:
A)255
B)135
C)225
D)125
E)175
Rationale: We have to determine the total number of three digits numbers formed by using the digits 1,2,3,4,5. Clearly the repetition of digits allowed.Units place can be filled by any of the digits in 5 ways. Simillarly each one of the tens and hundreds place can be filled in 5 ways. Total number of required number =5x5x5 =125 Answer : D
Answer: D
Question: If 4 people are selected from a group of 5 married couples, what is the probability that none of them would be married to each other?
Options:
A)1/33
B)2/33
C)1/3
D)16/33
E)8/21
Rationale: If we are to select 4 people from 5 couples WITHOUT any restriction, how many ways can we make the selection? 10!/4!6! = 210
If we are to select 4 people from 5 couples WITH restriction that no married couple can both make it to the group, only a representative?
5!/4!1! = 5
But we know that to select a person from each couple, take 2 possibilities
5*2*2*2*2 = 80
Probability = Desired/All Possibilities = 80/210 = 8/21
Answer: E
Answer: E
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
Options:
A)1/8
B)1/7
C)1/3
D)1/5
E)1/2
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Answer: B
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 3.
Options:
A)8
B)5
C)11
D)3
E)4
Rationale: 6 * 15 * 3 = (√(6 + 2)(15 + 3) )/ (3 + 1)
= (√8 * 18) / 4
= (√144) / 4
= 12 / 4 = 3.
Answer is D.
Answer: D
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^26, then n =
Options:
A)3
B)6
C)12
D)23
E)25
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^26
=> 4 x 2^2n = 4^26 = 2^52
=> 2^2 x 2^2n = 2^52
=> 2^(2n+2) = 2^52
=> 2n+2 = 52=> n =25
So. Answer will be E
Answer: E
Question: A train 125 m long passes a man, running at 7 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)35 km/hr
B)50 km/hr
C)45 km/hr
D)52 km/hr
E)87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 7) km/hr. x - 7 = 45 ==> x = 52 km/hr.
Answer: D
Answer: D
Question: A man's speed with the current is 20 kmph and speed of the current is 2 kmph. The Man's speed
against the current will be
Options:
A)16 kmph
B)12 kmph
C)14 kmph
D)17 kmph
E)None of these
Rationale: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 2 = 18
Now speed against the current will be
speed of the man - speed of the current
= 18 - 2 = 16 kmph
Answer: A
Answer: A
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
Options:
A)33.8
B)33.5
C)33.3
D)33.9
E)33.1
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer:C
Answer: C
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)28 sec
B)16 sec
C)39 sec
D)18 sec
E)17 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 150 = 390 m.
Time taken = 390/10 = 39 sec.
Answer:C
Answer: C
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 3 kg more than Peter. Together the three of them picked 27 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
Options:
A)6, 9 and 12
B)12, 9 and 6
C)9, 6 and 12
D)12, 6 and 9
E)6, 12 and 9
Rationale: M = 2P
L = P+3
M + P + L = 27
2P + P + (P+3) = 27
P = 6, M = 12, L = 9
Therefore, Mary, Peter, and Lucy picked 12, 6, and 9 kg, respectively.
The answer is D.
Answer: D
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 55 different possible selections of the 2 members, how many members does the club have?
Options:
A)11
B)27
C)40
D)57
E)95
Rationale: I have done this problem by substituting numbers
We have n!/2!(n-2)! = 55
or n(n-1)/2 = 110 or n^2-n -110 =0 or n^2-11n+10n-110 =0 or n(n-11) +10(n-11) =0 or (n-11)(n+10)=0
n=11 satisfies the equation
A
Answer: A
Question: If N = 3^0.15 and N^b = 9, b must equal
Options:
A)3/80
B)3/5
C)4
D)5/3
E)40/3
Rationale: 15/100 = 3/20
N = 3 ^ 3/20
N^b = 3^2
(3^3/20)^b = 3^2
b = 40/3
Answer: E
Answer: E
Question: The ratio of 2 numbers is 5:2 and their H.C.F. is 20. Their L.C.M. is ?
Options:
A)400
B)300
C)200
D)100
E)40
Rationale: Let the numbers be 5x and 2x
Their H.C.F. = 20
so the numbers are 5*20 , 2*20 = 100, 40
L.C.M. = 200
Answer is C
Answer: C
Question: If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Options:
A)2:5
B)2:4
C)3:0
D)2:1
E)2:3
Rationale: 5M + 2B = 4(1M + 1B)
5M + 2B = 4M + 4B
1M = 2B
The required ratio of work done by a man and a boy = 2:1 .Answer: D
Answer: D
Question: The effective annual rate of interest corresponding to a nominal rate of 8% per annum payable half-yearly is?
Options:
A)6.06%
B)8.16%
C)6.08%
D)6.09%
E)6.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 4/100)2] = Rs. 108.16 Effective rate = (108.16 - 100) =8.16%
ANSWER:B
Answer: B
Question: If x is real, find the maximum value of the expression -2x^2 + 5x + 7.
Options:
A)6.125
B)8.125
C)10.125
D)12.125
E)14.125
Rationale: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+5x+7 = (-2x+7)(x+1)
The roots are 7/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 1.25
The maximum value is -2(1.25)^2+5(1.25)+7 = 10.125
The answer is C.
Answer: C
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $540 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Options:
A)23,000
B)24,500
C)25,500
D)26,500
E)27,500
Rationale: Let the weekly sales of both = x
540+(x−1000)8/100=10/100x
x = 23000
ANSWER:A
Answer: A
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 90 km/hr. When will he overtake the thief?
Options:
A)6 p.m
B)9 p.m
C)4 p.m
D)2 p.m
E)1 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 90(x - 1/2) => x = 3/2 hrs.
So, the thief is overtaken at 4 p.m.'
Answer: C
Answer: C
Question: REDO’s manufacturing costs for sets of horseshoes include a $10,500 initial outlay, and $30per set. They can sell the sets $60. If profit is revenue from sales minus manufacturing costs, and the company producessells 1000 sets of horseshoes, what was their profit?
Options:
A)$19500
B)$15500
C)$29500
D)$39500
E)$1500
Rationale: Total Manufacturing cost = 10500+1000*30 = 40500
Total Selling cost = 1000*60= 60000
Profit = 60000-40500 = 19500
Answer : A
Answer: A
Question: The sum of ages of 5 children born at the intervals of 3 years each is 65 years. What is the age of the youngest child?
Options:
A)3 years
B)4 years
C)6 years
D)7 years
E)8 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 65
5x = 35
x = 7.
Age of the youngest child = x = 7 years.
D)
Answer: D
Question: If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of EVEN integers from 30 to 50, inclusive, what is the value of x+y ?
Options:
A)810
B)811
C)830
D)850
E)851
Rationale: Since the integers from 30-50 are consecutive we can use the "median x # of terms formula" to determine x. There are 21 terms and the median is 40. This gives a total of 21x40 = 840. There are 11 even integers from 30-50 = y. Therefore, x+y = 851. Answer: E
Answer: E
Question: A farmer has a rose garden. Every day he either plucks 7 or 6 or 24 or 23 roses. The rose plants are intelligent and when the farmer plucks these numbers of roses, the next day 37 or 36 or 9 or 18 new roses bloom in the garden respectively. On Monday, he counts 189 roses in the garden. He plucks the roses as per his plan on consecutive days and the new roses bloom as per intelligence of the plants mentioned above. After some days which of the following can be the number of roses in the garden?
Options:
A)6
B)7
C)6
D)4
E)1
Rationale: If he plucks 23, then only 18 grows the next day. This means total roses get decreases by 5. So after n days assume the number of roses got decreased 185 where n = 37, then 4 roses left.
Answer:D
Answer: D
Question: Find the cost of fencing around a circular field of diameter 30 m at the rate of Rs.5 a meter?
Options:
A)288
B)132
C)772
D)592
E)471.25
Rationale: 2 * 22/7 * 15 = 94.25
94.25 * 5 = Rs.471.25
Answer: E
Answer: E
Question: If y > 0, (9y)/20 + (3y)/10 is what percent of y?
Options:
A)40%
B)50%
C)60%
D)70%
E)75%
Rationale: can be reduced to 9y/20+6y/20 =15y/20=75%
Answer E
Answer: E
Question: A code is to be made by arranging 6 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B and one of the letters used will be the letter C . If there is only one way to present each letter, how many different codes are possible?
Options:
A)230
B)360
C)420
D)840
E)5,040
Rationale: we have 6 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 6!/2!1!=360
ans B
Answer: B
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards W will he need to gain this Sunday if he wants to keep his season average above 100 yards?
Options:
A)101
B)116
C)130
D)W=131
E)W=141
Rationale: Sorry the answer W=141 is D.
Answer: D
Question: 120 +520 ÷ 5.00 = ?
Options:
A)100
B)150
C)120
D)520
E)None
Rationale: Answer
Given expression = 120 +520 ÷ 5.00
= 120 + 104
= 224
Correct Option: E
Answer: E
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 4200. What was Simran share in the profit?
Options:
A)s 9500
B)s 1080
C)s 1008
D)s 1820
E)s 1800
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.4200x 3/7	= Rs. 1,800.
ANSWER :E
Answer: E
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options:
A)2:3
B)1:1
C)3:4
D)4:3
E)5:5
Rationale: 5/100A+4/100B = 2/3(6/100A+8/100B)
=>1/20A+1/25B= 1/25A+4/75B
=> (1/20-1/25)B= 1/25A+4/75B
(1/20-1/25)A = (4/75-1/25)B
1/100A=1/75B
A/B=100/75=4/3
REQ RATIO = 4:3
ANSWER D
Answer: D
Question: A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number.
Options:
A)81
B)90
C)100
D)61
E)73
Rationale: Let the ten's digit be x. Then, unit's digit = (9 - x).
Number = l0x + (9 - x) = 9x + 9.
Number obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.
therefore, (9x + 9) - 63 = 90 - 9x => 18x = 144 => x = 8.
So, ten's digit = 8 and unit's digit = 1.
Hence, the required number is 81.
Answer A)81.
Answer: A
Question: The number 219 can be written as sum of the squares of 3 different positive integers. What is the difference of these 2 different larger integers?
Options:
A)6
B)2
C)3
D)5
E)4
Rationale: sum of the squares of 3 different positive integers = 219
13^2 + 7^2 + 1^2 = 219
now,
difference of these 2 different larger integers = 13 - 7 = 6
Ans - A
Answer: A
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 3/4 brand A and 1/4 brand B. what fraction of the cost of the blend is Brand A?
Options:
A)a. 1/3
B)b. 2/5
C)3. 1/2
D)4. 2/3
E)5. 6/7
Rationale: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.75 A and 0.25 B ---> Cost of the blend = Cbl = 0.75*200+0.25*100= 175
Thus fraction of A in the blend = 0.75*200/175 = 6/7.
Answer : E
Answer: E
Question: A car manufacturer produces only red and blue TCS Models which come out of the final testing area at random. What are the odds that five consecutive cars of same color will come through the test area at any one time?
Options:
A)1 in 16
B)1 in 125
C)1 in 32
D)1 in 25
E)1 in 15
Rationale: p(5 consecutive cars of same color)=p(5 red)+p(5 blue)
=1/2^5+1/2^5
=1/16
ANSWER:A
Answer: A
Question: In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (14, 2), (14,-5)?
Options:
A)90
B)95
C)104
D)117
E)182
Rationale: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (8 + 7) × 12 = 90.
The answer is A.
Answer: A
Question: Find the income derived from 88 shares of $ 25 each at 5 premium,
brokerage being (1/4) per share and the rate of dividend being 7(1/2)% per annum. Also, find the rate of interest on the investment.
Options:
A)6.2%
B)7.5%
C)6.5%
D)8.2%
E)4.6%
Rationale: Cost of 1 share = $ [25+5+1/4)] = $ (121/4).
Cost of 88 shares = $[(121/4)*88] = $ 2662.
Therefore Investment made = $ 2662.
Face value of 88 shares = $ (88*25) = $ 2200.
Dividend on $ 100 = (15/2).
Dividend on $ 2200 = $ [(15/20*(1/100)*2200] = $ 165.
 Income derived = $ 165.
Rate of interest on investment = [(165/2662)*100] = 6.2 %.
Answer A.
Answer: A
Question: In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that
the proportion of manganese becomes 10%
Options:
A)1.5 Kg
B)2 Kg
C).5 Kg
D)1 Kg
E)None of these
Rationale: Explanation :
By the rule of alligation, we have
Percentage concentration of
manganese in the mixture : 20 Percentage concentration of
manganese in pure iron : 0
Percentage concentration of manganese in the final mixture
10
10 - 0 = 10 20 - 10 = 10
=> Quantity of the mixture : Quantity of iron = 10 : 10 = 1 : 1
Given that Quantity of the mixture = 1 Kg
Hence Quantity of iron to be added = 1 Kg
Answer : Option D
Answer: D
Question: A fair white coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
Options:
A)A)37/256
B)B)56/256
C)C)65/256
D)D)70/256
E)E)81/256
Rationale: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
Answer: A
Question: The owner of a local jewelry store hired four watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/4 of the diamonds he had then, and 4 more besides. He escaped with 4 diamonds. How many did he steal originally?
Options:
A)4384
B)3384
C)2384
D)None of these
E)Cannot be determined
Rationale: Explanation :
Since, thief escaped with 4 diamonds,
Before 4th watchman, he had ( 4 + 4 ) x 4 = 32 diamonds.
Before 3rd watchman, he had (32+ 4 ) x 4 = 144 diamonds.
Before 2nd watchman, he had ( 144 + 4 ) x 4 = 592 diamonds.
Before 1st watchman, he had ( 592 + 4 ) x 4 = 2384 diamonds.
Answer : C
Answer: C