mathewhe/aqua_rat huggingface dataset:
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 2. What is the radius of circle O?
(A) –2/pi
(B) 1
(C) 3
(D) 4
(E) 5
Rationale: pi*r^2 + 2r -2*pi*r = 2
Simplifying the equation: pi*r(r-2)+2r=2
Without much algebraic: We can Test the answers quickly, then 1 is the only possible answer that will eliminate pi from equation.
Answer is B
Answer: (B) 1
Question: BCB, DED, FGF, HIH, ___
(A) KOP
(B) QLM
(C) JKJ
(D) PSQ
(E) IOP
Rationale: This series consists of a simple alphabetical order with the first two letters of all segments: B, C, D, E, F, G, H, I, J, K. The third letter of each segment is a repetition of the first letter.
ANSWER:C
Answer: (C) JKJ
Question: All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes are there whose three faces are coloured ?
(A) 4
(B) 8
(C) 16
(D) 24
(E) 2
Rationale: There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm
Number of small cubes having three faces coloured = No. of corners = 8
Answer: B
Answer: (B) 8
Question: Jerry has 3 flavors of ice cream in his parlor. How many options are there for George to pick a one-flavor, two-flavor or three-flavor order?
(A) 2
(B) 3
(C) 4
(D) 7
(E) 8
Rationale: 3C1 + 3C2+ 3C3 = 7.
Ans D.
Answer: (D) 7
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 229
(B) 288
(C) 600
(D) 888
(E) 121
Rationale: D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Answer: C
Answer: (C) 600
Question: In a group of 1 boy and 9 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?
(A) 60
(B) 68
(C) 76
(D) 84
(E) 92
Rationale: Number of ways to select four children is 10C4 = 210
Number of ways to choose only girls is 9C4 = 126
Number of ways that at least one boy is selected is 210 - 126 = 84
The answer is D.
Answer: (D) 84
Question: How much 60% of 50 is greater than 45% of 30?
(A) 18
(B) 91
(C) 16.5
(D) 17
(E) 12
Rationale: (60/100) * 50 – (45/100) * 30
30 - 13.5 = 16.5
Answer: C
Answer: (C) 16.5
Question: If 3-X < (2-5X)/3, which of the following is correct?
(A) X < -7/2.
(B) X > -5.
(C) X > 5.
(D) -5 < X < 0.
(E) 0 < X < 5.
Rationale: 3-X < (2-5X)/3
9-3X < 2- 5X
7 < -2X
-7/2>X
A is the answer
Answer: (A) X < -7/2.
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes?
(A) 5!
(B) 10!/(5!5!)
(C) 10!/5!
(D) 10!
(E) 10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations R of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: (B) 10!/(5!5!)
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
(A) 1/80
(B) 1
(C) 40
(D) 1/40
(E) 80
Rationale: Let the required number of days be x.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
Cows	1:40 :: 40 : x
Bags 40:1
1 * 40 * x = 40 * 1 * 40
x = 40.
Answer is C.
Answer: (C) 40
Question: A snooker tournament charges $45.00 for VIP seats and $20.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
(A) 200
(B) 276
(C) 230
(D) 240
(E) 250
Rationale: let no of sits in vip enclosure is x then x*45 +20( 320-x) =7500 or 25x = 7500 -6400 , x = 1100/25 =44
vip =44 general 320-44 = 276
B
Answer: (B) 276
Question: A bag has 9 green balls and 23 pink balls. How many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1:1?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Suppose x green balls need to be added.
Then, the number of green balls becomes 9 + x, and the number of pink balls remains the same, 23.
But now the ratio of green and pink balls is 1:1
This means,
(9 + x)/23 = 1/1
Solving this we get x = 14.
Ans E
Answer: (E) 14
Question: A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
(A) 24 km/hr
(B) 25 km/hr
(C) 26 km/hr
(D) 23 km/hr
(E) 22 km/hr
Rationale: Speed upstream =8/(24/60) = 20 km/hr
Speed of the stream = 4 km/hr
speed of boat in still water = (20+4) = 24 km/hr
Answer : Option A
Answer: (A) 24 km/hr
Question: If by reduction of rupee 1 per kg in the price,a person can buy one kg more for Rs.56. find the original price of the per kg?
(A) 7rs/kg
(B) 8rs/kg
(C) 9rs/kg
(D) 6rs/kg
(E) 5rs/kg
Rationale: for Rs.56 he can buy = 56/8rs = 7kg rice. (Original Price)
By reduction of Rs.1 per kg, = 56/7rs = 8kg rice. (As per reduction)
Original Price(8rs), he can buy = 7kg of rice
ANSWER:B
Answer: (B) 8rs/kg
Question: Of the 500 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
(A)  65
(B)  100
(C)  115
(D)  130
(E)  325
Rationale: 300 prefer X (Group 1);
200 prefer Y (Group 2).
City Y needs 375 people: letall 200 who prefer Y (entire Group 2) be relocated there, the rest 175 will be those who prefer X from Group 1;
City X needs 125 people: 300-175=125 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 200+125=325.
Answer: E.
Answer: (E)  325
Question: one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is?
(A) 150
(B) 133
(C) 175.5
(D) 178
(E) 190
Rationale: Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. 126 + 135 = Rs. 130.50
2
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind
Rs. 130.50	Mean Price
Rs. 153	Rs. x
(x - 153)	22.50
x - 153	= 1
22.50
x - 153 = 22.50
x = 175.50
C
Answer: (C) 175.5
Question: A train covers a distance of 36 km in 12 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?
(A) 330
(B) 340
(C) 350
(D) 360
(E) 370
Rationale: Speed = (36/12 * 60) km/hr = (180 * 5/18) m/sec = 50 m/sec.
Length of the train = 50 * 7 = 350 m.
Answer: Option C
Answer: (C) 350
Question: Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?
(A) 26/36
(B) 26/31
(C) 26/19
(D) 26/33
(E) 26/38
Rationale: Let ages of Ramu and Shyam be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x- 7)/(y - 7) = 2/3
=> 3x - 21 = 2y - 14 => 3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28years
=> x = 21 years
Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.
Answer:D
Answer: (D) 26/33
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
(A) 1510
(B) 1315
(C) 1015
(D) 1215
(E) 1715
Rationale: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
Answer: Option C
Answer: (C) 1015
Question: 15 : 5 seconds :: ? : 10 minutes
(A) 10
(B) 15
(C) 30
(D) 25
(E) 30
Rationale: 15*10=5*x
x=30
ANSWER:C
Answer: (C) 30
Question: Certain sum becomes 3 times it self at compound interest in 10 years. In how many years it becomes 9 times?
(A) 10 Years
(B) 20 Years
(C) 30 Years
(D) 40 Years
(E) 45 Years
Rationale: P(1 + R/100)10 = 3P
=> P(1 + R/100)10 = 3
Let P(1 + R/100)n = 9P
=> (1 + R/100)n = 9
=> 32 = [(1 + R/100)10]2
=> (1 + R/100)n => (1 + R/100)20
=> n = 20 Years.
B
Answer: (B) 20 Years
Question: Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?
(A)  25%
(B)  22.2%
(C)  20%
(D)  12.5%
(E)  11.7%
Rationale: Welcome, just post the question and the choices
Let's see, the way I did it was
1/6 are clerical out of 3600 so 600 are clerical
600 reduced by 1/3 is 600*1/3
so it reduced 200 people , so there is 400 clerical people left
but since 200 people left, it also reduced from the total of 3600 so there are 3400 people total
since 400 clerical left / 3400 people total
you get (A) 11.7%
Answer :E
Answer: (E)  11.7%
Question: Two circles are there one with arc area 60digree equal to 45digree of another circle find the area of circle1:circle2 ratio
(A) 3:4
(B) 1:4
(C) 1:2
(D) 2:3
(E) 1:3
Rationale: area for first circle=(3.14*r^2)/6
area of second circke=(3.14*R^2)/8
therefore, ratio=3:4
ANSWER:A
Answer: (A) 3:4
Question: A $500 investment and a $1,500 investment have a combined yearly return of 22 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?
(A) 29%
(B) 20%
(C) 27%
(D) 25%
(E) 12%
Rationale: The equation we can form the question :
Return on Total Investment = Sum of individual Investments
(500+1500)(22)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.
Solving the equation, we get x = 27% ( Option C )	ANSWER:C
Answer: (C) 27%
Question: Robert tossed a fair coin 3 times. What is the probability that the coin landed heads up exactly twice?
(A) 0.125
(B) 0.250
(C) 0.375
(D) 0.75
(E) 0.875
Rationale: Total number of outcomes = 2 * 2 * 2 = 8
Out of 3 times we need heads exactly 2 times = 3C2 = 3
Probability = 3/8 = 0.375
The answer is, therefore, (C).
Answer: (C) 0.375
Question: Two unbiased coins are tossed. What is probability of getting at most one tail ?
(A) 1/2
(B) 1/3
(C) 3/2
(D) 3/4
(E) None of these
Rationale: Explanation:
Total 4 cases = [HH, TT, TH, HT]
Favourable cases = [HH, TH, HT]
Please note we need atmost one tail, not atleast one tail.
So probability = 3/4
Option D
Answer: (D) 3/4
Question: Sara and Alan start a company with Rs.100000 and Rs.50000 respectively. how should they share their profits at the end of one year?
(A) 1:2
(B) 3:4
(C) 3:8
(D) 3:1
(E) 3:2
Rationale: The ratio of the investments made by A and B =
100000: 50000=> 2:1.Answer: A
Answer: (A) 1:2
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time F will it take to fill the tank now?
(A)  50% less time
(B)  50% more time
(C)  75% less time
(D)  75% more time
(E)  100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that is F=50 % less.A
Answer: (A)  50% less time
Question: Dawson sold an item for Rs.3600/- and incurred a loss of 10%. At what price should he have sold the item to have gained a profit of 10%?
(A) 4000
(B) 4100
(C) 4200
(D) 4300
(E) 4400
Rationale: Explanation:
10% loss means SP = 90% of CP
:. CP = Rs.3600x100/90 = Rs.4000.
The SP for a gain of 10% = 4000+10% of 4000 = 4000+400 =Rs4400.
Answer: Option E
Answer: (E) 4400
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability Y that at least one will be orange?
(A) Y=7/10
(B) Y=3/5
(C) Y=2/5
(D) 3/10
(E) 1/10
Rationale: Method 1
Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: (A) Y=7/10
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 7m
(B) 8m
(C) 4m
(D) 3m
(E) 2m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:E
Answer: (E) 2m
Question: How many numbers between 10 - 99 yield a reminder of 8 when divided by 10 and also yield a remainder of 2 when divided by 8?
(A) One
(B) Three
(C) Two
(D) Five
(E) Four
Rationale: Answer = B) Three
Numbers between 10 - 99 giving remainder 8 when divided by 10 = 18, 28, 38, 48, 58, 68, 78, 88, 98
The above Numbers giving remainder 2 when divided by 8 = 18, 58, 98 = 3
Answer: (B) Three
Question: In how much time will a train of length 100 m, moving at 54 kmph cross an electric pole?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: Convert kmph to mps. 54 kmph = 54 * 5/18 = 15 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/15= 6.7 sec.
Answer:D
Answer: (D) sec
Question: There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback?
(A) 75
(B) 120
(C) 210
(D) 246
(E) 252
Rationale: Paperbacks - 4, hardbacks - 6
5 books in total and at least 1 from each.
Total combinations for 5 books = (1pb, 4 hb) + (4pb, 1hb) + (3pb, 2hb) + (2pb, 3hb)
1pb, 4hb = 4c1*6c4 = 60
4pb,1hb = 4c4*6c1 = 6
3pb,2hb = 4c3*6c2 = 60
2pb,3hb = 4c2*6c3 = 120
Total combinations of 5 books = 60+6+60+120 = >246
Ans D.
Answer: (D) 246
Question: If an integer n is to be chosen at random from the integers 1 to 84, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
(A) 9/14
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 84, there are 42 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (42 + 12)/84
= 54/84
= 9/14
Ans is A
Answer: (A) 9/14
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
(A) 90
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: 10 and 190 inclusive would mean there are 19 terms.
No need to add up all the terms and further divide by 19 since the terms are evenly spaced in ascending order from 10, 20, 30........190
The middle term is the average which is the tenth term = 100
C is the answer.
Answer: (C) 100
Question: 82*83*84*..89 what is the digit in units place?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: In the product
82*83*84 *85*86......*89
last( unit) digit will be zero as 82 * 85 will give zero as last (unit ) digit and further multiplication with any number will also give zero at unit place.
ANSWER:A
Answer: (A) 0
Question: A certain company’s profit in 1996 was 25 percent greater than its profit in 1995, and its profit in 1997 was 30 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
(A) 5%
(B) 62.5%
(C) 33%
(D) 35%
(E) 38%
Rationale: Profit in 1995 - 100
Profit in 1996 - 125
%increae Profit in 1997 in comparison to 1995 = 25 + 125*30%= 62.5
Correct Option : B
Answer: (B) 62.5%
Question: Average age of students of an adult school is 40 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
(A) 1200
(B) 120
(C) 360
(D) 240
(E) None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 40x + 120*32 = (x + 120)36 ⇒ x = 120
So, Required no. of students after joining the new students
= x + 120 = 240.
Answer : D
Answer: (D) 240
Question: A sum of money is sufficient to pay A's wages for 20 days and B's wages for 30 days. The same money is sufficient to pay the wages of both for?
(A) 12days
(B) 15days
(C) 20days
(D) 18days
(E) 22days
Rationale: Let the total money be $x
A's 1day work = $ x/20
B's 1day work = $ x/30
A+B 1day work = $ x/12
Money is sufficient to pay the wages of both for 12days
Answer is A
Answer: (A) 12days
Question: On a sum of money, the simple interest for 2 years is Rs. 326, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
(A) 15%
(B) 14.25%
(C) 8.58%
(D) 10.5%
(E) 11.5%
Rationale: Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 326 = 14
(R Ã— SI)/(2 Ã— 100) = 14
(R Ã— 326)/(2 Ã— 100) = 14
R = 8.58%
Answer: Option C
Answer: (C) 8.58%
Question: If 2x + 3y = 15; 2y + z = 19 and x + 2z = 29, what is the value of x + y + z ?
(A) 19
(B) 32
(C) 26
(D) 22
(E) None of these
Rationale: On solving equation we get
x = 3, y = 3, z = 13
Answer A
Answer: (A) 19
Question: There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
(A) 71 ways
(B) 83 ways
(C) 85 ways
(D) 91 ways
(E) 98 ways
Rationale: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.
case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.
Thus, total number of ways is 7+84= 91 ways.
D
Answer: (D) 91 ways
Question: An amount of Rs.3120 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
(A) 720
(B) 360
(C) 250
(D) 280
(E) 290
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 3120 = Rs. 720
Answer: A
Answer: (A) 720
Question: The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 239
(B) 277
(C) 205
(D) 88
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (170 + X)/30
= 25/2 ==> 2(170 + X) = 750 ==> X = 205 m.
Answer: C
Answer: (C) 205
Question: A man swims downstream 28 km and upstream 12 km taking 2 hours each time, what is the speed of the man in still water?
(A) 10
(B) 8
(C) 5
(D) 2
(E) 4
Rationale: 28 --- 2 DS = 14
? ---- 1
12 ---- 2 US = 6
? ---- 1 M = ?
M = (14 + 6)/2 = 10
Answer:A
Answer: (A) 10
Question: Combine terms: 12a + 26b -4b – 16a.
(A) 4a + 22b
(B) -28a + 30b.
(C) -4a + 22b
(D) 28a + 30b.
(E) -30b+28a
Rationale: 12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b
correct answer C
Answer: (C) -4a + 22b
Question: Kanul spent $35000 in buying raw materials, $40000 in buying machinery and 20% of the total amount he had as cash with him. What was the total amount?
(A) $87952
(B) $93750
(C) $89542
(D) $95820
(E) $84256
Rationale: Let the total amount be x
then, (100-20)% of x = 35000+40000
80% of x = 75000
80x/100 = 75000
x = $93750
Answer is B
Answer: (B) $93750
Question: In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
(A) 24
(B) 48
(C) 96
(D) 64
(E) none
Rationale: Solution:
5 questions can be selected in the following ways,
2 question from first group and 3 question from second group Or 3 question from first group and 2 question from second group.
(4C2 * 4C3) +(3C4 *2C4),
= 24 +24 = 48
Answer: Option B
Answer: (B) 48
Question: A worker's daily wage is increased by 40% and the new wage is $35 per day. What was the worker's daily wage before the increase?
(A) $20
(B) $21
(C) $24
(D) $25
(E) $28
Rationale: Let x be the daily wage before the increase.
1.4x = $35
x = $25
The answer is D.
Answer: (D) $25
Question: A division of a company consists of six men and six women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 5/22
(B) 7/22
(C) 5/33
(D) 7/33
(E) 5/66
Rationale: The total number of ways to choose two representatives is 12C2=66.
The number of ways to choose two females is 6C2=15.
P(choosing two female representatives)=15/66=5/22
The answer is A.
Answer: (A) 5/22
Question: There are 12 towns grouped in four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that each every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required ?
(A) 72
(B) 90
(C) 96
(D) 144
(E) 128
Rationale: Explanation :
There are 3 towns.
Each town connects with the other town in 3 lines.
Hence total number of lines is 3 x 3 = 9.
Hence 1 zone has 9 direct links within it.
So 4 zones have 9 x 4 = 36 direct links within it.
Now, between zones/ interzone:
Consider a town in Zone 1. There are 9 towns outside this zone.
Hence 9 lines are required to connect between this town and the other 9 towns.
Similarly, there are 12 towns, each with 9 towns outside its own zone.
So, totally, there will be 9 x 12 / 2 = 9 x 6 = 54 lines inter zone (Divided by 2 comes here because, after half, it is repeated).
So, the total number of lines will be 36 (within zone) + 54 ( inter zone) = 90.
Answer : B
Answer: (B) 90
Question: In an examination, 25% of total students failed in Hindi, 48% failed in English and 27% in both. The percentage of these who passed in both the subjects is :
(A) 23
(B) 54
(C) 28
(D) 40
(E) 81
Rationale: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 25 + 48 â€“ 27 = 46
Therefore students who passed = 100 â€“ 46 = 54.
Answer: B
Answer: (B) 54