divelab/Sys2Bench huggingface dataset:
Question: In a simultaneous throw of two coins, the probability of getting atleast one headis:
Options:
A)1/2
B)1/3
C)2/3
D)3/4
E)1/4
Rationale: n(S)=4
E = even getting at least one head
N(E)=3
P(E)=3/4
ANSWER D 3/4
Answer: D
Question: A right circular cylinder has a height of 22 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
Options:
A)500(π – 3)
B)500(π – 2.5)
C)500(π – 2)
D)550(π – 1.5)
E)500(π – 1)
Rationale: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
The square base has sides of sqrt(50) due to the 45-45-90 triangle
22*25*pi - 15*sqrt(50)^2
=550(π – 1.5)
D. 500(π – 1.5)
Answer: D
Question: A table is bought for Rs.1000/- and sold at Rs.1500/- find gain or loss percentage
Options:
A)25% gain
B)35% gain
C)45% loss
D)50% gain
E)None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (1500 - 1000)/1000 = 50% gain
D
Answer: D
Question: 7^6n -1^ 6n When n is an integer > 0 is divisible by
Options:
A)112
B)127
C)145
D)187
E)185
Rationale: 127
B
Answer: B
Question: The sum of three consecutive integers is 93. What are the integers?
Options:
A)20,21,22
B)10,11,12
C)30,31,32
D)40,41,42
E)30,31,32
Rationale: First x Make the first number x
Second x+1 To get the next numberwe go up one or+1
Third x+2 Add another 1(2 total) to get the third
F +S +T =93 First (F) plus Second (S) plusThird (T) equals 93
(x)+(x+1)+(x+2)=93 Replace F with x, S with x+1, and T with x+2
x+x+1+x+2=93 Here the parenthesis aren′t needed.
3x+3=93 Combine like terms x+x+x and 2+1
−3 −3 Add 3 to both sides
3x=90 The variable ismultiplied by 3
3 3 Divide both sides by 3
x=30 Our solution for x
First 30 Replace x in our origional listwith 30
Second (30)+1=31 The numbers are 30, 31, and 32
Third (30)+2=32
correct answer E
Answer: E
Question: A rectangular plot measuring 60 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
Options:
A)44m
B)66m
C)26m
D)56m
E)25m
Rationale: Perimeter of the plot = 2(60+50) = 220m
no of poles =220/5 =44m
Answer: A
Answer: A
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 10 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
Options:
A)32
B)53
C)74
D)86
E)95
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 10.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 11, 32, 53, 74, 95,...
The answer is D.
Answer: D
Question: A train 1600 m long can cross a pole in 40 sec and then find the speed of the train?
Options:
A)140
B)142
C)144
D)146
E)148
Rationale: Length = Speed * time
Speed = L/T
S = 1600/40
S = 40 M/Sec
Speed= 40*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 144 Kmph
Answer:C
Answer: C
Question: 2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations.what is the ratio of their speeds ?
Options:
A)11:9
B)11:2
C)91:9
D)11:1
E)11:5
Rationale: In same time ,they cover 110km & 90 km respectively so ratio of their speed =110:90
= 11:9
Answer:A
Answer: A
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
Options:
A)20,000 square meters.
B)40,000 square meters.
C)60,000 square meters.
D)80,000 square meters.
E)100,000 square meters.
Rationale: Let us first find the distance d jogged
distance = rate ? time = (12 km / hr) ? 30 minutes
= (12 km/hr) ? 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer A
Answer: A
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)35 cm2
B)37 cm2
C)87 cm2
D)16 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2
=35 cm2
Answer: E
Answer: E
Question: If the complement of a certain angle is one time the measure of that certain angle, then what is the measure of that certain angle?
Options:
A)45°
B)30°
C)22.5°
D)18°
E)15°
Rationale: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is x, and together, these add up to 90 degrees.
x + x = 90
2x = 90
x =45°
Answer = (A)
Answer: A
Question: A train , having a length of 165 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
Options:
A)9 sec
B)8 sec
C)6 sec
D)4 sec
E)2 sec
Rationale: Explanation:
Distance = 165 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 165/(110/6) = 9 s
Answer: Option A
Answer: A
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:
Options:
A)240
B)120
C)190
D)200
E)250
Rationale: Let C's share = Rs. x
Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6
Therefore, x/6 + x/4 + x = 1360
=17x/12 = 1360
x = 1360 x 12/17= Rs. 960
Hence, B's share = Rs. (960/4)= Rs. 240.
Answer is A.
Answer: A
Question: Mazy bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
Options:
A)$10
B)$11
C)$12
D)$13
E)$14
Rationale: From the given information,we can conclude that Mazy bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Answer: B
Question: A bag contains 5 white marbles and 5 red marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
Options:
A)1/6
B)1/35
C)1/3
D)1/462
E)1/126
Rationale: first, total ways to select for all boys and girls, i.e 10!/(5!*5!) = 252
then there are one two way girls can have all same colors, either white or red.
The number of ways in which 5 girls can select 5 white balls = 5C5 = 1
The number of ways in which 5 girls can select 5 red balls = 5C5 = 1
Therefore, total favorable outcomes/total outcomes = 2/252= 1/126
E
Answer: E
Question: If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x?
I. 1/2x
II. -2/x
III. 3/x
Options:
A)I only
B)II only
C)I and II
D)I and III
E)II and III
Rationale: (xy)^2-xy-6=0
(xy-3)(xy+2)=0
so either xy=3 i.e. y=3/x
or xy=-2 i.e. y=-2/x
so E is the ans
Answer: E
Question: During the break of a football match, the coach will make 3 substitutions. If the team consists of 14 players among which there are 2 forwards, what is the probability that none of the forwards will be substituted?
Options:
A) 21/55
B) 18/44
C) 21/99
D) 28/44
E) 36/55
Rationale: Required probability = no. of favorable outcome/ total no. of outcomes
out of 14 players any 3 can be selected in 14C3 ways
after removing 2 forwards any 3 players can be selected from the remaining 9 players in 9C3 ways
thus required probability = 9C3/14C3 =21/99
Answer: C
Question: In the equation 2x – cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 3 ?
Options:
A)−9/2
B)-4
C)-3
D)4
E)9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=3, c=-3, x=
x=9/2
ANSWER:E
Answer: E
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 25% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Options:
A)976374
B)979923
C)980241
D)1178125
E)1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 25/100)(1 - 35/100)(1 + 45/100)
= 1178125
D
Answer: D
Question: A sum fetched a total simple interest of Rs. 929.20 at the rate of 8 p.c.p.a. in 5 years. What is the sum?
Options:
A)2323
B)1223
C)2563
D)1853
E)2353
Rationale: Explanation :
SI = Rs.929.20
P = ?
T = 5 years
R = 8%
P = 100×SI/RT
=100×929.20/8×5
= Rs.2323
Answer : Option A
Answer: A
Question: A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?
Options:
A)$5.60
B)$7.20
C)$8.80
D)$9.60
E)$15.20
Rationale: Cost price is $16. Lowest possible price is when max discount is applied.
So Discount of 40% first and then 25%.
Final price = 16 * (1-40/100) * (1- 25/100) = 16 * 60/100 * 75/100 = 7.2
Ans B
Answer: B
Question: Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 8 hours to paint a wall with dimensions a and c. He takes 4 hours to paint a wall with dimensions b and c and 12 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 12, then what is the volume of the room?
Options:
A)218 cubic meters
B)224 cubic meters
C)230 cubic meters
D)288 cubic meters
E)It can’t be determined.
Rationale: Time to paint each wall as given in problem:
AC = 8 hours
BC = 4 hours
AB = 12 hours
Since he works at constant rate and it takes him twice as long to paint AC compared to BC
AC=2BC
Plug in 6 for A and you find that B=6
Since painting AB takes 3 times as long compared to BC,
AB=3BC
Plug in 6 for A and 3 for B and you find that C=4
A*B*C=12*6*4=288 cubic meters
Answer: D
Answer: D
Question: The time it took car P to travel 150 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
Options:
A)23
B)50
C)60
D)70
E)80
Rationale: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(150/x)-(150/(x+10))=2
Solving for x=23 miles\hr.
A
Answer: A
Question: What sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?
Options:
A)667
B)500
C)266
D)288
E)211
Rationale: 70 = (P*3*7/2)/100
P = 667
Answer: A
Answer: A
Question: In a group of 100 adults, 80 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
Options:
A)48
B)52
C)54
D)60
E)40
Rationale: 12 left-haded women compose 100-80=20% (or 1/5) of all women, so there are total of 5*12=60 women --> 100-60=40men.
Answer: E.
Answer: E
Question: For what values of k will the pair of equations (3x + 4y)/2 = 6 and kx + 12y = 30 does not have a unique solution?
Options:
A)12
B)9
C)3
D)7.5
E)2.5
Rationale: we have 2 equations
1. (3x + 4y)/2 = 6 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Answer: B
Question: A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6p.a for 2 years. Find his gain in the transaction per year.
Options:
A)Rs. 112.50
B)Rs. 125
C)Rs. 150
D)Rs. 167.50
E)Rs. 175
Rationale: Gain in 2 years
= Rs.[(5000 x (25/4)	x(2/100))-((5000 x 4 x 2)/100)]
= Rs. (625 - 400)
= Rs. 225.
Gain in 1 year = Rs.(225/2)
= Rs. 112.50
ANSWER :A
Answer: A
Question: After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6600. Find the actual price of the good.
Options:
A)s. 6000
B)s. 9000
C)s. 10800
D)s. 9649
E)s. 9980
Rationale: Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6600
1 = 6600/68.4
100 = (6600*100)/68.4 = Rs. 9649.
Answer: Option D
Answer: D
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
A)22
B)12
C)88
D)99
E)27
Rationale: 1/8 + 1/24 = 1/6
6 * 2 = 12
Answer:B
Answer: B
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
Options:
A)29,000 square meters
B)16,000 square meters
C)20,000 square meters
D)32,000 square meters
E)45,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate ? time = (12 km / hr) ? 30 minutes
= (12 km/hr) ? 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer C
Answer: C
Question: Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 5,000 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?
Options:
A)11.0
B)12.0
C)13.0
D)14.0
E)15.0
Rationale: Solution:H stopped 1000 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs.
this means she reached there at 11:00.
speed difference between them is 800-500=300 ft/hr
so by the time H stops they have 1500 ft of distance
so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00
means 12:00 is the answer.
B
Answer: B
Question: Two cars, Car1 and Car2 move towards each other from R and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach R starting from Y?
Options:
A)15.5 sec
B)8.4 sec
C)33.6 sec
D)31.11 sec
E)16.8 sec
Rationale: R--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance RY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: D
Question: An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of?
Options:
A)100km/hr
B)150km/hr
C)200km/hr
D)250km/hr
E)300km/hr
Rationale: Distance = 100*2 = 200 km
Required speed = 200 *1 = 200km/hr
Answer is C
Answer: C
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)22
B)29
C)23
D)12
E)13
Rationale: 2 * 22/7 * 14 * x = 1056 => x
= 12
Answer:D
Answer: D
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds. What is the length of the train in meters?
Options:
A)400 meters
B)120 meters
C)1777 meters
D)60 meters
E)None of these
Rationale: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)
Relative speed= 100-64= 36Km/h = 36000 m/h
time= 12 seconds
Distance= speed*time
36000* 12/3600= 120 meters.
B is the answer.
Answer: B
Question: A can have a piece of work done in 4 days, B can work two times faster than the A, C can work three times faster than A. How many days will they take to do the work together ?
Options:
A)3/4 days
B)6/7 days
C)1/4 days
D)can't say
E)none
Rationale: A's 1 day work is 1/6
B's 1 day work is 2/6
C's 1 day work is 3/6
(A+B+C)'s 1 day work(1/6+2/6+3/6) is 7/6
so, they can finish the work in 6/7 days
ANSWER:B
Answer: B
Question: A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
Options:
A)3/4
B)4
C)18/19
D)9
E)12
Rationale: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/2
Lets say x machines are used to attain the desired rate, thus
x/36+x/2 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+18x)/36 = 1/2
19x/36 = 1/2
x = 18/19.
QA = 18/19 (ANSWER C)
Answer: C
Question: Last year, Company M made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive?
Options:
A)q/4
B)q/5
C)q/6
D)q/7
E)q/8
Rationale: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 3
Profit to each partner = (q/2)/3 = q/6
Answer: C
Answer: C
Question: Barbata invests $2600 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
Options:
A)1200
B)3000
C)1300
D)3600
E)2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2600+0.05*2600+x+0.08x = 2600+x+0.06(2600+x)
0.05*2600+0.08x = 0.06x+0.06*2600
0.02x = 2600(0.06-0.05)
x = 2600*0.01/0.02 = 1300
Ans: "C"
Answer: C
Question: An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth
Options:
A)333
B)500
C)887
D)299
E)132
Rationale: Explanation:
Let the total sale be Rs. x.
Then, 2.5%. of x = 12.50 <=> (25/100 * 1/100 * x) = 125/10 <=> x = 500.
Answer: B) 500
Answer: B
Question: The slant height of a cone is 10 cm and radius of the base is 5cm, find the curved surface of the cone?
Options:
A)150
B)155
C)158
D)157
E)190
Rationale: π * 10 * 5
= 157
Answer:D
Answer: D
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $76, how much does one shirt cost?
Options:
A)$10
B)$12
C)$13.20
D)$15
E)$18
Rationale: 3J + 2S = 69
2J + 3S = 76
----------------
5J + 5S = 145 ----(divide by 5)---> J + S = 29
3J + 2S = J + 2(J + S) = J + 58 = 69 ---> J = 11
3*11 + 2S = 69
33 + 2S = 69
2S = 36
S = 18
Answer: E
Answer: E
Question: In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?
Options:
A)6
B)21
C)27
D)189
E)192
Rationale: Another approach is to use TWO variables.
Let M = present number of males
Let F = present number of females
The ratio of male to female employees is 7:8
So, M/F = 7/8
Cross multiply to get 7F = 8M
If 3 more men were hired, this ratio would increase to 8:9
So, (M+3)/F = 8/9
Cross multiply to get 9(M+3) = 8F
Expand: 9M + 27 = 8F
We now have a system of two equations and two variables:
7F = 8M
9M + 27 = 8F
Solve to get: M = 189 and F = 216
ANSWER:D
Answer: D
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: D = 110 + 150 = 260 m
S = 60 * 5/18 = 50/3
T = 260 * 3/50 = 15.6 sec
Answer: D
Answer: D
Question: If r + | r | = 0, which of the following must be true?
Options:
A)r > 0
B)r≥0
C)r < 0
D)r≤0
E)r = 0
Rationale: Manipulate the equations:
r + | r | = 0
|r| = -r
-r > 0 OR -r = 0
This means r could be 0 or r is less than 0.
D. r≤0
E. r=0
Answer: D
Answer: D
Question: In the city of San Durango, 90 people own cats, dogs, or rabbits. If 60 people owned cats, 20 owned dogs, 40 owned rabbits, and 18 owned exactly two of the three types of pet, how many people owned all three?
Options:
A)1
B)3
C)6
D)11
E)12
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
90 = 60 + 20 + 40 - (18) - 2x
x = 6
So, answer will be C
Answer: C
Question: For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*?
Options:
A)0.2
B)1.2
C)1.8
D)2.2
E)4.0
Rationale: Since s* is defined as the greatest positive even integer less than or equal to s, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: B
Question: If the volume of two cubes are in the ratio 8:1, the ratio of their edges is:
Options:
A)2:1
B)3:2
C)3:5
D)3:7
E)None of these
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=8/1
=>(a/b)3=(2/1)3
a/b=2/1
=>a:b=2:1
Option A
Answer: A
Question: Solve the quickfire maths brain teaser âˆš25% = ?
Options:
A)30%
B)40%
C)50%
D)19%
E)29%
Rationale: âˆš25%
=> âˆš25/âˆš100
=> 5/10
=> 50/100
=> 50%
C
Answer: C
Question: The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
Options:
A)58%
B)90%
C)80%
D)50%
E)54%
Rationale: Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=> 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> 16r/100 + 8r2/(100)2 = 20r/100
=> 4r/10 = 8r2/(100)2
=> 8[r/100]2 - 4r/100 = 0
=> r/100 {8r/100 -4} = 0
=> r = 0% of 50%
Since r!= 0%, r =50%
Answer: D
Answer: D
Question: 3 candidates in an election and received 1000, 2000 and 4000 votes respectively. What % of the total votes did the winning candidate got in that election?
Options:
A)45%
B)50%
C)57.14%
D)60%
E)65.12%
Rationale: Total number of votes polled = (1000 + 2000 + 4000) = 7000
So, Required percentage = 4000/7000 * 100 = 57.14%
C
Answer: C