divelab/Sys2Bench huggingface dataset:
Question: Of the p students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
Options:
A) p + w- x- y
B) p - w- x- y
C) p- w - x + y
D) w + x + y- z
E) w - x - y - z
Rationale: {Total} = {French} + {German} - {Both} + {Neither}
p = x + y - w + {Neither}
{Neither} = p + w - x - y.
Answer: A.
Answer: A
Question: Ravi and Kavi start a business by investing â‚¹ 4000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
Options:
A)2 : 28
B)5 : 28
C)7 : 18
D)1 : 18
E)3 : 18
Rationale: Ratio of profit = Ratio of investments
= 4000 : 72000 = 1 : 18
Answer : D
Answer: D
Question: Shruti purchased several number of three articles P, Q and R in the proportion 3 : 2 : 3. If the unit costs of the articles P, Q and R are 200, Rs. 90 and Rs. 60 respectively, how many articles of Q must have been purchased in the total purchases of Rs. 4800?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Explanation:
Let the number of articles of types P, Q and R be 3a, 2a and 3a respectively.
Thus, we get,
(200 x 3a) + (90 x 2a) + (60 x 3a) = 4800
960a = 4800
a = 5
Hence, the number of articles of type “Q” = 2x5 = 10
ANSWER B
Answer: B
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 588 as interest at the end of the loan period, what was the rate of interest?
Options:
A)7
B)6
C)18
D)24
E)None of these
Rationale: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 588
12R2 = 588
R2 = 49
R = 7.
Answer: Option A
Answer: A
Question: A normal six-sided die bearing the numbers 1, 2, 3, 4, 5, and 6 is thrown until the running
total surpasses 6. What is the most likely total that will be obtained?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The total before the last throw could be any number between one and six. The last
throw will also be a number between one and six but with equal probability. Seven is the only
final total that can come from each of these possibilities. Therefore seven is the most likely
final total.
correct answer A
Answer: A
Question: Mike earns $12per hour and Phil earns $6 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
Options:
A)50%
B)32.5%
C)37%
D)37.5%
E)40%
Rationale: What % less of 12 is 6
let it be x % less ,then
=12(1-x/100)=6
1-x/100=6/12
x=100/2
x=50%
Ans A
Answer: A
Question: A man can row 4.2 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
Options:
A)1.9
B)1.7
C)1.4
D)1.5
E)1.1
Rationale: Speed of boat in still water (b) = 4.2 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.4 km/hr.
Answer: C
Answer: C
Question: A candidate scoring 25% in an examination fails by 30 marks , while another candidate scores 50 % mark, gets 20 marks more than the minimum pass marks . Find the minimum pass marks. Find the minimum pass percentage.
Options:
A)40
B)50
C)60
D)25
E)30
Rationale: x/4+30 = x/2-20
maximum marks = 200
min pass marks = 200/4+30 = 80
=>80/200*100=40%
ANSWER A
Answer: A
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
Options:
A)$35
B)$43
C)$50
D)$65
E)$72
Rationale: Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
Answer: C
Question: Michelle has $80 to buy a new outfit. She found a skirt for $20, a blouse
for $25, and a belt for $8. How much does she have left to buy shoes?
Options:
A)$27 left.
B)$37 left.
C)$47 left.
D)$57 left.
E)$67 left.
Rationale: 80 – 20 – 25 – 8 = 27
She has $27 left.
correct answer A
Answer: A
Question: A container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?
Options:
A)2:5
B)3:7
C)3: 5
D)4:7
E)7:3
Rationale: Container 1 has 12 ounces in the ratio 1:2
or,
x+2x=12 gives x(alcohol)=4 and remaining water =8
container 2 has 8 ounces in the ratio 1:3
or,
x+3x=8 gives x(alcohol)=2 and remaining water =6
mixing both we have alcohol=4+2 and water =8+6
ratio thus alcohol/water =6/14=3/7
ANSWER:B
Answer: B
Question: The ratio of men to women in a class is 4 to 3. If 2 men and 7 woman drop out of the class and the ratio of men to women after the drop out is 2 to 1, then how many men are currently in the class?
Options:
A)22
B)20
C)18
D)19
E)24
Rationale: Equation on the basis of question
4x-2/3x-7=2/1
x=6
Original number of men = 4*6=24
Original Number of Women = 3*6=18
Current number of men = 24-2=22 (Answer)
Current number of women = 18-7=11
Ratio = 22/11= 2/1 ( Just to verify)
Ans A
Answer: A
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 35% but the selling price
remains constant, approximately what percentage of the selling price is the profit
Options:
A)68%
B)80%
C)90%
D)100%
E)None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 135% of Rs. 100 = Rs. 135
New S.P. = Rs. 420.
Profit = Rs. (420 - 135) = Rs. 285
Required percentage = (285/420) * 100
= 68%(approx)
Answer: A
Answer: A
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)3989
B)2772
C)2500
D)2888
E)1551
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
Answer: C
Answer: C
Question: A factory produced 2300 TV sets in its first year of production. 4500 sets were produced in its second year and 500 more sets were produced in its third year than in its second year. How many TV sets were produced in three years?
Options:
A)11,800
B)15,900
C)13,250
D)17,900
E)20,000
Rationale: 500 TV sets were produced in the third year than in the second year. The number of sets produced in the third year is equal to
4,500 + 500 = 5,000
The number of TV sets produced in three years is equal to sum of the number of TV sets produced in each year
2,300 + 4,500 + 5,000 = 11,800
correct answer A
Answer: A
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 384 ?
Options:
A)8
B)9
C)67
D)5
E)2
Rationale: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 384 => a * r^(n-1) = 384
=> 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7)
=> n-1 = 7 => n = 8.
Answer: A) 8
Answer: A
Question: A Baker decides to make a cake of 5 layers, one of strawberry, chocolate, butterscoch, vanila and pista. Baker decides not to put the layers of butterscoch and vanila next to each other as they both are white in colour. How many different type of such cakes can he make?
Options:
A)5! - (4!×2!)
B)4! - (6!×2!)
C)3! - (2!×4!)
D)4! - (4!×2!)
E)5! × (4!×3!)
Rationale: We can find the answer by substracting the number of arrangements in which V and B comes together from the total number of arrangements of 5 layers. Arrangements in which V and B comes next to each other: We can consider V and B as a single object having 2! Variations(VB and BV). VB, S, C, P can be arranged in 4! Ways. In total there are 4!×2! Ways of arranging 5 layers with B and V layers coming next to each other. Required answer = A. 5! - (4!×2!)
Answer: A
Question: Two trains start from a certain place on two parallel tracks in the same directions. The speed of the trains are 45km/hr. and 40km/hr. respectively. The distance between the two trains after 45 minutes will be
Options:
A)2 km 500 m
B)2 km 750 m
C)3 km 750 m
D)3 km 250 m
E)None of these
Rationale: Explanation:
In one hour the distance between the trains is 5 km.
In 45 mins = ¾ hour the distance would be equal to ¾ X 50
= 3.75 Km = 3 Km 750 m.
Answer D
Answer: D
Question: Given that R is between 0 and 1, which of the following expressions has the greatest possible value?
Options:
A)(R-2)^4
B)(R+14)
C)(R+99)^(1/2)
D)(R+1)/(R-1)
E)(R-2)/(R-1)
Rationale: Two of these expressions include division by a term that includes R. In both cases, the value of the denominator can be made arbitrarily close to zero, making the magnitude of the expression increase without bound. However, (R+1)/(R-1) will always have a positive numerator and negative denominator, so the expression will always be negative. (R+1)/(R-1) will always have a negative numerator and negative denominator, so the value will be positive. Therefore the answer is E.
Answer: E
Question: 550, 620, 589, 100, 560, 50, 100
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
Options:
A)200
B)310
C)480
D)550
E)570
Rationale: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 50,100 ,100,550, 560, 580,620,
Median is very easy to tell - its 550. Now we want a number lower than 550 and greater than mean. How many numbers are lower than 550? DE are already out.
Now, we have 200, 310 and 480 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 480. (Notice, if 200 is more than mean then 480 is also. If 31 is more than mean, 480 is also. )
Hence C it is!
Answer: C
Question: A rectangle having length 89 cm and width 34 cm. If the length of the rectangle is increased by eighty percent then how much percent the breadth should be decreased so as to maintain the same area.
Options:
A)25%
B)33.33%
C)47.33%
D)75%
E)None of these
Rationale: Explanation :
Solution: (80/(89+80) * 100)% = 47.33%
Answer : C
Answer: C
Question: In a game of 80 points. A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?
Options:
A)9 points
B)6 points
C)8 points
D)10 points
E)11 points
Rationale: A can give B 5 points :- A / B = 80 / 75
A can give C 15 points :- A / C = 80/ 65
B can give C a points of ( B / A ) * ( A / C)
(75 / 80) * ( 80 / 65)
(75 / 65) = 15/13
As we have to find in a game of 60 , so multiply numerator and denominator with 4 such that the ratio becomes 60/52
therefore B can give C of (60-52) = 8 points
ANSWER:C
Answer: C
Question: In a jar there are 20 white balls, 24 green balls and 30 blue balls. How many balls must be taken out in order to make sure we have 21 balls of the same color?
Options:
A)a)	23
B)b)	46
C)c)	57
D)d)	60
E)e)	67
Rationale: Here, we need to find minimum number of marbles to be taken out to get 21 marbles of same color.
For a instance, if we take 19 white marbles 1st and followed by 20 Green and then 20 Blue.
Total will be 19 + 20+ 20= 59 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 21.
So Minimum we need to take 59+1 = 60 Times to get 21 marbles of same color(either Green or Blue).
Answer : D.
Answer: D
Question: A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 65 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
Options:
A) 16
B) 20
C) 32
D) 40
E) 48
Rationale: lets say x ounces of P is mixed with Q.
=> 65-x ounces of Q is present in the mixture (as the total = 65 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(65-x) = 15
=> x = 25
=> 65-25 = 40 ounces of Q is present in the mixture.
Answer is D.
Answer: D
Question: Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is
Options:
A)290/289
B)1/289
C)290/90
D)290/19
E)None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.
1/a2+1/b2=1/1(2)+1/17(2)
=290/289
Option A
Answer: A
Question: Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 10% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
Options:
A)9% less than N
B)25% less than N
C)equal to N
D)20% greater than N
E)25% greater than
Rationale: Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 10% it becomes price2=P/N*1.10
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.10) i.e. N/1.1 i.e. .91%
Answer: A
Question: If 4x=6y=z, what is x+y, in terms of z?
Options:
A)z/2
B)5z/12
C)z/3
D)3z/5
E)z/9
Rationale: 4x=6y=z
x = z/4
and y = z/6
x+y = z/4 + z/6 = 5z/12
Answer is B
Answer: B
Question: By walking at 3/4th of his usual speed, a man reaches office 15 minutes later than usual. What is his usual time?
Options:
A)45min
B)50min
C)65min
D)60min
E)70min
Rationale: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+15
4T=3T+45..therefor T=45min
ANSWER:A
Answer: A
Question: the sides of a triangle are in the ratio 37.if the perimeter is 60 cms, the longest side is
Options:
A)7
B)30
C)28
D)14
E)16
Rationale: Triangle property: sum of any two sides is always greater than the third one.
and Here we have been asked for longest side...
now we can have longest side as 29 or 28 but not 30
because 31>29 and 32>28 is true but 30>30 is not true
hence Answer is 28
ANSWER:C
Answer: C
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Options:
A)4:3:2
B)4:2:3
C)3:2:4
D)2:3:4
E)None of them
Rationale: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
= (140/100 x 5x), (150/100 x 7x) and (175/100 x 8x)
= 7x, 21x/2 and 14x.
Therefore, The required ratio = 7x : 21x/2 : 14x
= 14x : 21x : 28x
= 2 : 3 : 4.
Answer is D.
Answer: D
Question: Find the compound interest and the amount on Rs.5000 at 5% per annum for 3 years when C.I is reckoned yearly?
Options:
A)s.1261.13
B)s.1440.13
C)s.1185.13
D)s.1346.13
E)s.788.13
Rationale: A = 5000(21/20)3
= 5788.13
= 5000
---------
788.13
ANSWER:E
Answer: E
Question: When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
Options:
A)4.5
B)5
C)5.6
D)5.7
E)6.5
Rationale: if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A
Answer: A
Question: In a is a positive integer smaller than 200 and (14a)/60 is an integer, then a has how many different positive prime factors?
Options:
A)2
B)3
C)5
D)6
E)8
Rationale: 7a/30 tells us that a is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Answer: B
Question: A thief goes away with a MARUTHI car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?
Options:
A)8 hrs
B)2 hrs
C)5 hrs
D)4 hrs
E)1 hrs
Rationale: Explanation:
|-----------20--------------------|
50 40
Difference = 20kms
Relative Speed = 50 â€“ 40 = 10 kmph
Time = 20/10 = 2 hours.
Answer: B
Answer: B
Question: A room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
Options:
A)107
B)144
C)175
D)165
E)130
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 7 meters and 68 centimeters = 768 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 768 and 432 = 48
Thus, the number of square tiles required = (768 x 432 ) / (48 x 48) = 16 x 9 = 144
Answer: B
Answer: B
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
Options:
A)100
B)102
C)110
D)90
E)None of these
Rationale: Explanation :
Let the total number of students = x
Given that 20% of students are below 8 years of age
then The number of students above or equal to 8 years of age = 80% of x -----(Equation 1)
Given that number of students of 8 years of age = 48 -----(Equation 2)
Given that number of students above 8 years of age = 2/3 of number of students of 8 years of age
=> number of students above 8 years of age = (2/3) × 48 = 32-----(Equation 3)
From Equation 1,Equation 2 and Equation 3,
80% of x = 48 + 32 = 80
⇒ 80x/100 = 80
⇒ x/100 = 1
⇒ x = 100
Answer : Option A
Answer: A
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?
Options:
A)210
B)220
C)230
D)240
E)250
Rationale: distance covered in 1 min=(66*1000)/60=1100m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=1100/4.4=250
ANSWER:E
Answer: E
Question: If a number p is prime, and 2p+5 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 1/7 = 014285... (a repeating pattern one digit long)
A
Answer: A
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
Options:
A)81000
B)81028
C)81287
D)29766
E)81372
Rationale: 64000* 9/8 * 9/8
= 81000
Answer: A
Answer: A
Question: 7log7(8) = ?
Options:
A)1
B)2
C)3
D)4
E)8
Rationale: Exponential and log functions are inverse of each other. Hence
aloga(x) = x , for all x real and positive.
and therefore
7log7(8) = 8
correct answer E
Answer: E
Question: In a certain population, there are 4 times as many people aged thirtty-one or under as there are people over thirtty-one. The ratio of those thirty-one or under to the total population is
Options:
A) 1 to 2
B) 1 to 3
C) 4 to 5
D) 2 to 3
E) 3 to 4
Rationale: Consider the ratio of the under population of 21 to over the 21 as 4:1
therefore 4x:1X
Now the ratio of the under to the whole population becomes 4x/4x+1x
= 4/5
Answer is C
Answer: C
Question: † and ¥ represent nonzero digits, and (†¥)² - (¥†)² is a perfect square. What is that perfect square?
Options:
A)121
B)361
C)576
D)961
E)1089
Rationale: If AB is a 2 digit number such that A is the tens digit and B is the units digit, the place value of A is 10 and place value of B is 1.
So AB = 10A + B
Say, AB = 15
A = 1
B = 5
Is AB = A + B? No. 15 is not equal to 1 + 5 = 6
AB = 10A + B = 10*1 + 5 = 15
When you square AB, what will you get?
Is it (A + B)^2 = (1 + 5)^2 = 36? No. 15^2 = 225
Then what is missing? A's place value of 10.
So it will be (10A + B) = (10*1 + 5)^2 = 225
So, in terms of AB, AB^2 = (10A + B)^2.
Answer: E.
Answer: E
Question: If a 3-digit integer is selected at random from the integers 300 through 349, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to two more than the middle digit?
Options:
A) 50/349
B) 1/313
C) 1/49
D) 1/100
E) 1/50
Rationale: Hundreds digit has to be 3 . So units digit needs to 3 as well
And both Hundreds and Units digit needs to be 2 more than ten's digit
The number is 313
Total numbers between 300 and 349 = (349-300)+1 = 50
Probability = 1/50
Answer E
Answer: E
Question: 18 men can complete a piece of work in 20 days. In how many days can 15 men complete that piece of work?
Options:
A)23
B)27
C)20
D)24
E)11
Rationale: 18 * 20 = 15 * x => x = 24 days
Answer:D
Answer: D
Question: A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.
Options:
A)24 km
B)26 km
C)21 km
D)23(23/59) km
E)None
Rationale: Solution: Average speed = total distance covered/ total time
Total distance = (16+40+10) = 46 km
Time taken = (16/20)+ (20/40)+ (10/15) = 59/30
Average speed = 46*30/59 = 23(23/59) km/hr.
Answer: Option D
Answer: D
Question: The circumferences of two circles are 268 meters and 380 meters. Find the difference between the areas of the larger and the smaller circles.
Options:
A)388.15
B)2992
C)4312.5
D)2887.27
E)5773.09
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 268 and 2∏l = 380
s = 268/2∏ and l = 380/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1902/∏2 - 1342/∏2}
= 1902/∏ - 1342/∏
= (190 - 134)(190 + 134)/∏
= (56)(324)/(22/7) = (18144)/(22)(7) = 5773.09 sq m.Answer: E
Answer: E
Question: If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following?
Options:
A)m/3
B)9m
C)9m^2
D)m^2/3
E)m^2/9
Rationale: m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
m^2/9 = 3 ^ (4x-6)
Answer E
Answer: E
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Options:
A)67 min
B)45 min
C)97 min
D)30 min
E)16 min
Rationale: Part filled by (A + B) in 1 minute
= (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40)
= 1
x/2 * 1/15 = 1 => x
= 30 min.
Answer: D
Answer: D
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
C
Answer: C
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)1/209
B)1/211
C)1/216
D)1/117
E)1/119
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: 3 candidates in an election and received 1136, 8236 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?
Options:
A)40%
B)55.4%
C)57%
D)60%
E)62%
Rationale: Total number of votes polled = (1136 + 8236 + 11628) = 21000
So, Required percentage = 11628/21000 * 100 = 55.4%
B
Answer: B
Question: There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess?
Options:
A)320
B)120
C)400
D)420
E)514
Rationale: Sol. Let the original average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42		7x= 84		x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
ANSWER D
Answer: D
Question: What is the sum of natural numbers between 20 and 100
Options:
A)4800
B)4860
C)5000
D)5500
E)5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 20 and 100 numbers = 81 => 100 - 20 = 80 + 1 = 81
Sn = 81/2 × 120 = 81 × 60 = 4860
B)
Answer: B