mathewhe/aqua_rat huggingface dataset:
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
(A) 176
(B) 9
(C) 87
(D) 11
(E) 16
Rationale: Let the number of papers be x. Then,
63x + 20 + 2 = 65x
= 2x = 22
= x = 11.
Answer:D
Answer: (D) 11
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 48 seconds. Find the length of the faster train?
(A) 270
(B) 288
(C) 266
(D) 299
(E) 480
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 48 * 10 = 480 m.
The length of the faster train = 480 m.
Answer: E
Answer: (E) 480
Question: A person bought 110 glass bowls at a rate of Rs. 10 per bowl. He sold 100 of them at Rs. 14 and the remaining broke. What is the percentage gain for A?
(A) 40
(B) 300/11
(C) 243/7
(D) 279/11
(E) 279/8
Rationale: CP=110*10=1100 and SP=100*14=1400
Gain %= 100*(1400-1100)/1100= 300/11
ANSWER:B
Answer: (B) 300/11
Question: A, B and C started a shop by investing Rs. 27,000, Rs. 72,000 and Rs. 81,000 respectively. At the end of the year, the profits were distributed among them. If C’s share of profit be Rs. 36,000, then the total profit was :
(A) 30,000
(B) 60,000
(C) 80,000
(D) 120,000
(E) None
Rationale: Sol.
A : B : C = 27000 : 72000 : 81000 = 3: 8 : 9. so, C’s share : Total Profit = 9 : 20.
Let the total profit be Rs. x. Then, 9/20 = 36000/x or x
= 36000 * 20 / 9 = 80000.
Answer C
Answer: (C) 80,000
Question: The jogging track in a sports complex is 1040 m in circumference. Kapil and his wife start from the same point and walk in opposite directions at 7.5 km/hr and 3.7 km/hr respectively. They will meet for the first time in?
(A) 3.12 min
(B) 3.74 min
(C) 4.25 min
(D) 4.90 min
(E) 5.57 min
Rationale: Clearly, the two will meet when they are1040 m apart.
To be (7.5 + 3.7) = 11.2 km apart, they take 1 hour. THat is 60 minutes.
To be 1040m apart, they take
= (1040/11200 * 60) min
= 5.57 min.
Answer: E
Answer: (E) 5.57 min
Question: A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items?
(A) 15%
(B) 12.16%
(C) 13.4%
(D) 20.2%
(E) None of these
Rationale: Explanation :
Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively.
And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively.
Overall loss percentage of the 1st two items = 14.33%
=>(0.21p+0.11q)/(p+q)=0.1433
=>p/q=1/2.
Overall loss percentage of the 2nd and 3rd item =10.4%
=>(0.11q+0.1r)/(q+r)=0.104.
=>q/r=2/3.
Therefore, the overall loss percentage is :
=>(0.21p+0.11q+0.1r)x100/(p+q+r).
=>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3).
=>0.1216×100.
=>12.16%.
Answer : B
Answer: (B) 12.16%
Question: Three hundred multiples of seven are chosen at random, and 450 multiples of eight are chosen at random. Approximately what percentage of the 750 selected numbers are odd?
(A) 20%
(B) 25%
(C) 40%
(D) 50%
(E) 80%
Rationale: About half the multiples of seven will be odd while all the multiples of eight are even.
The percentage of odd numbers is about (1/2)(300) / 750 = 20%
The answer is A.
Answer: (A) 20%
Question: mixture contains alcohol and water in the ratio 4 : 3. If 6 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
(A) 10
(B) 6.8
(C) 27
(D) 22
(E) 29
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
24x = 4(3x+5)
12x = 20
x = 1.7
Quantity of alcohol = (4 x 1.7) litres = 6.8 litres.
Answer: B
Answer: (B) 6.8
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 14 sec
(B) 87 sec
(C) 48 sec
(D) 17 sec
(E) 16 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Answer: (C) 48 sec
Question: A certain no. when divided by 65 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
65 + 25 = 90/15 = 6 (Remainder)
C
Answer: (C) 6
Question: Kateys mom has $137 to pay 12 kids to clean up her backyard. How much more money does she need to be able to pay each of the 12 kids $12?
(A) 8
(B) 7
(C) 9
(D) 11
(E) 4
Rationale: 12*12=144, not 137.
144-137=7
Kateys mom needs 7 more dollars to be able to pay each kid $12
Therefore B is correct
Answer: (B) 7
Question: A car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 50 miles per hour, how many hours long is the trip?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let T be the total time of the trip.
35*4 + 53(T-4) = 50T
3T = 212-140
T = 24
The answer is E.
Answer: (E) 24
Question: How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 32% iodine solution?
(A) 35
(B) 49
(C) 100
(D) 102
(E) 140
Rationale: Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.
Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.
Total iodine = 0.4x + 7
Total water = 0.6x + 28
The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 32/100
40x + 700 = 32x + 1120
8x = 820
x = 102 lts
Correct Option: D
Answer: (D) 102
Question: For which of the following “n” is the number 2^74 +2^2058+2^2n is a perfect square?
(A) 22777
(B) 2686
(C) 8667
(D) 2020
(E) 99771
Rationale: 2^74 +2^2058+2^2n = K2K2
2^74 +2^2058+2^2n = (237)2+22058+(2n)2(237)2+22058+(2n)2
We try to write this expression as (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2
Now a = 237237, 2ab = 2205822058 and b = 2n2n
Substituting the value of a in 2ab, we get b = 2020
Ans: D
Answer: (D) 2020
Question: A teacher will pick a group of 5 students from a group of 9 students that includes Bart Lisa and john. If one of all the possible 5-student groups is picked at random, what is the probability of picking a group that includes john Bart and Lisa?
(A) 5/97
(B) 3/41
(C) 7/41
(D) 5/42
(E) 2/21
Rationale: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 5 out of 9 = 9C5 = 9! / (5! * 4!) = 126
Favorable Outcomes= Total No. of ways of Picking Group of 5 out of 9 such that J, B and L are always in the group (i.e. we only have to pick remaining 2 out of remaining 6 as J, B and L must be there is group) = 6C2 = 15
Hence,Probability=15/126=5/42
Answer: Option D
Answer: (D) 5/42
Question: Which of these must the factor F of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
(A) 1,2 only
(B) F=2,3 only
(C) F=1,2,3 only
(D) F=1,2,3,4 only
(E) All of them
Rationale: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Answer: (D) F=1,2,3,4 only
Question: If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even?
(A) 1/6
(B) 1/3
(C) 2/3
(D) 1/2
(E) 5/6
Rationale: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: C.
Answer: (C) 2/3
Question: A candidate who gets 30% of the marks fails by 30 marks. But another candidate who gets 45% marks gets 15 marks more than necessary for passing. Find the number of marks for passing?
(A) 100 Marks
(B) 200 Marks
(C) 280 Marks
(D) 371 Marks
(E) 120 Marks
Rationale: 30% ------------ 30
45% ------------ 15
----------------------
15% ------------- 45
30% -------------- ?
90 + 30 = 120 Marks
Answer:E
Answer: (E) 120 Marks
Question: A ladder learning against a wall makes an angle of 60° with the ground. If the length of the ladder is 19 m, find the distance of the foot of the ladder from the wall.
(A) 9 m
(B) 9.5 m
(C) 10.5 m
(D) 12 m
(E) None
Rationale: Let AB be the wall and BC be the ladder.
Then, < ABC	= 60°
and, BC	= 19 m.;
AC = x metres
AC/BC	= cos 60°
= x / 19
=1 / 2
x= 19/2
= 9.5 m.
Answer B
Answer: (B) 9.5 m
Question: A family made a down payment of $75 and borrowed the balance on a set of encyclopedias that cost $300. The balance with interest was paid in 23 monthly payments of $12 each and a final payment of $3. The amount of interest paid was what percent of the amount borrowed?
(A)  23%
(B)  20%
(C)  25%
(D)  26%
(E)  24%
Rationale: borrowings = 300-75 = 225
total pmt = 23x12 + 3 = 279
so int = 279 - 225 = 54
interest in terms of borrowing = 54/225 = 24%
Answer is D
Answer: (D)  26%
Question: The average of 9 observations was 4, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 54
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Explanation:
1 to 9 = 9 * 4 = 36
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 36 = 54
Option A
Answer: (A) 54
Question: What is the square root of 225?
(A) 6
(B) 9
(C) 12
(D) 45
(E) 15
Rationale: 15X15 = 225
ANSWER E
Answer: (E) 15
Question: The average of 11 results is 55, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) A)46
(B) B)1
(C) C)66
(D) D)76
(E) E)74
Rationale: 1 to 11 = 11 * 55 = 605
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 –605= 1
Answer:B
Answer: (B) B)1
Question: Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day?
(A) Rs. 120
(B) Rs. 150
(C) Rs. 250
(D) Rs. 400
(E) None of these
Rationale: Solution: Ratio of number of men, women and children,
= (18/6): (10/5):(12/3) = 3:2:4
Total (Men +Women +Children) = 18
3X +2X +4X = 18
9X = 18
X = 2
Hence, number of women = 2X = 2*2 = 4
Share of all women = (10*4000)/40 = Rs. 1000 [18+10+12 =40]
Thus, share of each woman = 1000/4 = Rs. 250.
Answer: Option C
Answer: (C) Rs. 250
Question: A man swims downstream 30 km and upstream 20 km taking 5 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 2
(D) 5
(E) 4
Rationale: 30 --- 5 DS = 6
? ---- 1
20 ---- 5 US = 4
? ---- 1 M = ?
M = (6 + 4)/2 = 5
Answer:D
Answer: (D) 5
Question: A computer store offers employees a 30% discount off the retail price. If the store purchased a computer from the manufacturer for $1500 dollars and marked up the price 30% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (30% off retail price) as opposed to the final retail price.
(A) 525
(B) 545
(C) 565
(D) 575
(E) 585
Rationale: Cost price=1500
Profit=30% =30% of 1500=450
selling price=CP+ Profit
SP=1950
a Discount of 30% to employees means 30% off on 1950
so 30% of 1950= 585
Ans E
Answer: (E) 585
Question: What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?
(A) 1:1
(B) 1:2
(C) 2:3
(D) 2:1
(E) None of these
Rationale: Explanation:
As far as questions of Area or Volume and Surface area are concerned, it is all about formulas and very little logic. So its a sincere advice to get all formulas remembered before solving these questions.
Lets solve this,
Area of rectangle =l∗b
Area of triangle =1/2l∗b
Ratio =l∗b:1/2l∗b
=1:1/2
=2:1
Option D
Answer: (D) 2:1
Question: The average age of three boys is 20 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
(A) 6
(B) 9
(C) 8
(D) 4
(E) 12
Rationale: 3x + 5x + 7x = 60
x =4
3x = 12
Answer:E
Answer: (E) 12
Question: the average age of 56 employees in a company is 35. An employee aged 60 is retired and a fresher of age 20 is taken in. What is the new age average of employees?
(A) 25.45
(B) 32.26
(C) 33.13
(D) 34.28
(E) 35.55
Rationale: The sum of age of the employees when the age average is 35 = 35x56 =1960
The sum of ages of the employees of new group= (1960-60)+20 = 1920
The average age of the new group= 1920/56 = 34.28
Answer: D
Answer: (D) 34.28
Question: A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent R should the number of hours worked be increased?
(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 100%
Rationale: Correct Answer: C
Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked R will be 25% greater than the original number. The answer is C.
Answer: (C) 25%
Question: The average age of 6 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is?
(A) 10years
(B) 15years
(C) 20years
(D) 25years
(E) 30years
Rationale: Total age of 6 boys = 25*6 = 150
ratio of their ages = 3:5:7
Age of the youngest = 150*3/15 = 30 years
Answer is E
Answer: (E) 30years
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $25.5m
(C) $106.25m
(D) $127.5m
(E) $150m
Rationale: 2/10*1/6*(total) = 5
1/30*(total) = 5
(total) = 5*30 = 150
Answer: E.
Answer: (E) $150m
Question: When 10 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
(A) 3 : 4
(B) 4 : 1
(C) 3 : 2
(D) Data inadequate
(E) None of these
Rationale: Let the first and the second numbers be x and y respect then
y + 10% of x = 140% of y
or, y + 0.1x = 1.4y
or, 0.1x = 0.4y
∴ x : y = 0.4 : 0.1 = 4 : 1
Answer B
Answer: (B) 4 : 1
Question: If a train, travelling at a speed of 270 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 281 m
(B) 325 m
(C) 117 m
(D) 375 m
(E) 350 m
Rationale: D
D = 270 * 5/18 * 5 = 375 m
Answer: (D) 375 m
Question: Difference between two numbers is 6, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 5,6
(B) 7,9
(C) 9,15
(D) 11,12
(E) 13,14
Rationale: Explanation:
x – y = 6
4x – 6y = 6
x = 15 y = 9
C)
Answer: (C) 9,15
Question: If r and y are integers, then ry(r + y) is
(A) Always positive
(B) Always negative
(C) Positive when r is positive
(D) Negative when r is negative
(E) It cannot be determined by the information given
Rationale: Given r and y are integers, then ry(r + y)
Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..
I presume its Option E if am not missing anything.
r=-3 and y=1
ry(r + y) is positive = 6
Answer: (E) It cannot be determined by the information given
Question: What number has a 20:1 ratio to the number 10?
(A) 130
(B) 100
(C) 200
(D) 150
(E) 120
Rationale: 20:1 = x: 10
x = 10*20
x=150
ANSWER:C
Answer: (C) 200
Question: How many terms are there in 2,4,8,16,………..1024?
(A) 10
(B) 6
(C) 9
(D) 8
(E) 7
Rationale: Let the number of terms be n. Then,
2 * 2 ^n – 1 = 1024 ,
2^ n-1 = 512 = 2^ 9
n – 1 = 9, n = 10
ANSWER:A
Answer: (A) 10
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $174, how many hours overtime did he work?
(A) 8
(B) 5
(C) 9
(D) 6
(E) 10
Rationale: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $174 - $120 = $54 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $54/$6 = 9
Ans is C
Answer: (C) 9
Question: If x > 0.8, which of the following could be the value of x?
(A) √0.03
(B) √0.8
(C) √0.07
(D) √0.06
(E) √0.05
Rationale: Answer : B
Answer: (B) √0.8
Question: The average age of 15 men of a group is 17 years. Out of these, the average age of 5 men is 14 years and that of the other 9 men is 16 years. The age of the 15th man is?
(A) 11 years
(B) 17 years
(C) 41 years
(D) 14 years
(E) 12 years
Rationale: Age of the 15th student
=[15 * 17 - (14 * 5 + 16 * 9)]
= (255 - 214)
= 41 years.
Answer:C
Answer: (C) 41 years
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
(A) 288
(B) 528
(C) 299
(D) 277
(E) 200
Rationale: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
x = 528
Answer: B
Answer: (B) 528
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 22
(B) 30
(C) 99
(D) 88
(E) 11
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: B
Answer: (B) 30
Question: If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. b - a = 1
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
(A)  I only
(B)  II only
(C)  I and II only
(D)  II and III only
(E)  I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then b = a + 1, from which it follows that b - a = 1. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: E.
Answer: (E)  I, II, and III
Question: If 20 honey bees make 20 grams of honey in 20 days, then 1 honey bee will make 1 gram of honey in how many days?
(A) 1
(B) 3.5
(C) 20
(D) 49
(E) 30
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 20 :: 20 : x
Honey 20 : 1
=> 1 x 20 x x = 20 x 1 x 20
=> x = 20.
Answer : C
Answer: (C) 20
Question: there is a set of 52 card.1 card fall down.then we take 2 cards from the rest.that 2 cards are spade.what is the probablity of that fallen card is spade?
(A) 11/50
(B) 13/50
(C) 11/20
(D) 13/20
(E) 17/50
Rationale: there are total 13 spades card in a pack if we have drawn 2 spade cards from the pack then out of 13 cards only 11 cards are left.
and out 52 card only 50 cards are left in hand.
p(fallen card is spade)=11C1/50C1=11/50
ANSWER:A
Answer: (A) 11/50
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 98%
(B) 25%
(C) 29%
(D) 35%
(E) 12%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B
Answer: (B) 25%
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 33
(B) 77
(C) 24
(D) 55
(E) 88
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Answer: (C) 24
Question: If $650 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 7 years?
(A) $750.00
(B) $823.50
(C) $973.25
(D) $921.75
(E) $110.00
Rationale: Using CI Formula:
A=P(1+r/n)^n*t
A=650(1+5/7)^5*7
A=921.75
Option: D
Answer: (D) $921.75
Question: If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book.
(A) 1079
(B) 1000
(C) 1100
(D) 1075
(E) None of these
Rationale: Explanation:
Number of digits used in 1 digit numbers = 1*9 = 9
Number of digits used in 2 digit numbers = 2*90 = 180
Number of digits used in 3 digit numbers = 3*900 = 2700
Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320
Hence, number of pages with 4 digit number = 320/4 = 80
Total number of pages = 1079
ANSWER: A
Answer: (A) 1079
Question: A train 441 m long can cross an electric pole in 21 sec and then find the speed of the train?
(A) 88 Kmph
(B) 89 Kmph
(C) 76 Kmph
(D) 16 Kmph
(E) 18 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 441/21
S = 21 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 76 Kmph
Answer: C
Answer: (C) 76 Kmph
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent T of thatbeforeJuly 1 last year?
(A) 90%
(B) 99%
(C) 100%
(D) 101%
(E) 110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before T= [0.9n (1.1x)]/xn= 0.99 or 99%.B
Answer: (B) 99%
Question: What is the probability of tossing a coin five times and having heads appear at least two times?
(A) 1/32
(B) 1/16
(C) 15/16
(D) 13/16
(E) 7/8
Rationale: If 'n' coins are tossed there will
nc0 outcomes in which n coins will show head
nc1 outcomes in which 1 head will appear
and so on
Here 5 coins are tossed so the total outcomes = 2 ^5 = 32
Outcomes in which at least 2 heads will appear = 32 - 5c0 - 5c1 = 26
Prob at least two heads will appear = 26/32 = 13/16
ANSWER:D
Answer: (D) 13/16
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/22
(C) 5/20
(D) 5/18
(E) 5/19
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21
Answer: A
Answer: (A) 5/21
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 1.01%
(B) 5.01%
(C) 3.01%
(D) 2.01%
(E) 4.01%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
ANSWER:D
Answer: (D) 2.01%