mathewhe/aqua_rat huggingface dataset:
Question: The sum of all solutions for x in the equation x^2 – 8x + 21 = |x – 5|+ 4 is equal to:
(A) –7
(B) 7
(C) 20
(D) 12
(E) 14
Rationale: x^2 - 8x + 17 = |x-5|
RHS can be -ve or +ve
x^2 - 9x + 22 = 0
x^2 - 7x + 12 = 0
x= 11,4,3,2
We test all 3 values in original equation, all ok.
Thus, Sum = 11 + 4 +3 + 2= 20
Ans (C)
Answer: (C) 20
Question: If log10 2 = 0.3010, the value of log10 80 is:
(A) 2.65
(B) 1.903
(C) 3.05
(D) 6.487
(E) 5.98
Rationale: Explanation:
log10 80	= log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
answer B
Answer: (B) 1.903
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
(A) 10.45
(B) 10.35
(C) 10.15
(D) 10.05
(E) 10.25
Rationale: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer:E
Answer: (E) 10.25
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 4000 Km?
(A) 10.
(B) 25.
(C) 30.
(D) 38.
(E) 200.
Rationale: Total distance= Distance travelled by A +Distance travelled by car B
Distance= speed*time
Distance of A= 3x * 6
Distance of B= x*2
(3x * 6) + (x*2) = 4000
x= 200 KM/hr
E is the answer
Answer: (E) 200.
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 3377
(B) 2788
(C) 27999
(D) 11750
(E) 17881
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Answer: (D) 11750
Question: John is traveling to a meeting that is 24 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
(A) 25 mph
(B) 37 mph
(C) 48 mph
(D) 49 mph
(E) 56 mph
Rationale: Well 48mph. C. Time*rate=distance --> 0.5*rate=24 --> rate=48
Answer: (C) 48 mph
Question: What is the units digit of (493) (915) (381) (756) (22)
(A) 0
(B) 1
(C) 4
(D) 5
(E) 6
Rationale: Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.
I also tried it using the calculator and the answer is 1.
IMO B.
Answer: (B) 1
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 186 m
(B) 176 m
(C) 120 m
(D) 178 m
(E) 187 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer:C
Answer: (C) 120 m
Question: Tomy started a software business by investing Rs.50,000. After 6months, Nanda joined her with a capital of $80,000. After 3years, they earned a profit of $24,500. What was Simran's share in the profit?
(A) $8,500
(B) $9,500
(C) $10,500
(D) $11,500
(E) $12,500
Rationale: Tomy : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Tomy 's share = $24500 x	3/7	= $10,500.
C
Answer: (C) $10,500
Question: If n = 7^11 – 7, what is the units digit of n?
(A) 0
(B) 1
(C) 4
(D) 6
(E) 8
Rationale: Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 7^3 - 7. Now 7^3 has last digit 3. Since 7^11 (or for that matter 7^3) is greater than 7, we subtract 7 from 13 ( the 10+3 --> 10 has come from carry over from the tenth place). thus 13 - 7 = 6 is the answer. Option D
Answer: (D) 6
Question: Three persons A, B and C are standing in a queue. There are five persons between A and B and eight persons between B and C. If there be three persons ahead of C and 21 persons behind A, what could be the minimum number of persons in the queue?
(A) 33
(B) 37
(C) 28
(D) 36
(E) 19
Rationale: Explanation:
Three persons A, B, C can be arranged in a queue in six different ways, ie ABC, CBA, BAC, CAB, BCA, ACB. But since there are only 3 persons ahead of C, so C should be in front of the queue. Thus, there are only two possible arrangements, ie CBA and CAB.
We may consider the two cases as under:
Case I:
Clearly, number of persons in the queue = (3+1+8+1+5+1+21=) 40
Case II:
Number of persons between A and C
= (8 - 6) = 2
Clearly number of persons in the queue = (3+1+2+1+21) = 28
Now, 28 < 40. So, 28 is the minimum number of persons in the queue.
Answer: C) 28
Answer: (C) 28
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 6 p.c?
(A) 38028
(B) 38000
(C) 32977
(D) 37600
(E) 38982
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(94/100)
= 37600
Answer:D
Answer: (D) 37600
Question: A number when divided by a divisor leaves a remainder of 21. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 12
(B) 13
(C) 34
(D) 37
(E) 59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+21
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 34
as D is also integer and 34 is a prime number, the D should be 34 to satisfy the above equation.
Hence answer is 'D'
Answer: (D) 37
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 65%. Staff are allowed a further 60% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) 0.15D
(B) 0.16D
(C) 0.65D
(D) 0.14D
(E) 0.05D
Rationale: Effective discount = a + b + ab/100 = - 65 - 60 + (-65)(-60)/100 = -86
Sale price = D * ( 1 - 86/100)
Sale price = .14 * D
Answer (D)
Answer: (D) 0.14D
Question: A bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ?
(A) 25 km/hr
(B) 35 km/hr
(C) 40 km/hr
(D) 42 km/hr
(E) 45 km/hr
Rationale: Time = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42×75126⇒57 of the actual speed = 42×75126⇒actual speed = 42×75126×75=42×1518=7×153=7×5=35 km/hr
B
Answer: (B) 35 km/hr
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 12 1/2 years
(B) 12 1/8 years
(C) 17 1/2 years
(D) 12 3/2 years
(E) 15 1/2 years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years
Answer:A
Answer: (A) 12 1/2 years
Question: 4+4
(A) 8
(B) 2
(C) 1
(D) 5
(E) 2
Rationale: C
Answer: (C) 1
Question: If sum of three numbers in A.P is 33 and sum of their squares id 491, then what are the three numbers.
(A) 5,11,17
(B) 7,11,15
(C) 9,11,13
(D) 3,11,19
(E) 3,12,19
Rationale: a + (a + d ) + ( a + 2d ) = 3( a + d ) = 33,
a + d = 11, or second term = 11 , first term = 11– d ,
Then ( 11- d ) 2 + 11 2 + ( 11 + d ) 2 = 491
2 d 2 = 491 - ( 3 * 121 ) = 491 - 363 = 128
d 2 = 64, d = 8, a = 3,
ANSWER:D
Answer: (D) 3,11,19
Question: How many number are immediately preceded and immediately followed by different numbers?
7 7 7 5 7 5 7 5 7 7 7 7 5 7 5 7 5 7 7 7 7 7 5 7 5
(A) 2
(B) 3
(C) 4
(D) 5
(E) 1
Rationale: five
ANSWER:D
Answer: (D) 5
Question: An exhibition was conducted for 4 weeks. The number of tickets sold in 2nd work week was increased by 20% and increased by 16% in the 3rd work week but decreased by 20% in the 4th work week. Find the number of tickets sold in the beginning, if 1392 tickets were sold in the last week
(A) 6
(B) 35
(C) 120
(D) 1250
(E) 740
Rationale: Answer: 1250
Explanation:
let initially A ticket has been sold.
So now in 2nd week 20% increases so
A × 120100120100
In 3rd week 16% increases so
A × 120100120100 × 116100116100
In 4th week 20% decrease so
A × 120100120100 × 116100116100 × 120100120100 = 1392
A = 1250
Answer:D
Answer: (D) 1250
Question: Let exp(m,n) = m to the power n. If exp(10, m)= n exp(2,2) where m and n are integers then n= ___?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: 10^m=n*(2^2)
(2*5)^m=n*(2^2)
(2^m)*(5^m)=n*(2^2) now equate both side we get m=2 and (5^m)=n
(5^2)=n=>n=25
ANSWER:B
Answer: (B) 25
Question: Difference of 2 numbers is 100. If 5% of one number is 10% of the other number, find the addition of2 numbers?
(A) 150
(B) 300
(C) 210
(D) 290
(E) 180
Rationale: Let the numbers be x and y
5% of x = 10% of y
x = 2y
x-y = 100
2y - y =100
y = 100
x = 2y = 200
x+y = 300
Answer is B
Answer: (B) 300
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 24p, in terms of p?
(A) p
(B) 2p
(C) 6p
(D) 8p
(E) p^2
Rationale: y = 30p = 2*3*5*p
24p = 2^3*3*p
The greatest common factor of 30p and 20p is the product of all the common prime factors, using the lower power of repeated factors. The greatest common factor is 2*3*p = 6p
The answer is C.
Answer: (C) 6p
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be
(A) 22
(B) 24
(C) 26
(D) 20
(E) 28
Rationale: Explanation :
Let number of hens = h and number of cows = c
number of heads = 48
=> h + c = 48 ---(Equation 1)
number of feet = 140
=> 2h + 4c = 140
=> h + 2c = 70 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 70 - 48
=> c = 22
Substituting the value of c in Equation 1, we get
h + 22 = 48
=> h = 48 - 22 = 26
i.e., number of hens = 26
Answer : C
Answer: (C) 26
Question: It takes 8 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 8 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 2:00 pm?
(A) 5:10 pm
(B) 5:30 pm
(C) 5:50 pm
(D) 6:10 pm
(E) 6:30 pm
Rationale: Each student paints at a rate of 1/80 of the house per hour.
In 5 hours, the 8 students can paint 40/80 of the house.
From 2 pm to 3 pm, 9 students paint another 9/80 for a total of 49/80.
From 3 pm to 4 pm, 10 students paint another 10/80 for a total of 59/80.
From 4 pm to 5 pm, 11 students paint another 11/80 for a total of 70/80.
12 students can paint the remaining 10/80 of the house in 10/12 of an hour = 50 minutes.
The house is completed at 5:50 pm.
The answer is C.
Answer: (C) 5:50 pm
Question: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?
(A) 23267
(B) 2677
(C) 1800
(D) 2778
(E) 76611
Rationale: Explanation:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400 - 1600) = Rs. 1800.
Answer: C) 1800
Answer: (C) 1800
Question: There are 8 stores in town that had a total of 23 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 8 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 8 people visited 2 stores each for 16 visits.
To maximize the number of stores that one person visited, let's assume that 3 people visited 1 store each. The number of remaining visits is 23 - 16 - 3 = 4, which is the maximum that one person could have visited.
The answer is C.
Answer: (C) 4
Question: A car traveling at a certain constant speed takes 4 seconds longer to travel 1 km than it would take to travel 1 km at 80 km/hour. At what speed, in km/hr, is the car traveling?
(A) 70
(B) 72
(C) 74
(D) 75
(E) 78
Rationale: Time to cover 1 kilometer at 80 kilometers per hour is 1/80 hours = 3,600/80 seconds = 45 seconds;
Time to cover 1 kilometer at regular speed is 45 + 4 = 49 seconds = 49/3,600 hours = 1/74 hours;
So, we get that to cover 1 kilometer 1/74 hours is needed --> regular speed 74 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: C
Answer: (C) 74
Question: One night a certain hotel rented 3/5 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
(A) 50%
(B) 55%
(C) 60%
(D) 65%
(E) 70%
Rationale: The rooms which were not rented is 2/5
The AC rooms which were not rented is (1/3)*(3/5) = 1/5
The percentage of unrented rooms which were AC rooms is (1/5) / (2/5) = 1/2 = 50%
The answer is A.
Answer: (A) 50%
Question: How many seconds will a train 150 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 28 sec
(B) 23 sec
(C) 29 sec
(D) 30 sec
(E) 36 sec
Rationale: D
D = 150 + 150 = 300
S = 36 * 5/18 = 10 mps
T = 300/10 = 30 sec
Answer: (D) 30 sec
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
(A) 65 kmph
(B) 28 kmph
(C) 54 kmph
(D) 26 kmph
(E) 87 kmph
Rationale: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5
= 54 kmph
Answer:C
Answer: (C) 54 kmph
Question: In 2008, a certain factory produced 40% more widgets than it did in 2007, and its production in 2009 was 140% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?
(A) 33%
(B) 44%
(C) 49%
(D) 60%
(E) 80%
Rationale: Let P be the original level of production in 2007.
Let x be the rate of production in 2010 compared to 2009.
x*1.4*1.4*P = P
x = 1/1.96 = 0.51 which is a decrease of 49%.
The answer is C.
Answer: (C) 49%
Question: The number of times 99 is subtracted from 1111 so that the remainder is less than 99 is
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Sol.
Let it be n times.
Then, (1111 - 99n) < 99.
By hit and trial, we find that n = 11.
Answer B
Answer: (B) 11
Question: From a group of 3 women and 3 girls, 4 are to be randomly selected. What is the probability that equal numbers of women and girls will be selected?
(A) 3/5
(B) 1/5
(C) 2/5
(D) 4/5
(E) 1
Rationale: Using the first example, here is the probability of THAT EXACT sequence occurring:
wwGG = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
wGwG = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
A
Answer: (A) 3/5
Question: The sale price sarees listed for Rs.150 after successive discount is 20% and 10% is?
(A) 187
(B) 120
(C) 108
(D) 178
(E) 175
Rationale: 150*(80/100)*(90/100)
= 108
Answer:C
Answer: (C) 108
Question: In a certain sequence, each term except for the first term is one less than twice the previous term. If the first term is 1.5, then the 3rd term is which of the following?
(A) −1.5
(B) −1
(C) 0
(D) 3
(E) 2
Rationale: First = 1.5
Second = 2*1.5-1 = 2
Second = 2*2-1 = 3
Answer: option D
Answer: (D) 3
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 2/7% loss
(C) 16 8/3% loss
(D) 96 2/3% loss
(E) 16 4/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer:A
Answer: (A) 16 2/3% loss
Question: The cost to park a car in a certain parking garage is $12.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?
(A)  $1.09
(B)  $2.69
(C)  $2.25
(D)  $2.37
(E)  $2.50
Rationale: Total cost of parking for 9 hours = 12$ for the first 2 hours and then 1.75 for (9-2) hours = 12+7*1.75 = 24.25
Thus the AVERAGE parking price = 24.25/9 = 2.69 $
B is the correct answer.
Answer: (B)  $2.69
Question: A tank is filled in 10 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 30 hours
(B) 35 hours
(C) 70 hours
(D) 50 hours
(E) 58hours
Rationale: Let the pipe A can fill the tank in x hours
Then pipe B can fill the tank in x/2 hours and pipe C can fill the tank in x/4 hours
Part filled by pipe A in 1 hour = 1/x
Part filled by pipe B in 1 hour = 2/x
Part filled by pipe C in 1 hour = 4/x
Part filled by pipe A, pipe B and pipe C in 1 hour =( 1/x)+(2/x)+(4/x)=7/x
i.e., pipe A, pipe B and pipe C can fill the tank in x/7 hours
Given that pipe A, pipe B and pipe C can fill the tank in 10 hours
x/7=10
x=10×7=70 hours
Answer is C
Answer: (C) 70 hours
Question: The rational number for recurring decimal 0.125125.... is:
(A) 125/990
(B) 125/999
(C) 125/900
(D) 12/999
(E) 12/990
Rationale: 0.125125...
= 0.125
= 125/999
Answer is B.
Answer: (B) 125/999
Question: The 19th of September 1987 was Saturday. What day was the 20th of September 1990 if 1988 was a leap-year?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: There are 365 days in an ordinary year and 366 days in a leap-year.
365 divided by 7 (a week period) yields a remainder of 1, thus the same date after an ordinary year would fall on the next day of a week;
366 divided by 7 (a week period) yields a remainder of 2, thus the same date after a leap-year would fall two days after in a week;
Thus 3 years, 1988, 1989 and 1990, will accumulate 2+1+1=4 days, plus 1-day difference between 19th and 20th, which gives total of 5-day difference (5-day shift). Thus, 20th of September 1990 was Saturday+5 days=Thursday
Answer: D
Answer: (D) Thursday
Question: A fruit seller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%
(A) Rs 8.81
(B) Rs 9.81
(C) Rs 10.81
(D) Rs 11.81
(E) None of these
Rationale: Explanation:
85 : 9 = 105 : x
x= (9×105/85)
= Rs 11.81
Option D
Answer: (D) Rs 11.81
Question: Length of a rectangular plot is 10 mtr more than its breadth. If the cost of fencin g the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 46 m
(B) 55 m
(C) 58 m
(D) 78 m
(E) 80 m
Rationale: Let breadth = x metres.
Then, length = (x + 10) metres.
Perimeter = 5300/26.5 = 200 m.
2[(x + 10) + x] = 200
2x + 10 = 100
2x = 90
x = 45.
Hence, length = x + 10 = 55 m
B
Answer: (B) 55 m
Question: A car is purchased on hire-purchase. The cash price is $26 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
(A) $603
(B) $624
(C) $625
(D) $626
(E) $627
Rationale: Explanation:
Cash price = $26 000
Deposit = 10% Ã— $26 000 = $2600
Loan amount = $26000 âˆ’ $2600
Number of payments = 60
= $23400
I=p*r*t/100
I=14040
Total amount = 23400 + 14040 = $37440
Regular payment = total amount /number of payments= 624
Answer: B
Answer: (B) $624
Question: Rahim and his uncle differ in their ages by 30 years. After 7 years, if the sum of their ages is 66, what will be the age of the uncle ?
(A) 41
(B) 36
(C) 48
(D) 33
(E) 44
Rationale: A
41
Let uncle’s present age = x
Rahim's present age = y
y– x= 30 ...(i)
After 7 year
(x + 7) + (y+ 7) = 66
x + y + 14 = 66
x + y = 52 ...(ii)
combining (i) and (ii) we get
(x + y = 52) + (x – y = 30)
2x= 82
x= 41
Uncle's age is 41
Answer: (A) 41
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 600. What is their H.C.F.?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x
60x = 600
x = 10
The numbers are (3 x 10), (4 x 10) and (5 x 10).
The H.C.F. is 10.
The answer is A.
Answer: (A) 10
Question: As part of a game, six people each must secretly choose an integer between 1 and 6, inclusive. What is the approximate likelihood that all six people will choose different numbers?
(A) 2%
(B) 12%
(C) 16%
(D) 20%
(E) 25%
Rationale: Ans:a)
1st person has option no's- (1,2,3,4,5,6) - there fore probability of getting a no = 6c1/6c1 = 1
2nd person has option no's any five ,
he has to choose a no from five no's - there fore probability of getting a no = 5c1/6c1 = 5/6
3rd person has option no's any four ,
he has to choose a no from four no's -there fore probability of getting a no = 4c1/6c1 = 4/6
4th person has only one option - there fore probability of getting a no= 3c1/6c1 =3/6
5th person has only one option - there fore probability of getting a no= 2c1/6c1 = 2/6
6th person has only one option - there fore probability of getting a no= 1c1/6c1 = 1/6
=1*5/6*4/6*3/6*2/6*1/6 = 2%
Answer: (A) 2%
Question: 2. The value of x + x(xx) when x = 2 is:
(A) 5
(B) 10
(C) 8
(D) 15
(E) 20
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer : B
Answer: (B) 10
Question: The average age of M boys is â€˜bâ€™ years and of â€˜nâ€™ girls â€˜câ€™ years. The average age of all together is?
(A) (mb + nc)/ (m + m) years
(B) (mb + nn)/ (m + n) years
(C) (mb + nc)/ (m + n) years
(D) (nb + nc)/ (m + n) years
(E) (mn + nc)/ (m + n) years
Rationale: Explanation:
(mb + nc) / (m+ n)
Answer:C
Answer: (C) (mb + nc)/ (m + n) years
Question: There are 9 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 10
(B) 36
(C) 45
(D) 60
(E) 90
Rationale: 10 players are there.
two players play one game with one another.
so 9C2=9*8/2
=36
SO OPTION B is correct
Answer: (B) 36
Question: Find the simple interest on Rs. 5000 at 6 % per annum for the period from 5th Feb to 19th April, 2015.
(A) Rs. 40
(B) Rs. 50
(C) Rs. 60
(D) Rs. 70
(E) None of these
Rationale: Explanation:
Given:
1) Principal = Rs. 5000
2) Rate of interest = 6 %
3) Time = 5th Feb to 19th April, 2015
First find the time period 5th Feb to 19th April, 2015
Feb = 28 – 5 = 23 days
March = 31 days
April = 19 days
Total days = 23 + 31 + 19 = 73 days
Convert days into years, by dividing it by 365
Time =	73/365	=	1/5
Simple Interest =	(P × R × T)/100
=	[5000 × 6 × (1/5)]/100
=Rs.60
Simple Interest = Rs. 60
ANSWER IS C
Answer: (C) Rs. 60
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train?
(A) 150
(B) 872
(C) 287
(D) 200
(E) 212
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter
Answer:D
Answer: (D) 200
Question: The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 4. What is the ratio of their heights?
(A) A)2:5
(B) B)2:7
(C) C)2:2
(D) D)2:1
(E) E)4:3
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(4)2h2
=> h1/h2 = 4/3
i.e. h1 : h2 = 4 : 3
Answer: E
Answer: (E) E)4:3
Question: One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in 4 hours. How long would it take to fill the pool if only the slower pipe is used?
(A) 11.25
(B) 11.52
(C) 1.25
(D) 9
(E) 7.2
Rationale: Say the rate of the slower pipe is R pool/hour, then the rate of the faster pipe would be 1.25R=5R/4. Since when both pipes are opened, they fill the pool in four hours, then their combined rate is 1/4 pool/hour.
Thus we have that R + 5R/4 = 1/4 --> R = 1/9 pool/hour --> time is reciprocal of rate thus it's 9/1 =9 hours.
Answer: D.
Answer: (D) 9
Question: 1000 boys have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 12
(B) 12.5
(C) 13
(D) 13.5
(E) 14
Rationale: Explanation:
1000*15 = 1200*x
x = 12.5
B
Answer: (B) 12.5