mathewhe/aqua_rat huggingface dataset:
Question: At a special sale, 12 tickets can be purchased for the price of 4 tickets. If 12 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 12 tickets?
(A) 20%
(B) 33.3%
(C) 40%
(D) 60%
(E) 66.6%
Rationale: let the price of a ticket be Rs.100, so 4 tickets cost 400 & 12 tickets cost 1200
12 tickets purchased at price of 4 tickets ie., for 400, so amount saved s Rs.800,
% of 5 tickets = (800 /1200)*100 =66.6 %
ANSWER:E
Answer: (E) 66.6%
Question: Twelve machines, each working at the same constant rate, together can complete a certain job in 6 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 3 days?
(A) 14
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: Rate of one machine = 1 job / (12*6) days
let X = number of machines needed to complete the job in 3 days
1/(12*6) * 3 * X = 1 job
X = 24
24-12= 12
ANSWER: B
Answer: (B) 12
Question: What is the units digit of 31! + 50! + 2! + 3!?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 2 + 6 = 8
The units digit is 8.
The answer is E.
Answer: (E) 8
Question: In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people?
(A) 11C6 * 9! *4!
(B) 11C3 * 6! *3!
(C) 15C4 * 9! *3!
(D) 15C2 * 10! *3!
(E) 16C5 * 10! *4!
Rationale: 7 people can be selected from 11 people in 11C7 ways.
Remaining 4 people can be selected from 4 people in 4C4 ways.
Now, arranging 7 people on a round table = (7-1) ! = 6!
Arranging 4 people on a round table = (4-1) ! = 3!
Hence, total number of ways = 11C7 * 6! * 4C4 * 3!
= 11C3 * 6! * 3!
B
Answer: (B) 11C3 * 6! *3!
Question: Divide Rs. 1800 among A, B and C so that A receives 2/5 as much as B and C together and B receives 1/5 as A and C together. A's share is?
(A) 400
(B) 500
(C) 375
(D) 450
(E) 600
Rationale: A+B+C = 1800
A = 2/5(B+C); B = 1/5(A+C)
A/(B+C) = 2/5
A = 1/6 * 3600=> 600
Answer: E
Answer: (E) 600
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
(A) 5
(B) 7
(C) 18
(D) 10
(E) 11
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
5x = 45
x = 9.
Hence, B's age = 2x = 18 years.
Answer: Option C
Answer: (C) 18
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 231 but three tickets from city A to B and two tickets from city A to C cost Rs. 219. What are the fares for cities B and C from A ?
(A) s. 4, Rs. 23
(B) s. 13, Rs. 17
(C) s. 15, Rs. 14
(D) s. 17, Rs. 51
(E) s. 39, Rs. 51
Rationale: If fares for cities B and C from A are x and y respectively, then
2x+3y=231 or 6x+9y= 693
3x+2y =219 or 6x+4y= 438
subtracting
5y = 255
y= Rs 51.
Hence E. Rs. 39, Rs. 51
ANSWER:E
Answer: (E) s. 39, Rs. 51
Question: A trader purchases several articles at the rate of 13 for Rs. 10 and sells them at the rate of 10 for Rs. 13. What is his gain/loss?
(A) 69 % gain
(B) 56.25 % gain
(C) 56.25 % loss
(D) 25 % loss
(E) None of these
Rationale: Explanation:
We have, C. P of 13 articles = Rs. 10
& S. P of 10 articles = Rs. 13
S. P of 13 articles = ?
= (13 * 13) / 10 = 16.9
Gain = [(16.9 – 10)/10] * 100 = 69 %
ANSWER: A
Answer: (A) 69 % gain
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 45 percent butterfat to obtain milk that is 20 percent butterfat?
(A) 6
(B) 12
(C) 14
(D) 16
(E) 20
Rationale: Equate the fat:
0.1x + 0.45*8 = 0.2(x + 8) --> x = 20.
Answer: E.
Answer: (E) 20
Question: The inverse ratio of 3: 2: 1 is?
(A) 1:2:3
(B) 2:3:1
(C) 3:1:2
(D) 2:3:6
(E) 4:5:7
Rationale: Explanation:
1/3: 1/2: 1/1 = 2:3:6
ANSWER IS D
Answer: (D) 2:3:6
Question: What is the sum of all even numbers from 1 to 401?
(A) 122821
(B) 281228
(C) 281199
(D) 122850
(E) 40200
Rationale: Explanation:
400/2 = 200
200 * 201 = 40200
Answer: E
Answer: (E) 40200
Question: ?% of 360 = 165.6
(A) 277
(B) 36
(C) 64
(D) 72
(E) 46
Rationale: ?% of 360 = 165.6
or, ? = 165.6×100/360=46
Answer E
Answer: (E) 46
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph. A man rows to place at a distance of 170 km and comes back to the starting point. The total time taken by him is:
(A) 12 hours
(B) 68 hours
(C) 36 hours
(D) 58 hours
(E) None
Rationale: Sol.
Speed upstream = 3 kmph; Speed downstream = 15 kmph.
∴ total time taken = [105/7.5 + 105/10.5] hours = 68 hours.
Answer B
Answer: (B) 68 hours
Question: One quarter of the workers at the factory is clerical, one fifth is technical, half are administrative and the other 25 are managerial. How many workers total are there in the factory?
(A) 250
(B) 366
(C) 400
(D) 500
(E) 2500
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 25
x= 25*20= 500
D is the answer
Answer: (D) 500
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 50 kmph
(B) 65 kmph
(C) 75 kmph
(D) 85 kmph
(E) 90 kmph
Rationale: Explanation:
S = (90 + 60)/2 = 75 kmph
C)
Answer: (C) 75 kmph
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
(A) 4/5
(B) 5/4
(C) 3/5
(D) 2/5
(E) 3/4
Rationale: Let the required fraction be x. Then 1/X - X = 9/20
(1-X^2)/X = 9/20 ==> 20 - 20X^2 = 9X
20X^2 + 9X - 20 = 0
20X^2 + 25X - 16X - 20 = 0
5X(4X + 5) - 4(4X + 5) = 0
(4X + 5)(5X - 4) = 0
X = 4/5 (neglecting -ve value)
Answer A)4/5
Answer: (A) 4/5
Question: An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 4.04
(B) 4.02
(C) 4.01
(D) 4.05
(E) 4.06
Rationale: Formula for Calculation of Percentage error is:
=(x−y−(xy)/100)%
=(2+2+(2×2)/100)%=4.04%
Answer is A.
Answer: (A) 4.04
Question: What percent of a day is 6 hours?
(A) 6.25%
(B) 20%
(C) 25%
(D) 12.5%
(E) 18%
Rationale: Total hours in a day = 24
Required percent
=6/24×100=25% Answer: Option C
Answer: (C) 25%
Question: An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.40 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
(A) 130,000
(B) 300,000
(C) 380,000
(D) 550,000
(E) 420,000
Rationale: Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000
Remaining books = 180,000/0.4 = 450,000
Total books = 450,000+100,000 = 550,000 Answer D
Answer: (D) 550,000
Question: Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 55 percent of the total number of employees work in research, how many male employees do NOT work in research?
(A)  520
(B)  480
(C)  392
(D)  138
(E)  88
Rationale: total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =55% =550
Total male employees =48%=480
male employees working in research =550-208=342
male employees not working in research =480-342=138
Answer D
Answer: (D)  138
Question: A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
(A) A)$200
(B) B)$1000
(C) C)$819
(D) D)$1200
(E) E)$400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+4*4X+1*X=8600
25X+16X+X=8600
42X=8600, X=204.76.
Daughter receives four times of nephew so 4 * 204.76= 819.
So Each Daughter receives $800. answer is option C) $819.
Answer: (C) C)$819
Question: You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs.
In what number alternative ways you'll climb ten stairs?
(A) 99
(B) 79
(C) 55
(D) 89
(E) 66
Rationale: D
Answer: (D) 89
Question: The sale price sarees listed for Rs.175 after successive discount is 20% and 5% is?
(A) 187
(B) 133
(C) 142
(D) 178
(E) 175
Rationale: 175*(80/100)*(95/100)
= 133
Answer:B
Answer: (B) 133
Question: The radius of a semi circle is 7 cm then its perimeter is?
(A) 32.8
(B) 36
(C) 32.1
(D) 32.2
(E) 32.9
Rationale: Radius = 7 cm then Diameter = 14 cm
1/2*22/7*14+14 = 36
Answer : B
Answer: (B) 36
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time?
(A) s. 53.30
(B) s. 53.22
(C) s. 51.219
(D) s. 53.18
(E) s. 51.10
Rationale: Explanation:
Sum = (52 * 100) / (2 * 5) = Rs. 520
Amount = [520 * (1 + 5/100)2] = Rs. 573.3
C.I. = (573.3 - 520) = Rs. 53.30.
Answer:A
Answer: (A) s. 53.30
Question: What is the least positive integer that is not a factor of 30! and is not a prime number?
(A) 31
(B) 32
(C) 33
(D) 62
(E) 64
Rationale: A) 31 is prime and per the question stem we cannot use this
B) 32 = 2 * 16 - within 30! we have a 2 and 16 so 32 will be a factor of 30!
C) 33 = 3 *11 - again within 30! we have a 3 and an 11 so 33 will be a factor of 30!
D) 62 = 31 * 2 - Bingo 31 is not included in 30!
E) 64 = 16 * 4 - both 16 and 4 are multiplied in 30!
Answer is D!
Answer: (D) 62
Question: Find the slope of the line perpendicular to the line y = (1/2)x - 7
(A) 1
(B) 2
(C) -2
(D) 4
(E) 5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 2. If m is the slope of the line perpendicular to the given line, then
m × (1/2) = -1
Solve for m
m = - 2
correct answer C) -2
Answer: (C) -2
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 1350
(B) 1197
(C) 1927
(D) 1112
(E) 1921
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer: A
Answer: (A) 1350
Question: There are 9 books on a shelf that consist of 4 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?
(A) 88
(B) 99
(C) 110
(D) 121
(E) 132
Rationale: The total number of ways to select 4 books is 9C4 = 126
The number of ways which do not include any paperbacks is 5C4 = 5
The number of combinations with at least one paperback is 126-5 = 121
The answer is D.
Answer: (D) 121
Question: A man ran 20 miles in 2 hours 2 minutes. What was the average speed of the man in miles per hour?
(A) 9.72 miles / hour
(B) 9.73 miles / hour
(C) 9.75 miles / hour
(D) 9.78 miles / hour
(E) 9.79 miles / hour
Rationale: We first convert the time of 2 hours 2 minutes in minutes
2 hours 2 minutes = 2* 60 + 2 = 122 minutes
Average speed S is given by distance / time. Hence
S = 20 miles / 122 minutes = 0.163mile / minute
= 9.78 miles / hour
correct answer D
Answer: (D) 9.78 miles / hour
Question: The current birth rate per thousand is 37, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by?
(A) 2.6%
(B) 3.2%
(C) 3.9%
(D) 4%
(E) 5.1%
Rationale: Net growth on 1000 = 37-11 = 26
Net growth on 100 = 26*100/1000 = 2.6%
Answer is A
Answer: (A) 2.6%
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg. How much amount did he pay to the shopkeeper?
(A) A)1040
(B) B)1045
(C) C)1055
(D) D)1060
(E) E)1235
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 75 × 9 = 675.
Total cost he has to pay = 560 + 675 = 1235.
E)
Answer: (E) E)1235
Question: The area of sector of a circle whose radius is 10 metro and whose angle at the center is 42Â° is?
(A) 36.7
(B) 52.9
(C) 52.8
(D) 52.1
(E) 52.2
Rationale: 42/360 * 22/7 * 10 * 10 = 36.7 m2
Answer: A
Answer: (A) 36.7
Question: A runs twice as fast as B and gives B a start of 64m.How long should the racecourse be so that A and B might reach in the same time?
(A) 75 m.
(B) 128 m.
(C) 150 m.
(D) 100 m.
(E) None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 64m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 64m is 64/1=64m
so the total time taken by a and b to reach =2*64=128m
ANSWER:B
Answer: (B) 128 m.
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 228
(B) 271
(C) 500
(D) 277
(E) 812
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.Answer: C
Answer: (C) 500
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 6
Rationale: Work done by A and B in two hours, = First hour A + Second hour B = (1/4) + (1/12) = 1/3.
total time required to complete the work = 2 (3) = 6 days
ANSWER E
Answer: (E) 6
Question: If x, y, and z are positive integers and x = 4y = 7z, then the least possible value of x + y + z is
(A) 33
(B) 40
(C) 49
(D) 39
(E) 84
Rationale: x + y + z = x/4 + x + x/7
= (7 + 28 + 4 )x/28 =39x/28
39 is not divisible by 28, so for least value, x = 28
Answer - D
Answer: (D) 39
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 399
(B) 240
(C) 277
(D) 299
(E) 712
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240
Question: At a certain company, two-thirds of the employees had cell phones and two-fifths had pagers. If one-third of the employees had neither cell phones nor pagers then what fraction of the employees had both cell phones and pagers?
(A) 7/5
(B) 6/11
(C) 2/5
(D) 1/3
(E) 4/15
Rationale: Let there be 15 employees
Cell Phone = 10
Pagers = 6
Neither Pager Nor Cell Phone = 5
So, 10 = 10 + 6 - x
Or, x = 6
So, fraction of the employees had both cell phones and pagers = 6/15 => 2/5
ANSWER:C
Answer: (C) 2/5
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
(A) 732.534 + 412.256 – 544.29
(B) 1256.214 – 355.514 – 300.2
(C) 246.86 + 439.38 – 80.74
(D) 1415.329 + 532.4 – 1347.229
(E) 398.14 – 239.39 + 441.75
Rationale: (c) = 605.5 whereas the other parts are equal to 600.5
Answer C
Answer: (C) 246.86 + 439.38 – 80.74
Question: On a test average (arithmetic mean) test score for 9 students is 80. What must be 10th student's score that average score for 10 students to be 82?
(A) 100
(B) 90
(C) 80
(D) 70
(E) 60
Rationale: (9*80+x)/10=82
x=(10*82)-(9*80)
x= 820 - 720
total score required 820 - 720=100
Correct answer is A
Answer: (A) 100
Question: What is the greatest value of m such that 4^m is a factor of 29! ?
(A) 12
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Pretty simple, really.
If m = 12, then 4m = 48, which is 24x2, both of which are included in 29!
Since 12 is the largest number here, its the answer.
Answer is A
Answer: (A) 12
Question: A train passes a platform in 40 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 280 meter
(B) 240 meter
(C) 200 meter
(D) 300 meter
(E) None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/40 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 40
=> 300+L = 15×40 = 600
=> L = 600-300 =300 meter
Answer: Option D
Answer: (D) 300 meter
Question: If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: area of parallelogram is=base*height----1
area of triangle=1/2(base*height)-------2
devide equation 2 by 1
1/2
ANSWER:A
Answer: (A) 1/2
Question: If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
(A) 4
(B) 5
(C) 2
(D) 6
(E) 1
Rationale: .
If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
A.	4
B.	5
C.	6
D.	7
E.	8
Answer: Option C
Explanation:
72 = 9 x8, where 9 and 8 are co-prime.
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
Required value of * is 6.
ANSWER D
Answer: (D) 6
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 266
(B) 288
(C) 245
(D) 776
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: (C) 245
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 28%
(B) 25%
(C) 95%
(D) 05%
(E) 22%
Rationale: 800 --- 200
100 --- ? => 25%
Answer:B
Answer: (B) 25%
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 6 cannot appear more than once in the number.
(A) 2300
(B) 2385
(C) 2380
(D) 2375
(E) 2390
Rationale: N=(4*5-1)*5*5*5=2375
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 66 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}
D
Answer: (D) 2375
Question: Fresh grapes contain 75% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 25 kgs of raisins?
(A) 75 kgs
(B) 64kgs
(C) 72 kgs
(D) 65 kgs
(E) 70 kgs
Rationale: The weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-75=25% of whole weight),
so 25*0.75 = x*0.25
--> x = 75.
Answer: A.
Answer: (A) 75 kgs
Question: The average salary of all the employees in a small company is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of employees in the company is:
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Explanation :
Let the total number of employees be x. then,
8000x = (12000 x 7) + 6000 (x 7)
2000x = 42000
x = 21.
Answer : B
Answer: (B) 21
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (2)?
(A) 5
(B) 11
(C) 12
(D) 25
(E) 55
Rationale: (21)(3^7) is divisible by 3 but 2 is not divisible by 3.
Therefore (21)(3^7) - 2 is not divisible by 3 and thus not divisible by 12.
The answer is C.
Answer: (C) 12
Question: If Jake loses 8 pounds, he will weigh half as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?
(A)  131
(B)  135
(C)  188
(D)  147
(E)  188
Rationale: J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 8 = S/2
J = S/ + 8 (Equation 1)
Next, we are told that “Together they now weigh 278 pounds.” We can also put this into an equation.
J + S = 278 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
S/2 + 8 = 278-S
3S = 540
S = 90
J + 90 = 278
J = 188
Answer: C
Answer: (C)  188
Question: Club X has more than 70 but fewer than 100 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.
Rationale: The number of members is 4j+3 = 5k+3.
Let's start at 4(17)+3 = 71 and keep adding 4 until we find a number in the form 5k+3.
71, 75, 79, 83 = 5(16) + 3
The club has 83 members.
83/6 = 6(13) + 5
The answer is E.
Answer: (E) 5.
Question: If f(x) = 2x^2 + y, and f(2) = 60, what is the value of f(5)?
(A) 104
(B) 60
(C) 52
(D) 50
(E) 102
Rationale: f(x) = 2x^2 + y
f(2) = 60
=> 2*(2)^2 + y = 60
=> 8 + y = 60
=> y = 52
f(5)= 2*(5)^2 + 52
= 102
Answer E
Answer: (E) 102
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
(A) 10,573
(B) 11,908
(C) 12,322
(D) 13,924
(E) 14,537
Rationale: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is D.
Answer: (D) 13,924
Question: A man purchased a grinder for Rs. 660 and sold it at a profit of 10%. The selling price is:
(A) Rs. 736
(B) Rs. 812
(C) Rs. 660
(D) None of these
(E) Cannot be determined
Rationale: s.p.=110/100 × 600 = 660
Answer: C
Answer: (C) Rs. 660
Question: Of the 5 distinguishable wires that lead into an apartment, 3 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Given:
Total number of wires = 5
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y = 7
Answer is Option B
Answer: (B) 7
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 1 is rolled?
(A) 25/216
(B) 50/216
(C) 25/72
(D) 25/36
(E) 5/6
Rationale: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 1, there are three ways:
A 1 on the first roll and non 1 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 1 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Answer: (C) 25/72