mathewhe/aqua_rat huggingface dataset:
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 10 liters
(B) 11 liters
(C) 18 liters
(D) 19 liters
(E) 12 liters
Rationale: Number of liters of water in 125 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters
Let us Assume that another 'P' liters of water are added to the mixture to make water 25% of the new mixture. So, the total amount of water becomes (30 + P) and the total volume of the mixture becomes (150 + P)
Thus, (30 + P) = 25% of (150 + P)
Solving, we get P = 10 liters
Answer: A
Answer: (A) 10 liters
Question: There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last no. is?
(A) 8
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 7200 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
(A) 9000
(B) 98000
(C) 40000
(D) 11000
(E) 12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 7200 ( 18 × 400 = 7200)
100% -------> 40000 votes (100 × 400 = 40000)
C
Answer: (C) 40000
Question: What is the smallest positive integer nn such that 6,480∗n√6,480∗n is a perfect cube?
(A) 5
(B) 5^2
(C) 30
(D) 30^2
(E) 30^4
Rationale: Sol: Let's factorize 6480 and we get 6480= 3^4*2^4*5
Now we need to see for what minimum value of n√n*6480= a^3 where a is an Integer
So from 6480 we already have 2^4*3^4*5*n√n = (2^2)^3* (3^2)^3*(5)^3 why cause a is an integer which will need to be have the same factors which are in LHS
solving for n√n = (2^6*3^6*5^3)/ 2^4*3^4*5 and we get
n√n= 2^2*3^2*5^2
Or n = 2^4*3^4*5^4 or 30^4
Ans is E
Answer: (E) 30^4
Question: One side of a rectangular field is 16 m and one of its diagonal is 17 m. Find the area of the field.
(A) 100
(B) 120
(C) 91.2
(D) 180
(E) None
Rationale: Solution
Other side = √(17)2 - (16)2
= √289 - 256
= √33
= 5.7 m.
∴ Area = (16 x 5.7)m2 = 91.2 m2.
Answer C
Answer: (C) 91.2
Question: Robert is travelling on his cycle and has calculated to reach the point A at 2 pm .if he travells at 10kmph;he will reach there at 12 noon if he travels at 15 kmph . at what speed he must travel to reach A at 1p.m
(A) 65km
(B) 85km
(C) 36km
(D) 12km
(E) 369km
Rationale: let the distance travelled be x km
Then x/10-x/15=2
3x-2x=60
x=60km
time taken to travel 60km at 10km/hr=(60/10)hrs=60hrs
so robert stared 6hrs before 2p.m ie 8 A.m
therefore the required speed =(60/5)kmph =12kmph
answer is (D)
Answer: (D) 12km
Question: Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(25 Ã— 26)
so that the result is equal to 1?
(A) 5/13
(B) 6/13
(C) 7/13
(D) 8/13
(E) 9/13
Rationale: The given expression
= 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(25 Ã— 26)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/25 - 1/26)
= 1/2 - 1/26 = 12/26
Thus, the fraction we should add = 1 - 12/26 = 7/13
The answer is C.
Answer: (C) 7/13
Question: The total age of A and B is 14 years more than the total age of B and C. C is how many year younger than A
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Given that A+B = 14 + B + C
=> A ? C = 14 + B ? B = 14
=> C is younger than A by 14 years
Answer: Option D
Answer: (D) 14
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine P is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine P can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
(A) 14
(B) 13
(C) 11
(D) 9
(E) 7
Rationale: machine P finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of P = 5 shifts/day
rate of B = 4 shifts/day
rate of (P+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D
Answer: (D) 9
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 24 minutes. The waste pipe can empty the full cistern in?
(A) A)7
(B) B)6
(C) C)8
(D) D)9
(E) E)5
Rationale: 1/10 + 1/15 - 1/x = 1/24
x = 8
Answer:C
Answer: (C) C)8
Question: Rates for having a manuscript typed at a certain typing service are $10 per page for the first time a page is typed and $5 per page each time a page is revised. If a certain manuscript has 100 pages, of which 20 were revised only once, 30 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $1200
(B) $1500
(C) $1400
(D) $1250
(E) $1350
Rationale: 50 pages typed 1x
20 pages typed 2x (original + one revision)
30 pages typed 3x (original + two revisions)
50(10)+20(10+5)+30(10+5+5)=500+300+600=1400
Answer - C
Answer: (C) $1400
Question: If 1/(x+5)+1/(x-5)=1/(x-5), what is the value of x?
(A) -1
(B) 3
(C) 1
(D) 2
(E) 5
Rationale: If we solve the question, we get x=5.
Option: E
Answer: (E) 5
Question: Five points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
(A) 4
(B) 10
(C) 6
(D) 15
(E) 5
Rationale: Number of triangles can be formed out of 6 points= 5C3=10
Number of quadrilaterals can be formed out of 6 points= 5C4=5
10-5=5.
Answer=E
Answer: (E) 5
Question: A sum of Rs. 4000 amounts to Rs. 4600 in 5 years at a certain rate of simple interest. What would be the amount, if the rate of interest is increased by 3 %.
(A) Rs. 5202
(B) Rs. 5200
(C) Rs. 5228
(D) Rs. 5212
(E) Rs. 5182
Rationale: Explanation:
Principal = Rs. 4000, Amount = Principal + SI = Rs. 4600
SI = Amount – Principal = 4600 – 4000 = Rs. 600
Given : Principal = Rs. 4000, Time = T = 5 years and SI = Rs. 600
SI =PRT/100
600 = 4000 *R * 5/100
600 = 200R
R = 3 % p.a.
Now the new interest rate is = 3% + 3% = 6 % p.a.
SI = PRT/ 100 = 4000 * 6 * 5/ 100 = Rs. 1200
Amount = Principal + SI
= 4000 + 1200
= 5200
ANSWER:B
Answer: (B) Rs. 5200
Question: A man's speed with the current is 22 km/hr and the speed of the current is 5 km/hr. The man's speed against the current is
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Man's rate in still water = (22 - 5) km/hr = 17 km/hr.
Man's rate against the current = (17 - 5) km/hr = 12 km/hr.
Answer:D
Answer: (D) 12
Question: The diagonal of a rhombus are 70 m and 160 m. Its area is:
(A) 1940
(B) 4800
(C) 5600
(D) 5200
(E) 5000
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 70 Ã— 160) Cm(power)2
= 70 Ã— 80 = 5600 Cm(power)2
Answer is C.
Answer: (C) 5600
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 18.12%
(E) 18%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: The jogging track in a sports complex is1100m in circumference. Prakash and his wife start from the same point and walk in opposite directions at 5.2 km/hr and 5.6 km/hr respectively. They will meet for the first time in?
(A) 6.11 min
(B) 6.88 min
(C) 7.18 min
(D) 8.33 min
(E) 9.00 min
Rationale: Clearly, the two will meet when they are 1100 m apart.
To be (5.2 + 5.6) = 10.8 km apart, they take 1 hour.That is 60 minutes.
To be1100 m apart, they take
= (1100/1080 * 60) min
= 6.11 min.
Answer: A
Answer: (A) 6.11 min
Question: In Sam's hanger there are 23 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 6 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.
Rationale: Total boxes = 23
Filled with toys = 16
Filled with appliance = 7
Total boxes for sale = 8
Toy boxes for sale = 6
Appliance boxes for sale = 2
Appliance boxes not for sale = 7 - 2 = 5
Correct Option: E
Answer: (E) 5.
Question: A box contains 10 tablets of medicine A and 13 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.
(A) 12
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: The worst case scenario will be if we remove all 13 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13+2=15 tablets.
Answer: B.
Answer: (B) 15
Question: A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?
(A) 7.33 days
(B) 7.678 days
(C) 9.38 days
(D) 7.38 days
(E) 7.32 days
Rationale: A + B = 1/8
B + C = 1/12
C + A = 1/16
-------------------------------
2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48
A + B +C = 13/96
96/13 = 7.38 days
Answer: D
Answer: (D) 7.38 days
Question: The perimeter of a triangle is 20cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
(A) A)72
(B) B)828
(C) C)25
(D) D)34
(E) E)35
Rationale: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 20/2 = 25 cm2
Answer: Option C
Answer: (C) C)25
Question: In Arun's opinion, his weight is greater than 64 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 67 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
(A) 86.5 kg
(B) 66.5 kg
(C) 46.5 kg
(D) 65.5 kg
(E) 16.5 kg
Rationale: Let Arun's weight be X kg.
According to Arun, 64 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 67.
The values satisfying all the above conditions are 65 and 66.
Required average = (65 + 66) / 2 = 65.5 kg
Answer: D
Answer: (D) 65.5 kg
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 90 student reduced from 75 to 60 . Due to this the average came down by 15 marks. What was the number of students who took the exam?
(A) 90
(B) 100
(C) 110
(D) 130
(E) 160
Rationale: Explanation :
Number of student = (75-60) * 90/15 = 90
Answer : A
Answer: (A) 90
Question: Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?
(A) 2502
(B) 2528
(C) 2573
(D) 2500
(E) 2503
Rationale: Let's Anil's salary be Rs. 100.
Money spent on Rent = 40% of 100 = Rs. 40.
Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.
Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40
Anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60
for 33.6 ---> 100 ; 840 ---> ?
Required salary = 840/33.6 * 100 = Rs. 2500
Answer:D
Answer: (D) 2500
Question: The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 96 square centimeters, what is the length of the rectangle in centimeters?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 96
2L^2/3 = 96
L^2 = 144
L = 12 cm
The answer is B.
Answer: (B) 12
Question: A train passes a station platform in 42 sec and a man standing on the platform in 12 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 227
(B) 450
(C) 460
(D) 480
(E) 171
Rationale: Speed = 54* 5/18 = 15 m/sec.
Length of the train = 15 * 12 = 180 m.
Let the length of the platform be x m . Then,
(x + 180)/42 = 15 => x = 450 m.
Answer:B
Answer: (B) 450
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 360-mile journey? Assume that the train makes no intermediate stops.
(A) 8
(B) 8.5
(C) 9
(D) 9.5
(E) 10
Rationale: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 360-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
7 70 280
8 80 360
It takes a total of Eight hours to cover the 360 mile distance.
ANSWER: A
Answer: (A) 8
Question: The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 75 and n is not prime, what is the greatest possible value of f(n)?
(A) 72
(B) 69
(C) 65
(D) 60
(E) 58
Rationale: Since we need the largest value of f (n), we will start with the largest option.
Option A: 2*2*2*2*2*2 = . This is not a product of distinct prime numbers. Hence incorrect
Option B: 69 = 3*23. This is a product of distinct prime numbers.
Rest all the options are smaller that 69.
Correct Option: B
Answer: (B) 69
Question: Village X has a population of 74000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
(A) 15
(B) 16
(C) 11
(D) 18
(E) 13
Rationale: Let the population of two villages be equal after p years
Then, 74000-1200p=42000+800p
2000p=32000
p=16
Answer is B.
Answer: (B) 16
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
(A) 5!
(B) 8!
(C) 9!
(D) 10!
(E) 11!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: (B) 8!
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
(A) 30720
(B) 153600
(C) 15360
(D) 307200
(E) 153700
Rationale: Perimeter = Distance covered in 8 min. =12000/60x 8	m = 1600 m.
Let length = 3x metres and breadth = 2x metres
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2
ANSWER:B
Answer: (B) 153600
Question: If (1*x)y=y, which of the following must be true?
(A) x=-1 or y=0
(B) x=0 or y=0
(C) x=1 or y=1
(D) x=-1 or y=-1
(E) x=0 or y=1
Rationale: We have (1*x)y=y.
If x=1, y=1 True
If y=1, (1*x)*1=1True
So, Cwill be the answer.
Answer: (C) x=1 or y=1
Question: What is the sum of all the numbers which divides 100 ?
(A) 408
(B) 102
(C) 816
(D) 916
(E) 416
Rationale: You first have to know all the divisor of 100. They are 2,4,5,10,20,25,50 and 100. If you add all these numbers together, you get 408.
Final Answer:
A
Answer: (A) 408
Question: Among 300 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
(A) 30
(B) 90
(C) 120
(D) 172
(E) 188
Rationale: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 90
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 132 + 168 - 90 = 210
So, in the image we know that the number of students in the zone with the black boundary = 210
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 300, we can write:
210 +b+w= 300
Or,b+w= 300 - 210 = 90
That is,b= 90 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 90
B
Answer: (B) 90
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 25
(B) 15
(C) 18
(D) 47
(E) 26
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18
= 47 min.
Answer:D
Answer: (D) 47
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.59000?
(A) 81000
(B) 81007
(C) 74671.875
(D) 81066
(E) 81022
Rationale: 59000* 9/8 * 9/8 = 74671.875
Answer:C
Answer: (C) 74671.875
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations P are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) P=8
Rationale: The combinations could be P{(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6) ,(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.E
Answer: (E) P=8
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Answer:A
Answer: (A) 1
Question: If the cost of k metres of cable wire is c rupees, then what is the cost of m metres of cable wire at the same rate?
(A) Rs. (mc)
(B) Rs. (mc/k)
(C) Rs. (kc)
(D) Rs. (km/c)
(E) None of these
Rationale: Explanation :
Cost of k metres = Rs. c
Cost of 1 metre=Rs.(c/k)
Cost of m metres=Rs.[(c/k).m]=Rs.(mc/k)
Answer : B
Answer: (B) Rs. (mc/k)
Question: Ravi covers a distance of 900mtrs in 180 secs. Find his speed in kmph?
(A) 10 kmph
(B) 18 kmph
(C) 20 kmph
(D) 26 kmph
(E) 28 kmph
Rationale: Given distance D= 900 meters and Time= 180 seconds
Speed = Distance/Time
= 900/180
= 5 m/s.
But speed is asked in kmph , to convert 5 mps to kmph , multiply it by
18/ 5
.
Speed in kmph = 5 x 18/5
= 18 kmph
B
Answer: (B) 18 kmph
Question: Light glows for every 13 seconds . How many times did it between 1:57:58 and 3:20:47 am
(A) 381
(B) 382
(C) 383
(D) 384
(E) 385
Rationale: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/13 = 382.
so total 383 times light ll glow
ANSWER:C
Answer: (C) 383
Question: If you add all the numbers on your mobile phone , what is the answer?
(A) 45
(B) 50
(C) 55
(D) 100
(E) 60
Rationale: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are in your mobile phone.
Therefore 0+1+2+3+4+5+6+7+8+9=45
Answer is A
Answer: (A) 45
Question: If the average cost of a house was $50,000 in 1955 and was x in 2005, what was the average increase in home prices per year over this period?
(A) A)(x+50,000)/40
(B) D)(50,000-x)/40
(C) C)(50,000/40)+x
(D) B)(x-50,000)/50
(E) E)x/40
Rationale: Average house price in 2005: x
Average house price in 1965: 50,000
2005-1955=50
Average increase per year: (x-50,000)/50
Answer is D
Answer: (D) B)(x-50,000)/50
Question: If it is 5:14 in the evening on a certain day, what time in the morning was it exactly 2,880,702 minutes earlier? (Assume standard time in one location.)
(A) 5:32
(B) 5:36
(C) 5:48
(D) 5:54
(E) 5:58
Rationale: 5:14 minus 2,880,702 must end with 2, the only answer choice which ends with 2 is A.
Answer: A.
Answer: (A) 5:32
Question: What is the greatest of 3 consecutive integers whose sum is 30?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 30 / 3 = 10
The three numbers are 9, 10, and 11.
The answer is D.
Answer: (D) 11
Question: What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 120° each?
(A) 72 cm
(B) 108 cm
(C) 120 cm
(D) 132 cm
(E) 144 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 120*n
from here
n =6
So perimeter becomes 12*6= 72
answer A
Answer: (A) 72 cm
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 656 ways
(B) 500 ways
(C) 716 ways
(D) 765 ways
(E) 142 ways
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
Answer: B
Answer: (B) 500 ways
Question: How many positive integers less than 256 are multiple of 4 but NOT multiples of 6?
(A) 20
(B) 31
(C) 42
(D) 53
(E) 44
Rationale: 248/4=64
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
64-20=44
Answer: E
Answer: (E) 44
Question: Kumar started from Chennai at x hrs y minutes and travelled to Vellore. He reached Vellore at y hrs z minutes. If the total travel time was z hrs and x minutes, his starting time in Chennai could have been ______ (Assume clock format to be 0 to 24 hrs).
(A) 02:08 hrs
(B) 13:03 hrs
(C) 00:02 hrs
(D) 12:01 hrs
(E) None of these
Rationale: DETAILED SOLUTION
x, y or z cannot be greater than 24
Also x + y + z cannot be greater than 24
Given x hrs + z hrs = y hrs
Also y min + x min = z min
The only value of x that will satisfy the above 2 equations is 0.
Hence, from among the choices given, the time could be 00:02 hrs
CORRECT ANSWER C.
Answer: (C) 00:02 hrs
Question: How many words can be formed by using all letters of the word 'MACHINE' ?
(A) 1120
(B) 1200
(C) 1570
(D) 5040
(E) 6040
Rationale: The word MACHINE contains 7 different letters
Required number of words = 7P7 = 7! = 7*6*5*4*3*2*1 = 120
Answer is D
Answer: (D) 5040
Question: Calculate how many seconds it eill take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 5, 8, 11 and 15 seconds. ?
(A) 1310
(B) 1320
(C) 1322
(D) 1323
(E) 1312
Rationale: LCM of 5, 8, 11 and 15 is
1320
LCM=1320
ANSWER:B
Answer: (B) 1320
Question: A bag contains 6 green jacks and 24 white jacks. One jack is drawn at random. What is the probability that the jack is white?
(A) 3/4
(B) 4/5
(C) 7/8
(D) 1
(E) None of these
Rationale: Explanation:
Total cases = 6 + 24 = 30
Favourable cases = 24
So probability = 24/30 = 4/5
Answer: A
Answer: (A) 3/4
Question: Evaluate : 86 x 863 - 86 x 237
(A) 45823
(B) 53836
(C) 44824
(D) 66524
(E) None of them
Rationale: 86 x 863 + 986 x 237 = 986 x (863 - 237) = 86 x 626 = 53836.
Answer is B
Answer: (B) 53836
Question: 5 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2 candidates. In how many ways can one cast his vote?
(A) 11
(B) 12
(C) 15
(D) 16
(E) 28
Rationale: There are 8 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 8C2 = 28
E
Answer: (E) 28