mathewhe/aqua_rat huggingface dataset:
Question: Three small cruise ships, each carrying 7 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
(A) 4328
(B) 5382
(C) 6174
(D) 7690
(E) 8436
Rationale: The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 7C2 = 21.
At Port B, the number of ways to choose one winner is 7.
At Port C, the number of ways to choose one winner is 7.
The total number of ways to give out gift certificates is 6*21*7*7 = 6174
The answer is C.
Answer: (C) 6174
Question: Calculate the average of all the numbers between 11 and 27 which are divisible by 2.
(A) 11
(B) 10
(C) 18
(D) 19
(E) 21
Rationale: Explanation:
numbers divisible by 2 are 12,14,16,18,20,22,24,26,
Average = (12+14+16+18+20+22+24+26, ) / 8 = 152/8 = 19
ANSWER: D
Answer: (D) 19
Question: Every day Daniel drives 120 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 60%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 120 miles at 4 miles/hour.
D = (R)(T)
120 = (4)(T)
120/4 = 30 = T
It takes 30 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (88 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
88 = (2)(T)
88/2 = 44 = T
It takes 44 hours for the second part
Total time to drive home on Monday = 4+44 = 48 hours
We're asked by what percent 48 hours is greater than 30 hours.
48/30 = 1.6, so it is 60% greater.
answer:E
Answer: (E) 60%
Question: A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that Exactly three are not spoiled.
(A) 116/495
(B) 224/495
(C) 129/495
(D) 187/495
(E) 197/495
Rationale: equired probability = 8C3 . 4C1/12C4 = 56 x 4/495
= 224/495.
ANSWER:B
Answer: (B) 224/495
Question: At a meeting, 8 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 12
(B) 72
(C) 120
(D) 1440
(E) 5040
Rationale: The number of arrangements of n distinct objects in a row is given by n!
The number of arrangements of n distinct objects in a circle is given by (n−1)!
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
R=n!-n=(n−1)!
(n−1)!=(8−1)!=5040
Answer: E
Answer: (E) 5040
Question: A train 120 m long crosses a platform 220 m long in 20 sec; find the speed of the train?
(A) 87 kmph
(B) 65 kmph
(C) 54 kmph
(D) 61 kmph
(E) 18 kmph
Rationale: D = 120 + 220 = 340
T = 20
S = 340/20 * 18/5 = 61 kmph
Answer:D
Answer: (D) 61 kmph
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
(A) 2318
(B) 2380
(C) 1277
(D) 2662
(E) 1321
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer: B
Answer: (B) 2380
Question: A man buys a cycle for Rs. 1800 and sells it at a loss of 25%. What is the selling price of the cycle?
(A) s. 1090
(B) s. 1160
(C) s. 1190
(D) s. 1350
(E) s. 1256
Rationale: S.P. = 75% of Rs. 1800 = Rs.75/100x 1800	= Rs. 1350
ANSWER :D
Answer: (D) s. 1350
Question: Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%?
(A) 10liters
(B) 15liters
(C) 20liters
(D) 18liters
(E) 22liters
Rationale: Quantity of water in 10 liters = 5% of 10 liters = 0.5 liters
Let x liters of pure milk be added.
Then, 0.5/(10+x) = 2/100
2x = 30
x=15 liters
Answer is B
Answer: (B) 15liters
Question: Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the pipes are opened simultaneously, and the pipe A is closed after 3 minutes, then how much more time will it take to fill the tank by pipe B?
(A) 5 minute 25 second
(B) 5 minute 45 second
(C) 5 minute 35 second
(D) 6 minute 45 second
(E) 7 minute 45 second
Rationale: Part filled by pipe A in 1 minute =1/8
Part filled by pipe B in 1 minute =1/14
Part filled by pipe A and pipe B in 1 minute =1/8+1/14=11/56
Pipe A and B were open for 3 minutes.
Part filled by pipe A and B in 3 minute=3 Ã— 11/56=33/56
Remaining part =1-33/56=23/56
Time taken by pipe B to fill this remaining part=(23/56)/(1/14)=23/4
=5 3/4 minutes
=5 minute 45 second
Answer is B
Answer: (B) 5 minute 45 second
Question: If x > 3000, then the value of (x)/(2x-42) is closest to?
(A) 1/6
(B) 1/3
(C) 10/21
(D) 1/2
(E) 3/2
Rationale: assume x = 3002
(x)/(2x-42) = 3002 / (3002*2-42)
=3002 / 5962
= = 1/2
Ans - D
Answer: (D) 1/2
Question: In a mixture of milk and water, the proportion of milk by weight was 90%. If, in a 120-gram mixture, 30 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?
(A) 91.4%
(B) 91.6%
(C) 91.8%
(D) 92.0%
(E) 92.2%
Rationale: The amount of milk is 0.9(120) + 30 = 138 grams.
The proportion is 138/150 = 0.92 which is 92%
The answer is D.
Answer: (D) 92.0%
Question: Farm Tax is levied on the 75% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
(A) 15%
(B) 25%
(C) 0.125%
(D) 0.2083%
(E) 16.667%
Rationale: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/75) = 16.667%
The correct answer is (E).
Answer: (E) 16.667%
Question: If (a-7)(b-2) =0, which of the following must be true ?
I. a=7 and b=2
II. if a is not 7, then b=2
III. if a=7, then b is not=2
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: (a-7)(b-2)=0
So either a=7 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Answer: (B) II only
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 100 that is both a prime and a palindrome. What is the sum of the digits of p?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Given that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
C
Answer: (C) 5
Question: A monkey start climbing up a tree 19 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
(A) 15 hrs
(B) 18 hrs
(C) 19 hrs
(D) 17 hrs
(E) 16 hrs
Rationale: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 16hrs it wil be 16ft.
Bt since the height of the tree is 19ft, so if the monkey hops up the tree in the next hr i.e 17th hr then it reaches at the top of the tree.
hence it takes 17 hrs for monkey to reach at the top
ANSWER:D
Answer: (D) 17 hrs
Question: In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?
(A) 70
(B) 66
(C) 68
(D) 69
(E) 72
Rationale: Solution: Member in group * age increased = difference of replacement
Or, 8*1 = new comer - man going out
Or, new comer = 8+60;
Or, new comer = 68 years.
Answer: Option C
Answer: (C) 68
Question: If there are 10 apples and 20 oranges, what is the ratio of apples to oranges?
(A) 10:20
(B) 2:4
(C) 1:2
(D) 4:8
(E) It cannot be determined from the information given
Rationale: A ratio should be reduced to the lowest common denominator.
10:20 means 10x:20x which can be written as 1(10):2(10)...
ANSWER:C
Answer: (C) 1:2
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 60 metres?
(A) 16 seconds
(B) 76 seconds
(C) 10.8 seconds
(D) 12 seconds
(E) 18 seconds
Rationale: Speed of the boat downstream = 15 + 5
= 20 kmph
= 20 * 5/18 = 50/9 m/s
Hence time taken to cover 60 m
= 60*9/50
= 10.8 seconds.
Answer: C
Answer: (C) 10.8 seconds
Question: Find the first term and the common ratio of a G.P whose fourth term is 250 and seventh term is 31,250
(A) 2/5,25
(B) 4,5/2
(C) 1,16
(D) 2,5
(E) 1,5
Rationale: a*r ^3 = 250, a *r ^6 =31,250, r ^3 =31,250/250 = 125
r = 5, a* 125 = 250, a = 2
ANSWER:D
Answer: (D) 2,5
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 13 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 10x/y
(B) 11x/y
(C) 9x/y
(D) 12x/y
(E) 13x/y
Rationale: velocity=distance/time;
since he ran at same rate both d tyms,
y/13=x/t
so t=13x/y
ANSWER:E
Answer: (E) 13x/y
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 5 min
(C) 3 min 4 sec
(D) 4 min 5 sec
(E) Data inadequate
Rationale: Explanation:
S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
ANSWER IS A
Answer: (A) 4 min
Question: Calculate the HCF of 64, 592, 960
(A) 15
(B) 16
(C) 13
(D) 14
(E) 12
Rationale: Explanation:
Lets solve this question by factorization method.
The factors of 64 are: 1, 2, 4, 8, 16, 32, 64
The factors of 592 are: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The factors of 960 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
Then the greatest common factor is 16.
Answer: Option B
Answer: (B) 16
Question: What is the next number in the series?
1,5,9,13...
(A) 19
(B) 17
(C) 24
(D) 25
(E) 28
Rationale: Adding (0,2,4,6,8,10) to the odd numbers
1+0=1
3+2=5
5+4=9
7+6=13
9+8=17
answer B
Answer: (B) 17
Question: A train takes 9 hrs to cover distance with the speed 85kmph. Find distance the train travelled.
(A) 750
(B) 850
(C) 725
(D) 765
(E) 675
Rationale: Length = Speed * time
Length =85kmph * 9 hrs
Length =765km
Ans : (D)
Answer: (D) 765
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?
(A) 16%
(B) 15%
(C) 12%
(D) 22%
(E) 19%
Rationale: S.I. for 3 years = (12005 - 9800) = Rs. 2205
S.I. for 5 years = Rs. 2205/3 * 5 = Rs. 3675.
Principal = (9800 - 3675) = Rs. 6125
Hence, rate = (100 * 3675) / (6125 * 5)
= 12%
Answer: C
Answer: (C) 12%
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 16% if no discount was offered?
(A) 17608
(B) 17606
(C) 17604
(D) 17600
(E) 18560
Rationale: Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 16% if no discount was offered = 16000 * 116/100 = Rs. 18560.Answer: E
Answer: (E) 18560
Question: There is enough provisions for 600 men in an army camp for 25 days. If there were 100 men less, how long will the provision last?
(A) 10days
(B) 50days
(C) 100days
(D) 150days
(E) 200days
Rationale: Exp: We have, M1D1 = M2D2
600*25= 100* D2
D2 = 600*25/100 = 150 days.
Answer: D
Answer: (D) 150days
Question: A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 5 cubic feet. If a large block has twice the width, twice the depth, and the same length of a normal block, what is the volume of cheese in a large block in cubic feet?
(A) 15
(B) 30
(C) 20
(D) 18
(E) 25
Rationale: Volume of cube=lbh=5
New cube l ,b, h are increases of l, 2b,2h
New volume of cube =l*2b*2h=4*lbh
=4*5
=20
Answer: C
Answer: (C) 20
Question: If the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?
(A) 120 cm2
(B) 750 cm2
(C) 216 cm2
(D) 197 cm2
(E) 275 cm2
Rationale: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.
Area of the triangle
= 1/2 * 60 * 25
= 750 cm2
Answer:B
Answer: (B) 750 cm2
Question: The ratio of two quantities is 3 to 4. If each of the quantities is increased 4 and 3 respectively, what is the ratio of these two new quantities?
(A) 3/4
(B) 8/9
(C) 18/19
(D) 23/24
(E) It cannot be determined from the information given
Rationale: 3/4 = 3x/4x
we need to find out (3x+4)/(4x+3) off course we cannot solve this to arrive at any rational number hence E.
Answer: (E) It cannot be determined from the information given
Question: Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1, A2, A3 .. be the areas and P1, P2, P3,…….. be the perimeters of S1, S2, S3,..., respectively, then the ratio (P1 + P2 +P3+ ......) / (A1 + A2 + A3 +.......) equals :-
(A) 2(1+√2)/a
(B) 2(2+√2)/a
(C) 2(2+√2)/a
(D) 2(1+2√2)/a
(E) None of these
Rationale: Explanation :
side of S1= a, perimeter of S1= 4a, area of S1 = a2
side of S2= a/√2 , perimeter of S2= 2√2a , area of S2 = a2/2
side of S3= a/2 , perimeter of S3= 2a , area of S3= a2/4
So, for P1 + P2 + P3 .... we will have a GP as below
4a + 2√2a + 2a + .....
First term =4a, common ratio = 1/√2, Sum = 4a/( 1-1/√2) = 4√2a/(√2 - 1)
For A1 + A2 + A3....we will have another GP
a2 + a2/2 + a2/4 .....
First term = a2 , common ratio = 1/2 , Sum = 2a2.
Hence, the required ratio :-
i.e (P1 + P2 + P3....) / (A1+ A2+A3....).
=> 4√2a / (√2 - 1) / 2a2.
=> 2√2(√2 + 1)/a.
=> 2(2 +√2)/a .
Answer : B
Answer: (B) 2(2+√2)/a
Question: A survey reveals that the average income of a company’s customers is $45,000 per year. If 40 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 30 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
(A)  $27,500
(B)  $35,000
(C)  $37,500
(D)  $42,500
(E)  $50,000
Rationale: let x be the average of 30 customers
30*x + 10* 75000 = 40*45000
solving this we have x= 35000
Answer is B.
Answer: (B)  $35,000
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 780m
(B) 180m
(C) 170m
(D) 140m
(E) 186m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: (B) 180m
Question: In a box, there are 7 red, 3 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
(A) 2/3
(B) 8/21
(C) 3/7
(D) 7/15
(E) 10/21
Rationale: Explanation:
Total number of balls = (7 + 3 + 5) = 15.
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 7.
P(E) = 7/15.
Answer: Option D
Answer: (D) 7/15
Question: The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?
(A) 55
(B) 56
(C) 57
(D) 58
(E) 59
Rationale: 20x + 46 = 21(x – 5)
X=59
ANSWER:E
Answer: (E) 59
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 10 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
(A) 22
(B) 21
(C) 88
(D) 30
(E) 29
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 10) + 6000 (v - 10) <=> 2000v = 60000 <=> v = 30
Answer: D) 30
Answer: (D) 30
Question: A 4-letter code word consists of letters D, E, and G. If the code includes all the three letters, how many such codes are possible?
(A) 72
(B) 48
(C) 36
(D) 24
(E) 18
Rationale: Note that the correct answer to this question is 36, not 72.
D-DEG can be arranged in 4!/2!=12 ways;
E-DEG can be arranged in 4!/2!=12 ways;
G-DEG can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: C.
Answer: (C) 36
Question: 3/4 of 1/2 of 2/5 of 5000 = ?
(A) 392
(B) 229
(C) 753
(D) 750
(E) 540
Rationale: D
750
? = 5000 * (2/5) * (1/2) * (3/4) = 750
Answer: (D) 750
Question: If x+y=3 and x2y3 + y2x3=27, what is the value of xy?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: xy=3
As x+y=3
x2y3+y2x3=27
x2y2(y+x)=27
Substituting x+y
x2y2=9
xy=3
ANSWER:C
Answer: (C) 3
Question: Without stoppages, a train travels certain distance with an average speed of 250 km/h, and with stoppages, it covers the same distance with an average speed of 125 km/h. How many minutes per hour the train stops ?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Due to stoppages, it covers 125 km less .
Time taken to cover 125 km = 125â„250h = 1â„2h
= 1â„2 Ã— 60 min = 30 min
Answer B
Answer: (B) 30
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit?
(A) 10.22%
(B) 20.22%
(C) 21.22%
(D) 42.5%
(E) Can't be calculated
Rationale: The owner buys 100 kg but actually gets 114kg;
The owner sells 100 kg but actually gives 80kg;
Profit: (114-80)/80*100=~42.5%
Answer: D.
Answer: (D) 42.5%
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is?
(A) 10
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x =600
x = 10
The numbers are 3*10 , 4*10 , 5*10
Hence required H.C.F. = 10
Answer is A
Answer: (A) 10
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint E, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2 1/2
(C) 3
(D) 3 1/2
(E) 4
Rationale: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
Answer: (B) 2 1/2
Question: Statement: The authorities in Society X are cracking down on street hawkers, blaming them for traffic jams near their society.
Actions:
I. Street hawkers should not be allowed during peak hours
II. Street hawkers should be warned and asked not to create chaos.
(A) Only I follows
(B) Only II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: Explanation: Here a situation of traffic jam is depicted and the actions mentioned, give different ways for improving the situation.
ANSWER IS B
Answer: (B) Only II follows
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 15 days starting with sunday is
(A) 280
(B) 285
(C) 290
(D) 295
(E) 570
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/15)=(8550/15)=570
Answer: Option E
Answer: (E) 570
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) 33388
(B) 27889
(C) 27889
(D) 59000
(E) 27991
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer:D
Answer: (D) 59000
Question: After working for 4 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
(A) 13 1/3 days
(B) 14 1/3 days
(C) 15 1/3 days
(D) 3 1/3 days
(E) 23 1/3 days
Rationale: 1/3 ---- 4
1 -------? A = 12
R = 1/12 * 60/100 = 1/20
1 ----- 1/20
2/3 ----? => 13 1/3 days
ANSWER:A
Answer: (A) 13 1/3 days
Question: Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
(A) 2:3
(B) 4:3
(C) 6:7
(D) 9:16
(E) 9:7
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
Answer :B
Answer: (B) 4:3
Question: x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be
(A) Between 1 and 10
(B) Between 11 and 15
(C) Between 15 and 20
(D) Between 20 and 25
(E) Greater than 25
Rationale: Factorial 2 +1=3
smallest factor is 3==>this is greater than 2
factorial 3 + 1=7
smallest factor is 7==>this is greater than 3
factorial 4 + 1 = 25
smallest factor is 5==>which is greater than 4
factorial 5 + 1= 121
smallest factor is 11==>which is greater than 5
(note: i am excluding 1 as a smallest factor)
now by seeing this pattern you can figure out that..
(factorial x + 1)==>smallest factor will always be greater than x
now coming to our problem
all even no.s between 2 to 50
2*4*6*8......*48*50
now take 2 from each number common.
2^25(1*2*3*4*5*......25)
or 2^25*factorial 25
now x+1= 2^25*factorial 25 + 1===>clearly smallest factor will be greater than 25(as proved above)
ANSWER:E
Answer: (E) Greater than 25