mathewhe/aqua_rat huggingface dataset:
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers D are possible?
(A) 2
(B) 4
(C) 6
(D) 3
(E) Not possible
Rationale: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total D of 6 possibilities.
C.
Answer: (C) 6
Question: Pat, kate and mark charged a total of 180 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
(A) 18
(B) 36
(C) 72
(D) 90
(E) 100
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 180 -total hours charged for,
x= 20.
Mat charged 6x-x or 5x for more hours than kate, or for 100 hours .
E is correct
Answer: (E) 100
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long?
(A) 266 Sec
(B) 180 Sec
(C) 776 Sec
(D) 166 Sec
(E) 997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1800 m
T = D/S
T = 1800/10
T = 180 Sec
Answer: B
Answer: (B) 180 Sec
Question: A train 210 m in length crosses a telegraph post in 13 seconds. The speed of the train is?
(A) 77 kmph
(B) 55 kmph
(C) 54 kmph
(D) 58 kmph
(E) 76 kmph
Rationale: S = 210/13 * 18/5
= 58 kmph
Answer: D
Answer: (D) 58 kmph
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 30 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
(A)  35
(B)  39
(C)  40
(D)  41
(E)  42
Rationale: 1.30x=45 --> 13/10*x=45 --> x=45*10/13=450/13=~35.
Answer: A.
Answer: (A)  35
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 20/8 sec
(B) 20/4 sec
(C) 20/7 sec
(D) 22/7 sec
(E) 60/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.Answer:C
Answer: (C) 20/7 sec
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 36, what is the total amount?
(A) 166
(B) 140
(C) 178
(D) 177
(E) 169
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 36
35 --- ? => 140
Answer: B
Answer: (B) 140
Question: If there are ten positive real numbers n1 < n2 < n3 … < n10, how many triplets of these numbers (n1, n2, n3), (n2, n3, n4) … can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number?
(A) 45
(B) 90
(C) 120
(D) 180
(E) 150
Rationale: Three numbers can be selected and arranged out of ten numbers in 10P3 ways=10!/7!=10*9*8. Now this arrangement is restricted to a given condition that first number is always less than the second number, and the second number is always less than the third number. Hence three numbers can be arranged among themselves in 3! ways.
Required number of arrangements=(10*9*8)/(3*2)=120
ANS:C
Answer: (C) 120
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 278
(B) 277
(C) 278
(D) 450
(E) 272
Rationale: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
Answer:D
Answer: (D) 450
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire?
(A) 7 meters
(B) 9 meters
(C) 8 meters
(D) 2 meters
(E) 3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 48,000 m : C is the circumference
C = 2 meters
correct answer D
Answer: (D) 2 meters
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
(A) 7 hour 15 minutes
(B) 7 hour 30 minutes
(C) 8 hour 15 minutes
(D) 8 hour 30 minutes
(E) 8 hour 45 minutes
Rationale: Explanation :
Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4
= 8 ¼ hours = 8 hour 15 minutes
Answer : Option C
Answer: (C) 8 hour 15 minutes
Question: When positive integer X is divided by positive integer Y, the remainder is 5.76. If X/Y = 96.12, what is the value of Y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: When positive integer x is divided by positive integer y, the remainder is 5.76 --> x=qy+5.76;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=5.76 --> y=48.
Answer: C.
Answer: (C) 48
Question: The sum of 33 consecutive integers is 3333. What is the greatest integer in the set?
(A) 113
(B) 115
(C) 117
(D) 119
(E) 121
Rationale: Let x be the first integer in the set, then x+32 is the largest integer.
The sum is: x+(x+1)+(x+2)+...+(x+32)
= 33x + 32*33/2
= 33(x+16)
Then x+16=101
x=85
The largest integer in the set is 85+32=117
The answer is C.
Answer: (C) 117
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.3 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 7/17
(B) 13/33
(C) 7/15
(D) 17/35
(E) 1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.3 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 26 hours.
Total hours = 66.
Then the fraction would be 26/66 = 13/33. Therefore answer B
B.
Answer: (B) 13/33
Question: A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
(A) s. 200
(B) s. 100
(C) s. 300
(D) s. 50
(E) s. 90
Rationale: A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 600 and 400.
difference in profit share = 600-400=200
ANSWER:A
Answer: (A) s. 200
Question: A store raised the price of an item by exactly 30 percent. Which of the following could NOT be the resulting price of the item?
(A) 19.5
(B) 195
(C) 325
(D) 168
(E) 18.2
Rationale: If it raised the value by 30% then the resulting price is 1.3 times the original price. So the final answer has to be a multiple of 1.3. Check the answers.
19.5 - Yes
195 - Yes
325 - Yes
168 - No
18.2 - Yes
Answer : D
Answer: (D) 168
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 8% dividend at the end of the year,then how much does he get ?
(A) Rs. 500
(B) Rs. 600
(C) Rs. 960
(D) Rs. 720
(E) None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(8/100x12000) = Rs. 960.
Answer C
Answer: (C) Rs. 960
Question: Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
(A) 0.121
(B) 0.125
(C) 0.122
(D) 0.123
(E) 0.124
Rationale: Ans: For approximation (50.2$ \times $0.49)/199.8 can be taken as
50$ \times $0.5/200 = 25/200 = 1/8 = 0.125
Answer:B
Answer: (B) 0.125
Question: At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number T of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Circular arrangements= (n-1)!
Hence (4!) = 24=T
Answer is C
Answer: (C) 24
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea?
(A) 23.75
(B) 21.6
(C) 20
(D) 19.2
(E) None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+35)/100×16=21.6
Answer B
Answer: (B) 21.6
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 36
(B) 53
(C) 88
(D) 66
(E) 22
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8
= 45 ==> x
= 53 km/hr.
Answer:B
Answer: (B) 53
Question: 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have beenwas full he finds the waste pipe open. He then closes the waste pipe and in another 4mins the cistern was full. In what time can the waste pipe empty the cistern when fill?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B
Answer: (B) 8
Question: An atom's atomic number is determined by the number of:
(A) neutrons minus protons
(B) protons
(C) electrons
(D) neutrons
(E) WW2
Rationale: protons
Answer:B
Answer: (B) protons
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 6
(B) 7
(C) 5
(D) 8
(E) 9
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer: D
Answer: (D) 8
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 11
(B) 5
(C) 70
(D) 11
(E) 13
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
Answer:D
Answer: (D) 11
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 65 cm2
(B) 30 cm2
(C) 76 cm2
(D) 68 cm2
(E) 46 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5
= 30 cm2
Answer: B
Answer: (B) 30 cm2
Question: If x > 0.6, which of the following could be the value of x?
(A) √0.6
(B) √0.007
(C) √0.006
(D) √0.008
(E) √0.009
Rationale: Answer : A
Answer: (A) √0.6
Question: Joseph completes work worth $3.25 in hour and his cost to company per hour is $2.85. Ray completes worth worth of $2.80 in an hour and his cost to company is $2.65 per hour. If Joseph works for 55,000 hours, how many must Ray work so that company makes at least as much in total gross profit as in case of Joseph ?
(A) 7,858
(B) 8,301
(C) 14,667
(D) 63,840
(E) 146,667
Rationale: Joseph : Profit/hour = 3.25-2.85 = 0.4
: No of hours = 55,000
: Gross Profit = 55,000*0.4 = 22,000
Ray : Profit/hour = 0.15
: Gross Profit = 22,000
: No of hours = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)
Answer E
Answer: (E) 146,667
Question: The simple form of the ratio 4/5:8/9 is?
(A) 5:8
(B) 4:9
(C) 5:9
(D) 5:3
(E) 9:10
Rationale: 4/5 : 8/9 = 9:10
Answer: E
Answer: (E) 9:10
Question: If 0.8 of a number is equal to 0.09 of another number, the ratio of the numbers i
(A) 2 : 3
(B) 3 : 4
(C) 9 : 80
(D) 20 : 3
(E) None
Rationale: Sol.
0.8A = 0.09 B â‡” A / B = 0.09 / 0.8 = 9/80 = .
âˆ´ A : B = 9 : 80.
Answer C
Answer: (C) 9 : 80
Question: A, B, and C working alone can finish constructing a house in 6, 8, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
(A) 11:36 am
(B) 11:48 am
(C) 12:05 pm
(D) 12:27 pm
(E) 12:43 pm
Rationale: A completes 1/6 of the job each hour.
B completes 1/8 of the work each hour.
C completes 1/12 of the work each hour.
A completes 1/6 of the work in the first hour.
Working together, A and B complete another 7/24 for a total of 11/24.
Working together, A, B, and C can complete 9/24 of the work each hour.
To complete 13/24, the time required is (13/24) / (9/24) = 13/9 hours.
The work will be completed at 12:00 plus 4*60/9 minutes which is about 12:27 pm.
The answer is D.
Answer: (D) 12:27 pm
Question: Machine A working alone can complete a job in 10 hours. Machine A+B working alone can do the same job in 16 hours. How long will it take machine B working at their respective constant rates to complete the job?
(A) 20/3
(B) 80/3
(C) 50/4
(D) 90/11
(E) 23/7
Rationale: Machines ( A ) ( B ) (A+B)
---Time - 10 - ( - ) -(16)
---Rate 16--- 6 -- 10
--Work 160 --160 -160
A+B = (160/6) = 80/3
B
Answer: (B) 80/3
Question: When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of y customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
(A) (n - 1) y
(B) n + y –1
(C) (n-1)/y
(D) y/(n-1)
(E) n/(y-1)
Rationale: C. (n - 1) / y
Answer: (C) (n-1)/y
Question: If D is the product of all positive integers less than 31, than what is the greatest integer k for which D/18^k is an integer?
(A) 3
(B) 6
(C) 7
(D) 14
(E) 26
Rationale: 30! D must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.
Answer: (C) 7
Question: What is the sum of the greatest common factor and the lowest common multiple of 45 and 125?
(A) 1920
(B) 2201
(C) 3240
(D) 1130
(E) 3840
Rationale: Prime factorization of the given numbers
45= 3^2
125= 5^3
Greatest common factor =5
Lowest common multiple = 3^2*5^2 *5 =1125
Sum = 5+ 1125 = 1130
Answer D
Answer: (D) 1130
Question: Two concentric circles form a ring. The inner and outer circumference of the ring are 352/7 m and 528/7m respectively.Find the width of the ring.
(A) 2
(B) 4
(C) 5
(D) 6
(E) 78
Rationale: Explanation:
let the inner and outer radii be r and R meters
then, \inline {\color{Black}2\prod r} = 352/7
=> r = (352/7) * (7/22) * (1/2) = 8m
\inline {\color{Black}2\prod R} = 528/7
=> R= (528/7) * (7/22) * (1/2)= 12m
width of the ring = R-r = 12-8 = 4m
Answer: B) 4
Answer: (B) 4
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 30 m
(B) 60 m
(C) 65 m
(D) 70 m
(E) 90 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: The present ages of A,B and C are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. What are their present ages (in years)?
(A) 20, 25 and 35
(B) 21, 18 and 36
(C) 18, 21 and 34
(D) 12, 14 and 18
(E) 16, 28 and 36
Rationale: Sum of their present ages =56+3×8=80
Present age of A =80×420=16
Present age of B =80×720=28
Present age of C =80×920=36
Answer is E.
Answer: (E) 16, 28 and 36
Question: If n is the smallest positive integer for which 2^n is a factor of 10!, then n =?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 10! = 3628800
A. 2^2 = 4 (3628800/4) - this is a factor of 10!
A is answer
Answer: (A) 2
Question: A company has 540 employees, 40% of whom are employed part time. If it hires 30 new employees, 20% of whom are employed part time, what will be the percent increase in part time employees?
(A) 2 7/9 %
(B) 2 2/3 %
(C) 4 %
(D) 4 1/6 %
(E) 9 %
Rationale: Total employee = 540
Part time Empl = 540 * 40/100 =216
New part time empl = 30 * (20/100)
= 6
Total new part time Emp = 6+216= 222
Old part time Emp = 216
% increase = (new - old)*100/old
=6*100/216
= 2.777%
Ans-A
Answer: (A) 2 7/9 %
Question: Convert the 13/48 m/s into kilometers per hour?
(A) 1.5 kmph.
(B) 0.91 kmph.
(C) 1.2 kmph.
(D) 1.5 kmph.
(E) 0.98 kmph.
Rationale: 13/48 m/s = 13/48 * 18/5 = 49/50 = 0.98 kmph.
ANSWER:E
Answer: (E) 0.98 kmph.
Question: A train 150 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 13 km/hr
(B) 59 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) 12 km/hr
Rationale: Speed of the train relative to man = (150/10) m/sec
= (15) m/sec. [15) * (18/5)] km/hr
= 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 54 ==> x
= 59 km/hr.
Answer:B
Answer: (B) 59 km/hr
Question: Jimâ€™s Taxi Service charges an initial fee of $2.35 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
(A) $3.15
(B) $4.45
(C) $4.80
(D) $5.50
(E) $5.40
Rationale: Let the fixed charge of Jimâ€™s Taxi Service = 2.35 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.35 + (3.6/.4) * .35
= 2.35 + 9*.35
= 5.5 $
Answer D
Answer: (D) $5.50
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
(A) 277
(B) 665
(C) 662
(D) 552
(E) 281
Rationale: 8 * 84 = 672 – 7 = 665
Answer:B
Answer: (B) 665
Question: The first three terms of a proportion are 5, 15 and 20. The fourth term is?
(A) 60
(B) 65
(C) 89
(D) 78
(E) 88
Rationale: (15*20)/5= 60
Answer:A
Answer: (A) 60
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 44 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 4 hours, how many machines of type R were used?
(A) 56/21
(B) 59/16
(C) 44/21
(D) 55/16
(E) 12/59
Rationale: Rate of machine R =1/44
Rate of machine S =1/20
since same no of machines used for R and S to do the same work in 4 hrs
So collective rate needed to finish the work in 4 hrs= 1/4
Let the no of machine be x
So, x/44 +x/20 =1/4
(5x+11x)/220=1/4
16x=55
x=55/16
So no of machine R is 55/16
Answer D
Answer: (D) 55/16
Question: If the remainder is 7 when positive integer n is divided by 10, what is the remainder when n is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 2
Rationale: Assume x is quotient here,
n=10x+7 ----------(1)
and n=5x+ ?
We can also write equation (1) as:
n=(10x+5)+2.
ie 5(2x+1)+1 ie the first term is perfectly divisible by 5.
So,the remainder left is 2
So,answer (E) is right choice.
Answer: (E) 2
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 180 pounds. What is Leo's current weight?
(A) 80
(B) 86
(C) 92
(D) 98
(E) 104
Rationale: L+K = 180 and so K = 180-L
L+10 = 1.5K = 1.5(180-L)
2.5L = 260
L = 104
The answer is E.
Answer: (E) 104
Question: If a boy travels with 5/6th of usual his speed,he is late by 10 mins.What is the usual time taken to travel?
(A) 44min
(B) 46min
(C) 48min
(D) 50min
(E) 52min
Rationale: speed=5/6*x
time=6/5t becz speed inversely proportional to time
6t/5-t=10
t=50min
ANSWER:D
Answer: (D) 50min
Question: Sum of the squares of 3 no. is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 21
(C) 25
(D) 26
(E) 27
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: A trader marked the price of his commodity so as to include a profit of 25%. He allowed discount of 16% on the marked price. His actual profit was :
(A) 4
(B) 5
(C) 10
(D) 12
(E) None
Rationale: Sol.
Let C.P. be Rs. 100. Then, marked price = Rs. 125.
S.P. = 84% of Rs. 125 = Rs. [84 /100 * 125] = Rs. 105.
∴ Profit% = (105 - 100)% = 5%.
Answer B
Answer: (B) 5
Question: In a store, the total price for 20 shirts is $360 and the total price for 45 sweaters is $900. By how much does the average (arithmetic mean) price of a sweater exceed that of a shirt in this store?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: The average price of a shirt is: $360 / 20 = $18.
The average price of a sweater is: $900 / 45 = $20.
The difference in price is: $20 - $18 = $2.
The answer is B.
Answer: (B) $2
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes Q of the competition are possible?
(A) 18
(B) 20
(C) 54
(D) 84
(E) 120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total Q=84 outcomes
D
Answer: (D) 84
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 20 days to complete the same work. then Q alone can do it in
(A) 20
(B) 22
(C) 25
(D) 27
(E) 40
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/20
Work done by P, Q and R in 1 day = 1/10 + 1/20 = 3/20
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 3/20
=> Work done by P in 1 day = 3/40
=> Work done by Q and R in 1 day = 3/40
Hence work done by Q in 1 day = 3/40 â€“ 1/20 = 1/40
So Q alone can do the work in 40 days
Answer is E.
Answer: (E) 40
Question: January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
(A) sunday
(B) friday
(C) monday
(D) wednesday
(E) thursday
Rationale: The year 2008 is a leap year. So, it has 2 odd days.
1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.
Answer: E) thursday
Answer: (E) thursday
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
(A) 277
(B) 960
(C) 277
(D) 266
(E) 121
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
Answer: B
Answer: (B) 960
Question: Find the odd man out.
1, 5, 2, 3, 6, 11, 13
(A) 6
(B) 5
(C) 1
(D) 13
(E) 11
Rationale: Explanation:
Each of the numbers except 6 is a prime number.
Answer: A) 6
Answer: (A) 6