divelab/Sys2Bench huggingface dataset:
Question: Find the area of a parallelogram with base 12 cm and height 8 cm?
Options:
A)96 cm2
B)104 cm2
C)78 cm2
D)86 cm2
E)76 cm2
Rationale: Area of a parallelogram = base * height = 12 * 8
= 96 cm2
Answer:A
Answer: A
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 25 p coins are there?
Options:
A)20
B)30
C)25
D)50
E)40
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = (25 x/100) + (20 x/100) + (15 x/100)
= 60 x /100
30 = 60 x / 100
x = 50 = 25 p coin
Ans - D
Answer: D
Question: A train 200 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds
Options:
A)12 sec
B)6 sec
C)7 sec
D)8 sec
E)9 sec
Rationale: Explanation:
Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 200/(50/3) = (200 Ã—(3/50)) sec =12 sec
Answer: Option A
Answer: A
Question: In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximately what %of the sp is the profit?
Options:
A)50%
B)70%
C)90%
D)100%
E)140%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
B
Answer: B
Question: If a - b = 5 and a2 + b2 = 29, find the value of ab.
Options:
A)A)2
B)B)12
C)C)15
D)D)18
E)E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 29 - 25 = 4
ab = 2.
Answer: A
Answer: A
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year old child. What is the average age of the family ?
Options:
A)21 years
B)20 years
C)18 years
D)19 years
E)17 years
Rationale: after 5 years the average age of the two will be 28.
now the child is one year old ,
total age = 28*2 + 1 = 57
average age = total age/family members(3)
=> 57/3 = 19
ANSWER:D
Answer: D
Question: If n = 8^8 – 7, what is the units digit of n?
Options:
A)0
B)1
C)2
D)7
E)4
Rationale: 8 ^ 8 - 8 = 8 (8 ^ 7 - 1)
==> 8 (2 ^ 21 - 1)
Last digit of 2 ^ 21 is 2 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit. Now on multiply this with 7, we get unit digit as 7
Answer : D
Answer: D
Question: 9.009/5.005 =
Options:
A)1.08
B)1.4
C)1.8018
D)1.4014
E)1.8
Rationale: 9.009/5.005 = 9009/5005 = 9(1001)/5(1001) = 9/5 = 1.8
The answer is E.
Answer: E
Question: Which of the following describes all values of x for which 36–x^2 >= 0?
Options:
A) x >= 1
B) x <= –1
C) -6 <= x <= 6
D) x <= –1 or x >= 1
E) –1 <= x <= 1
Rationale: 36 - x^2 >=0
means x^2 - 36 <=0
=> (x-6)(x+6) <= 0
=> -6 <= x <= 6
Answer - C
Answer: C
Question: In a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 55%, and the students on the make-up date had an average score of 95%, what was the average score for the entire class?
Options:
A)60%
B)65%
C)67%
D)70%
E)75%
Rationale: 70% of the class scored 55% and 30% of the class scored 95%.
The difference between 55% and 95% is 40%.
The average will be 55% + 0.3(40%) = 67%.
The answer is C.
Answer: C
Question: If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
Options:
A)10
B)15
C)20
D)25
E)None of them
Rationale: Let the required number of days be x.
More men, Less days (indirect proportion)
Less hours per day, More days (indirect proportion)
Men 18 : 15
Hours per day 8: 9 } : :16 : x
(18 x 8 x x)=(15 x 9 x 16)= x=(44 x 15)144 = 15
Hence, required number of days = 15.
Answer is B.
Answer: B
Question: The average of 50 numbers id 44. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
Options:
A)22.35
B)33.25
C)22.25
D)11.35
E)43.75
Rationale: Explanation:
Total of 50 numbers = (50×44)=2200
Total of 48 numbers =(2200-(45+55)]=2100
Required average = 2100/48=43.75
Answer:E
Answer: E
Question: 10% of inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants let the village. The population is then reduced to 4050. Find the original inhabitants
Options:
A)5500
B)6000
C)6500
D)7000
E)8000
Rationale: Explanation:
Let the total number is x,
then,
(100-25)% of (100 - 10)% x = 4050
=> 75% of 90% of x = 4050
=> 75/100 * 90/100 * x = 4050
=> x = (4050*50)/27 = 6000
Answer: Option B
Answer: B
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is?
Options:
A)9
B)11
C)15
D)12
E)20
Rationale: Age of the 15th student = 15*15 - (14*5+16*9) = 225-214 = 11 years
Answer is B
Answer: B
Question: Which of the following is a multiply of 4 number ?
Options:
A)120
B)130
C)45
D)82
E)17
Rationale: Explanation :
120 is a perfect multiply of 4
Answer : Option A
Answer: A
Question: There is a group of persons each of whom can completea piece of work in 16 days, when they are working individually. On the 1st day 1 person works, on the second day another person joins him, on the third day one more person joins them & this process continues till the work is completed. How many days are needed to complete the work?
Options:
A)5 1⁄2 days
B)5 1⁄3 days
C)5 1⁄6 days
D)6 1⁄6 days
E)7 1⁄6 days
Rationale: Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
…
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one.
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.
(Just for your reference, work done in 5 days = 15/16.
Pending work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working and work done = 6/16.
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 1⁄6 days
C
Answer: C
Question: What is the units digit of 6^m(2^7+1), for a positive integer m?
Options:
A)1
B)3
C)4
D)7
E)0
Rationale: Equation can be re-written as
6^m( 2^7 + 1)
=6^m ( 128 + 1)
=6^m (129)
Now, putting m= 0 ; Eqn = 129
putting m= 1 ; Eqn = 129. 6
putting m= 2 ; Eqn = 129 .36
putting m= 3 ; Eqn = 129 .216
We can see that there lies a pattern while multiplying 129 with multiples of 6 , units digit is always going to be 4
ANSWER:C
Answer: C
Question: Bill has a collection of new and used trading cards that he stores in two albums. His first album contains 200 cards, 60% of which are used. If 90% of the cards in his second album are used, and 65% of all of his cards are used, what is the total number of trading cards in Bill’s collection?
Options:
A)290
B)260
C)254
D)240
E)156
Rationale: Let, Total Cards in second collection = B
(60/100)*200 + (90/100)*B = (65/100)*(200+B)
i.e. B = 40
i.e Total cards = 200+B = 240
Answer: OPtion D
Answer: D
Question: Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 20 days.
Options:
A)12 days.
B)17 days.
C)18 days.
D)19 days.
E)20 days.
Rationale: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 20*6/10 = 12 days.
ANSWER:A
Answer: A
Question: 9, 35, 91, 189, 341, ?
Options:
A)502
B)521
C)559
D)611
E)712
Rationale: Explanation :
13 + 23 = 9
23 + 33 = 35
33 + 43 = 91
43 + 53 = 189
53 + 63 = 341
63 + 73 = 559
Answer : Option C
Answer: C
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)21 (1/8)kmph
B)21 (1/3)kmph
C)21 (7/3)kmph
D)27 (1/3)kmph
E)21 (1/8)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph
= 21 (1/3)kmph.
Answer:B
Answer: B
Question: A team of four entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Options:
A)288
B)329
C)168
D)127
E)664
Rationale: Explanation:
4 * 84 =336 - 7 = 329
Answer:B
Answer: B
Question: Product of two natural numbers is 5. Then, the sum of reciprocals of their squares is
Options:
A)290/289
B)26/25
C)290/90
D)290/19
E)None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 5,
as 17 is a prime number, so a = 1, b = 5.
1/a2+1/b2=1/1(2)+1/5(2)
=26/25
Option B
Answer: B
Question: In how many ways can the letters of the word WORDS be arranged in a row so that the vowels appear in alphabetic order?
Options:
A)210
B)120
C)180
D)220
E)160
Rationale: three letters can be arranged in ! ways.
only one combination AEI is required.
5 letters can be arranged in 5! ways.
thus 5!/ 1! * 1 = 120.
B
Answer: B
Question: Raj and Roshan has some money with them in the ratio 5:4 respectively. If Raj has Rs. 45. How much money Raj has more than Roshan?
Options:
A)5
B)9
C)16
D)12
E)18
Rationale: Let the money Roshan has be x then (45/x)=5/4
Upon cross multiplication and solving for x we get x=36
So Raj has Rs. 9 more than Roshan
Answer:B
Answer: B
Question: The average of seven numbers is 20. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)27
B)29
C)31
D)41
E)35
Rationale: The total of seven numbers = 7X20 = 140
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (140 - 99 ) = 41
D
Answer: D
Question: An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $2,395, what was the total number of pairs of contact lenses that she sold?
Options:
A) 11
B) 13
C) 15
D) 17
E) 19
Rationale: (x+5)*150 +x*85=2395
=>x=7
total lens=7+(7+5)= 19
Answer E
Answer: E
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 km/h and the speed of the boat in still water is 14 km/h, what is the distance between A and B?
Options:
A)200 km
B)180 km
C)160 km
D)220 km
E)None of these
Rationale: Speed of boat for downstream = 14 + 4 = 18 km/hr
Speed of boat for upstream = 14 – 4 = 10 km/hr
Distance = x
x / 18 + (x /2)/10 = 19
x = 180 km
Answer: B
Answer: B
Question: With the money I have , I can buy 50 pens or 150 pencils. I kept 10% aside for taxi fare. With the remaining , I purchased 54 pencils and P pens. What is the value of P?
Options:
A)32
B)30
C)27
D)25
E)23
Rationale: Since cost of, 50 pens = 150 pencils, With the cost of 3 pencils I can buy 1 pen. After
putting aside 10% for taxi I was left with 90% of the money , with which I can buy 135
pencils (90% of 150) or 45(90% of 50) pens, I bought 54 pencils and P pens, or I could have
bought ( 54 +3P ) pencils ,
54 +3P =135, 3P = 135-54 =81, P =27
ANSWER:C
Answer: C
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
Options:
A)2992
B)2882
C)1200
D)2999
E)2123
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer: C
Answer: C
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
Options:
A)3 9/16 hrs
B)3 9/19 hrs
C)3 9/17 hrs
D)3 3/17 hrs
E)4 9/17 hrs
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12
= 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer:C
Answer: C
Question: A basket has 7 apples and 5 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
Options:
A)45/99
B)43/99
C)42/99
D)49/99
E)52/99
Rationale: Total fruits = 12Since there must be at least two apples,(7C3 * 5C1)/12C4 + 7C4/12C4 = 42/99.Answer:C
Answer: C
Question: What is the product of all the prime factors of 21?
Options:
A)20
B)21
C)18
D)17
E)16
Rationale: factors : 1,3,7,21
3*7 =21
Answer : B
Answer: B
Question: In the Land of Oz only one or two-letter words are used. The local language has 67 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
Options:
A)65
B)66
C)67
D)131
E)134
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 67 letters is 67;
The number of 2 letter words (XX) that can be made from 67 letters is 67*67, since each X can take 67 values.
Total: 67+67*67.
Similarly:
The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.
The difference is (67+67*67)-(66+66*66)=134.
Answer: E.
Answer: E
Question: Two whales are moving in the same direction at 18 mps and 15 mps. The faster whale crosses the slow whale in 15 seconds. What is the length of the slower whale in meters?
Options:
A)45 m
B)56 m
C)39 m
D)33 m
E)62 m
Rationale: Relative speed = (18 - 15) = 3 mps.
Distance covered in 15 sec = 15 * 3 = 45 m.
The length of the faster train = 45 m.
Answer: A
Answer: A
Question: Little Krish had $200.50. He spent $35.25 on sweets and gave to his two friends $25.20 each. How much money was left?
Options:
A)$220.85
B)$214.85
C)$ 114.85
D)$314.85
E)$104.85
Rationale: Krish spent and gave to his two friends a total of
35.25 + 25.20 + 25.20 = $85.65
Money left
200.50 - 85.65 = $114.85
correct answer is C) $ 114.85
Answer: C
Question: The salary of A, B, C, D, E is Rs. 9000, Rs. 5000, Rs. 11000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
Options:
A)Rs. 7000
B)Rs. 8200
C)Rs. 8500
D)Rs. 9000
E)None
Rationale: Answer
Average salary
= 9000 + 5000 + 11000 + 7000 + 9000 / 5
= Rs. 8200
Correct Option: B
Answer: B
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm
Options:
A)178 cm2
B)179 cm2
C)266 cm2
D)167 cm2
E)197 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (14)
= 266 cm2
Answer: C
Answer: C
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)338
B)77
C)298
D)540
E)882
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: D
Question: In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)14 kmph
B)11 kmph.
C)51 kmph.
D)61 kmph.
E)71 kmph.
Rationale: Speed in still water =1/2(14+8) kmph = 11 kmph.
Answer: B
Answer: B
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
Options:
A)12
B)14
C)15
D)19
E)10
Rationale: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15. Answer:C
Answer: C
Question: Divide 952 to A,B,C IN 37:18:13 RATIO.CALCULATE PART OF A.
Options:
A)518
B)428
C)552
D)526
E)624
Rationale: ADDITION OF RATIO NO. =68
PART OF A=952×37/68=518
ANSWER A
Answer: A
Question: If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number
II. x is an odd number
III. x is a multiple of 5
Options:
A)I only
B)II only
C)III only
D)I and III
E)II and III
Rationale: I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.
Therefore C is the answer.
Answer: C
Question: 9. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is
Options:
A)41
B)42
C)32
D)37
E)39
Rationale: LCM of 3, 5, 7 and 8 = 840
28523 ÷ 840 = 33 remainder = 803
Hence the least number which should be added = 840 - 803 = 37 Answer: Option D
Answer: D
Question: The contents of two vessels containing copper and tin in the ratio 2:3 and 5:7 are mixed in the ratio 3:5. The resulting mixture will have copper and tin in the ratio?
Options:
A)210:283
B)312:433
C)178:213
D)197:283
E)145:256
Rationale: The ratio of copper and tin the new vessel= (2/5*3/8 + 5/12*5/8) : (3/5*3/8 + 7/12*5/8)
= 197/480 : 283/480 = 197:283
Answer is D
Answer: D
Question: Suraj has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13th innings?
Options:
A)48
B)64
C)36
D)72
E)27
Rationale: To improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings.
Thus, the average after the 13th innings
= 96 - 60 = 36.
ANSWER:C
Answer: C
Question: If a+b=−9, and a=30/b, what is the value of a^2+b^2?
Options:
A)31
B)21
C)41
D)61
E)51
Rationale: a^2 + b^2 should make you think of these formulas:
(a+b)(a+b) = a^2+b^2+2ab
We already know (a+b) = -9 and a*b = 30
(a+b)(a+b) = (-9)(-9) = a^2+b^2+2*(30)
a^2+b^2 = 81 - 60 = 21
Answer : B
Answer: B
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case.
Options:
A)627
B)528
C)626
D)657
E)673
Rationale: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
Answer:B
Answer: B
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph.
B)05 kmph.
C)18 kmph.
D)11 kmph.
E)12 kmph.
Rationale: Speed of the boat in still water = (70+80)/2 = 75 kmph. Speed of the stream = (80-70)/2
= 5 kmph.
Answer:B
Answer: B
Question: To create paint with a certain shade of gray, one must combine 2.016 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Options:
A)173.6
B)176.4
C)347.1
D)694.4
E)705.6
Rationale: Since the ratio of Black to White is 2.016 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.016:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer
ANSWER:A
Answer: A
Question: The equation of line s is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line s?
Options:
A)48
B)50
C)60
D)75
E)100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line s as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: C
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2017) = ?
Options:
A)2018
B)2088
C)270
D)1881
E)1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2017) = 2018
Ans: A
Answer: A
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
Options:
A)25600.24
B)25600.29
C)25600.29
D)25600.29
E)25600.29
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer: A
Answer: A
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. In how much time will the trains cross each other?
Options:
A)80/9 sec
B)80/7 sec
C)80/6 sec
D)89/7 sec
E)50/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s
= (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer:B
Answer: B
Question: What sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?
Options:
A)263
B)500
C)367
D)368
E)666.7
Rationale: 70 = (P*3*7/2)/100
P = 666.7
Answer: E
Answer: E
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
Options:
A)20
B)34
C)35
D)46
E)50
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: A
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Options:
A)9000
B)9400
C)9600 is greatest number
D)9670
E)9800
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600. Answer: Option C
Answer: C
Question: How many 4-digit positive integers are there in which all 4 digits are even?
Options:
A)625
B)600
C)500
D)400
E)256
Rationale: Positive integers - 2,4,6,8,0
Let the integers of a four digit positive number be ABCD
A can take four values (2,4,6,8)
B can take five values (0,2,4,6,8)
C can take five values (0,2,4,6,8)
D can take five values (0,2,4,6,8)
The total is 5*5*5*4
The answer according to me is 500
ANSWER:C
Answer: C
Question: The sum of two consecutive integers is 41. Find the numbers.
Options:
A)17, 18
B)7, 8
C)5, 6
D)20,21
E)8, 9
Rationale: n + (n + 1) = 41
2n + 1 = 41
2n = 40
n = 20
Answer: D
Answer: D
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 30 paise per sq. metre
Options:
A)s255
B)s780
C)s880
D)s480
E)s980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*30
= 25500p
in Rs =25500/100=Rs255
ANSWER:A
Answer: A