divelab/Sys2Bench huggingface dataset:
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 30 days more. What is the reinforcement?
Options:
A)1800 men
B)3900 men
C)600 men
D)3800 men
E)900 men
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*30 = 2000*39
x = 2600
2000
-------
600
ANSWER:C
Answer: C
Question: A girl has nine jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?
Options:
A)100
B)102
C)108
D)110
E)112
Rationale: The girl can select one jeans in nine ways.
The girl can select one shirt in 12 ways.
The number of ways in which he can select one jeans and one shirt is 9 * 12 = 108 ways.
C
Answer: C
Question: The L.C.M. of two numbers is 36. The numbers are in the ratio 2 : 3. Then sum of the number is:
Options:
A)28
B)30
C)40
D)53
E)54
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 36 or x = 6.
The numbers are 12 and 18.
Hence, required sum = (12 + 18) = 30.
Answer: Option B
Answer: B
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
Options:
A)9
B)10
C)11
D)14
E)2
Rationale: B
10
This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
Answer: B
Question: The minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is
Options:
A)4 tiles
B)5 tiles
C)6 tiles
D)7 tiles
E)8 tiles
Rationale: LCM of 16,24 = 48
48*48 is the minimum size of square made with 16 by 24 tiles
Number of tiles required = area of square/area of one tile
=48*48/(16*24)
= 6 tiles
ANSWER:C
Answer: C
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of an orange fruit ?
Options:
A)Green
B)BLUE
C)PINK
D)ORANCE
E)BLACK
Rationale: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of an orange fruit is 'Orange' but in coding language, 'Orange' is called 'Blue'.
ANSWER: B
Answer: B
Question: A bag contains 2 yellow balls, 3 white balls and 5 red balls. In how many ways can two balls be drawn from the bag?
Options:
A)2C2
B)10C2
C)8C2
D)5C2
E)6C2
Rationale: Total number of balls= 2+3+5 = 10
2 balls can be drawn from 10 balls in 10C2
ANSWER:B
Answer: B
Question: If a train, travelling at a speed of 160 kmph, crosses a pole in 18 sec, then the length of train is?
Options:
A)800
B)125
C)288
D)266
E)121
Rationale: D = 160 * 5/18 * 18
= 800 m
Answer: A
Answer: A
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 6hrs if the speed of the bike is twice speed of the tractor?
Options:
A)400 km
B)500 km
C)360 km
D)540 km
E)600 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 6 h is
90 × 6 = 540 km
Ans.(D)
Answer: D
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 50 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
Options:
A)150
B)500/3
C)400
D)480
E)600
Rationale: we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 50 then Y = 150
ANSWER:A
Answer: A
Question: What are the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
Options:
A)227
B)814
C)168
D)686
E)218
Rationale: In this type of questions, first we need to calculate the area of tiles. With we can get by obtaining the length of largest tile.
Length of largest tile can be obtained from HCF of length and breadth.
So lets solve this,
Length of largest tile = HCF of (1517 cm and 902 cm)
= 41 cm
Required number of tiles =
Area of floorArea of tile=(1517×90241×41)=814
Answer:B
Answer: B
Question: How much does a watch lose per day, if its hands coincide ever 64 minutes?
Options:
A)32 8/11
B)32 8/19
C)32 8/12
D)32 8/13
E)32 8/17
Rationale: 55min spaces are covered in 60min
60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.
loss in 64min=(65+5/11)- 64 =16/11
Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.
Answer: A) 32 8/11
Answer: A
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Options:
A)22
B)77
C)26
D)20
E)99
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
Answer: D
Answer: D
Question: Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second vessel. In what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of 2:5.
Options:
A)1:5
B)2:5
C)3:5
D)4:5
E)5:5
Rationale: Let 1st vessel contains X liters of mixture of milk and water.
Milk in 1st vessel = 4/13x
Water in 1st vessel=9/13x
Let 2nd vessel contains Y liters of mixture of milk and water
Milk in 2nd vessel = 2/9y
Water in 2nd vessel =7/9y
Let the two mixture combine such that the milk to water ratio is 2:5
4x/13 + 2y/9 / 9x/13 +7/9y =2/5
36x+26y/81x+91y=2/5
180x+130y=162x+182y
18x=52y
x/y=26/9
Hence mixture from vessel 1 and vessel 2 should be mixed in the ratio 26/9 for milk and water to be in ratio 2:5
ANSWER:B
Answer: B
Question: In six successive games, a baseball team scored 2 runs once, 5 runs twice, and 6 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
Options:
A)8
B)7
C)6
D)5
E)4
Rationale: 2 runs once (one game)
5 runs twice (two game)
6 runs three times (three games)
SO we have (2*1 + 5*2 + 6*3)/6 = 30/6 = 5.
ANS: D.
Answer: D
Question: If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true?
I. (x + z)^2 > y
II. yz > x
III. x+y>z
Options:
A)III only
B)II only
C)II,III only
D)I only
E)I,III only
Rationale: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.
III) x+y>z
Not necessarily true as 1+5<7
II) yz>x
Not necessarily true as 5.7<1
I) We don't need to check option as all the options except D can be discarded.
Thus Answer D
Answer: D
Question: A and B started a business with initial investments in the ratio 6 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
Options:
A)6 months
B)8 months
C)21 months
D)5 months
E)7 months
Rationale: Let Sumit in the business for ‘a’ months.
Investment Ratio Amit to Sumith = 6 : 3.
Profit sharing ratio = 8 : 7.
Amit is in the business for 12 months.
Then Sumit in the business for
(6× 12) / (3 × a) = 8 / 7 => 24a = 504 or
a = 504 / 24 = 21 or 21 months
Option C
Answer: C
Question: a little girl went to the farm to buy fruits. she bought 10 apples, 10 oranges and 30 strawberries. what is the ratio of the apples to all the fruits bought?
Options:
A)1/2
B)1/5
C)1/10
D)10/30
E)3/5
Rationale: total # of fruits is 10+10+30=50; ratio of her apples to all the fruits bought is 10/50 = 1/5
ANSWER:B
Answer: B
Question: The average (arithmetic mean) of 24, 35, and 58 is 6 more than the average of 19, 51, and x. What is x?
Options:
A)26
B)27
C)28
D)29
E)30
Rationale: The average of 24, 35, and 58 is 39.
The average of 19, 51 and x is 33.
Then 19 + 51 + x = 99.
x = 29.
The answer is D.
Answer: D
Question: A train traveling at 40 kms / hr while inside the tunnel meets another train of half its length traveling at 60 kms / hr and passes it completely in 4.5 seconds. Find the length of the tunnel if the first train passes completely through it in 4 minutes 37.5 seconds.
Options:
A)2000 meters
B)3000 meters
C)4000 meters
D)5000 meters
E)6000 meters
Rationale: 3000meters
ANSWER:B
Answer: B
Question: A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)240
B)250
C)260
D)230
E)220
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 36
=> 300+L = 15×36 = 540
=> L = 540-300 = 240 meter
Answer is A.
Answer: A
Question: How many times the keys of a writterhave to bepressed in order to write first 400 counting no.'s?
Options:
A)980
B)990
C)1092
D)1100
E)1230
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
C
Answer: C
Question: If j and k are integers, and 2j + k = 15, which of the following must be true?
Options:
A)j + k is odd.
B)j + k is even.
C)j is odd.
D)k is odd.
E)k > j
Rationale: 2j+k=15
even+odd=odd
So k is odd. D is the answer.
Answer: D
Question: Sheik Abdullah decides to buy 4 new cars for his collection. If he has to choose between eight different cars, what is the number of purchasing possibilities he has?
Options:
A)A)7
B)B)11
C)C)14
D)D)18
E)E)21
Rationale: Sheik Abdullah decides to buy 4 new cars for his collection. He has to choose between eight different cars
8C3= 8*7*6/(4*3*2*1) = 14 ANS:C
Answer: C
Question: A man took a loan from a bank at the rate of 11% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
Options:
A)Rs. 16363.64
B)Rs. 10,000.64
C)Rs. 15,000,64
D)Rs. 21,353.64
E)None
Rationale: Solution
Principal = Rs.(100x5400/11x3)= Rs. 16363.64.
Answer A
Answer: A
Question: A certain league has three divisions. The respective divisions had 10, 12 and 15 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Options:
A) 70
B) 72
C) 73
D) 78
E) 80
Rationale: Overall, there can be 73 minuses. Tus, it is C.
Answer: C
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)277
B)299
C)245
D)888
E)291
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer:C
Answer: C
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Options:
A)39
B)23
C)20
D)27
E)26
Rationale: 1/x + 1/(x + 10)
= 1/12
x = 20
Answer:C
Answer: C
Question: A charity collected $3,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
Options:
A)145
B)150
C)155
D)159
E)165
Rationale: Min fund = 20
Total = 3199
The closest multiple of 20 to 3199 is : 159
Which implies 158 people gave 20 and 1 person gave 39
Ans. D
Answer: D
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 17, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
Options:
A)6
B)7
C)9
D)10
E)11
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 17
5x = 15
x = 3.
Hence, B's age = 2x = 6 years.
Answer: Option A
Answer: A
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
Options:
A)21000
B)22882
C)12112
D)27788
E)27712
Rationale: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
Answer: A
Answer: A
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)76
B)87
C)72
D)11
E)26
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: C
Question: What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?
Options:
A)0
B)1
C)5
D)7
E)8
Rationale: 1/3 + 1/9 + 1/27 = 13/27. = .481481…
1/37=.027027…
13/27 + 1/27 = .508508..
Hence 101st digit is 0.(3*33 +2=> hence the second digit of the recurring decimal which is 0)
Answer:A
Answer: A
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 50% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
Options:
A)1 to 4
B)1 to 3
C)3 to 6
D)3 to 4
E)3 to 2
Rationale: Correct Answer: C
Solution: C. We know that when Pam and Stanley were both working, the ratio was 3 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 3 to 6. Answer C is correct.
Answer: C
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 15 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
Options:
A)40.2
B)40.4
C)40.5
D)40.8
E)None of the above
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 15 = 405
Hence, new average = 405⁄10 = 40.5
Answer C
Answer: C
Question: Solve the equation :
A) 7(3x – 6) + 5(x - 3) - 2(x - 7) = 5 ,
B) (x -3)(x + 4) - 2(3x - 2) = (x - 4)2,
C) (x + 1)3 – (x - 1)3 = 6(x2 + x + 1)
Options:
A)3, 8, -2/3
B)2, 8, -2/3
C)4, 8, -2/3
D)5, 8, -2/3
E)None
Rationale: Solution:
A) 21x - 42 + 5x - 15 - 2x + 14 = 5<=>
21x + 5x - 2x = 5 + 42 + 15 - 14<=>
24x = 48 <=> x = 2
B) x2 + 4x - 3x - 12 - 6x + 4 = x2 - 8x + 16 <=>
x2 - 5x – x2 + 8x = 16 + 12 – 4 <=>
3x = 24 <=> x = 8
C) x3 + 3x2 + 3x + 1 – (x3 - 3x2 + 3x - 1) = 6x2 + 6x + 6 <=>
x3 + 3x2 + 3x + 1 – x3 + 3x2 + 1 = 6x2 + 6x + 6 <=>
2 = 6x + 6 <=> 6x = -4 <=> x = -2/3
Answer B
Answer: B
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
Options:
A)31.9
B)31.2
C)31.6
D)71.2
E)31.1
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6'
Answer: C
Answer: C
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 12 times the probability that both events A and B occur. What is the probability that event A occurs?
Options:
A)21/26
B)25/26
C)11/26
D)6/26
E)22/33
Rationale: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 12 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 12*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 12*2b*b
3b-2b^2 = 24b^2
3b = 26b^2
b = 3/26 = 3/26
So, a = 2b = 6/26
THE CORRECT ANSWER IS D.
Answer: D
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
Options:
A)Rs. 50000
B)Rs. 52000
C)Rs. 57000
D)Rs. 60000
E)Rs. 62000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs. 57000
C
Answer: C
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 288. What is their H.C.F.?
Options:
A)18
B)24
C)36
D)42
E)48
Rationale: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 288
x = 24
HCF of 2x, 3x and 4x = x = 24
The answer is B.
Answer: B
Question: The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?
Options:
A)1/64
B)1/9
C)1/16
D)1/25
E)1/2
Rationale: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128
We will add the cases to get 1/64
Answer: A
Question: A rectangular block 10cm by 20cm by 30cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
Options:
A)6
B)10
C)15
D)40
E)22
Rationale: Volume of the block = 10*20*30 = 6000 cm^3
Side of the largest cube = H.C.F of 10,20,30 = 10cm
Volume of the cube = 10*10*10 = 1000 cm^3
Number of cubes = 6000/1000 = 6
Answer is A
Answer: A
Question: There are 8 stores in town that had a total of 24 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 9 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 9 people visited 2 stores each for 18 visits.
To maximize the number of stores that one person visited, let's assume that 2 people visited 1 store each. The number of remaining visits is 24 - 18 - 2 = 4, which is the maximum that one person could have visited.
The answer is C.
Answer: C
Question: Which of the following is closest to (20!-19!)/(20!+19!)?
Options:
A)1.25
B)0.9
C)2.1
D)0.3
E)1.69
Rationale: (20!-19!)/(20!+19!)
19! (20-1)/19! (20+1)
19/21 = 0.9
B is the answer
Answer: B
Question: If we multiply the digits of a number until we get a single digit, then which is the only two digit number which require multiplication of digits more than 3 times?
Options:
A)77
B)67
C)87
D)97
E)57
Rationale: 77 =7*7 =49
49 =4*9 =36
36 =3*6 =18
18 =1*8 =8
ANSWER:A
Answer: A
Question: A departmental store has 5 managers and 25 associates. The 5 managers have an average salary of $1500. The 25 associates have an average salary of $20,000. What is the average salary for the departmental store?
Options:
A)$14,000
B)$12800
C)$15,000
D)$14,500
E)$16,916.66
Rationale: Number of managers is 5
Their average salary is $1500
Number of associates is 25
Their average salary is $20,000
Total salary of managers is 5*1500=$7500
Total salary of associates is 25*20,000=$500,000
Total salary for the departmental store is 500,000+7500=50,7500
Average salary for the departmental store is 50,7500/5+25=16,916.66
Answer is E
Answer: E
Question: A man invests some money partly in 10% stock at 90 and partly in 5% stock at 90.To obtain equal dividends from both,he must invest the money in the ratio :
Options:
A)1 : 2
B)3 : 5
C)4 : 5
D)16 : 15
E)None
Rationale: Solution
For an income of Rs. 1 in 10% stock at 90, investment = Rs. (90/10)= Rs. 9 .
For an income of Rs. 1 in 5% stock at 90, investment = Rs.(90/5) = Rs. 18.
∴ Ratio of investments = 9 :18 =1:2
Answer A
Answer: A
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 50¢?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 50, the ratio should be 1:1.
Mary must put back 4 oranges.
The answer is D.
Answer: D
Question: A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options:
A)1km
B)1.5km
C)5km
D)3.2km
E)2.4km
Rationale: Speed of down stream = 5+1 = 6kmph
speed of upstream = 5-1 = 4kmph
Let the required distance be xkm
x/6 + x/4 = 1
2x+3x = 12
x = 2.4 km
Answer is E
Answer: E
Question: A FAIR AND LOVELY manufacturer produces 100 units of a certain model each month at a cost to the manufacturer of £10 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £10,000?
Options:
A)90
B)60
C)110
D)30
E)34
Rationale: 100(x-10)≥10,000
x-10≥100
x≥110
Answer: Option C
Answer: C
Question: How many integers are between 6 and 74/5, inclusive?
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: 74/5 = 14.xx
We are not concerned about the exact value of 74/5 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 6 and 74/5 would be 6, 7, 8, 9, 10, 11, 12,13,14
Total number of integers = 9
Option E
Answer: E
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Options:
A)7
B)5
C)4
D)2
E)1
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Answer: B
Question: A train 100 m long passed a pole in 20 sec. How long will it take to pass a platform 500 m long?
Options:
A)90 sec
B)100 sec
C)110 sec
D)120 sec
E)130 sec
Rationale: Speed = 100/20 = 5 m/sec.
Required time = (100 + 500)/5 = 120 sec
Answer:D
Answer: D
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: B
2
If the number 1056 is completely divisible by 23 means, remainder should come zero.
But if we divide 1056 by 23, the remainder is 2.
So if 2 is added to the 1056, we get remainder 0.
Therefore solution is 2
Answer: B
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost Z for a course at the gym's highest level?
Options:
A)$175
B)$245
C)$425
D)$675
E)$725
Rationale: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost Z of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Answer: A
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
Options:
A)1230
B)1280
C)1290
D)1340
E)1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: E
Question: 39! is divided by 41. Then what is the remainder?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: A