divelab/Sys2Bench huggingface dataset:
Question: The banker's discount on a sum of money for 1 1/2 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
Options:
A)10%
B)13%
C)12%
D)15%
E)11%
Rationale: B.D. for 3/2 years	= Rs. 558.
B.D. for 2 years
= Rs.(558 x 2/3 x 2)
= Rs. 744
T.D. for 2 years = Rs. 600.
Therefore, Sum = B.D. x T.D./B.D. - T.D
= Rs. (744 x 600/144	)= Rs. 3100.
Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.
Therefore, Rate =(100 x 744/3100 x 2)%
= 12%
Answer is C
Answer: C
Question: If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?
Options:
A)90
B)100
C)110
D)120
E)130
Rationale: The projectiles travel a total of 999 km per hour.
The time to meet is 1998/999=2 hours = 120 minutes
The answer is D.
Answer: D
Question: A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 35 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
Options:
A)525.
B)412.
C)432.
D)502.
E)522.
Rationale: Pastry is divided in 35 customers equally. So,total number of pastry must be a multiple of 35
Only option A satisfies the condition, and hence is the answer
Answer: A
Question: Worker A takes 8 hours to do a job. Worker B takes 6 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)20/9
B)40/9
C)50/9
D)24/7
E)80/9
Rationale: one day work of A = 1/8
one day work of B = 1/6
so one day work of A and B together = 1/8 + 1/6 = 7/24
so total days required = 24/7
ANSWER:D
Answer: D
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 10000
B)Rs. 5896
C)Rs. 2580
D)Rs. 3697
E)Rs. 60000
Rationale: Explanation:
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
1/3x=1/2(150000-x)
x/3+x/2=75000
x=75000*6/5=90000
Savings in Public Provident Fund = Rs.(150000-90000)=Rs. 60000
Answer:E
Answer: E
Question: If the average (arithmetic mean) of (2a+16) and (3a-8) is 84, what is the value of a?
Options:
A)25
B)30
C)28
D)32
E)42
Rationale: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 84
a= 32
The answer is D.
Answer: D
Question: Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Options:
A)20*(sqr2 -1)
B)8*(sqr3 -1)
C)4*(sqr7 - 1)
D)12* (sqr7 -1)
E)None of these
Rationale: I got 20/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer A
Answer: A
Question: If k^3 is divisible by 120, what is the least possible value of integer k?
Options:
A)12
B)30
C)60
D)90
E)120
Rationale: 120 = 2^3*3*5
Therefore k must include at least 2 * 3 * 5 = 30.
The answer is B.
Answer: B
Question: x is the product of each integer from 1 to 25, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
Options:
A)5
B)4
C)3
D)6
E)7
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*25 = 25!
No. of trailing zeros in 25! = 25/5 + 25/5^2 = 6
100^k = 10^2k → k = 6/2 = 3
C
Answer: C
Question: If n is a positive integer, which of the following expressions must be even?
Options:
A)(n − 1)( n + 1)
B)(n − 4)( n + 1)
C)(n − 2)( n + 6)
D)(n − 5)( n + 1)
E)(n − 3)( n + 3)
Rationale: Whether n is even or odd, (n-4)(n+1) will have one odd factor and one even factor.
The product will be even.
The answer is B.
Answer: B
Question: 30 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 3:4?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: Let x be the amount of liquid Q to be added.
(2/5)*30 + x = (4/7)*(30+x)
420 + 35x = 600 + 20x
15x = 180
x = 12
The answer is C.
Answer: C
Question: The speed at which a man can row a boat in still water is 21 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 90 metres?
Options:
A)23.46
B)27.46
C)28.46
D)12.46
E)25.46
Rationale: Speed of the boat downstream = 21 + 5 = 26 kmph= 26 * 5/18 = 7.22 m/sHence time taken to cover 90 m = 90/7.22= 12.46 seconds.Answer:D
Answer: D
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.28 at the candy store. What is John’s weekly allowance?
Options:
A)$2.40
B)$3.00
C)$3.20
D)$3.60
E)$4.80
Rationale: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$1.28
Therefore, X=$4.80. Answer E
Answer: E
Question: The simple interest at z% for z years will be $z on a sum of
Options:
A)$ (1000)/z
B)$(100)z^2
C)$ z
D)$ (100)/z
E)$ 100z
Rationale: Principal =$(100*z)/(z*z)=$(100/z).
Answer is D
Answer: D
Question: The ratio of two quantities is 3 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?
Options:
A)It cannot be determined from the information given.
B)5/9
C)12/13
D)15/14
E)16/14
Rationale: let the actual ratio be 3k/5k, increase numerator and denominator by 6 => 3k+6/5k+6
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 6 => 9/10
let the actual be 6/8. After increasing 6 => 12/14
Therefore without actual quantities we cannot determine the actual ratio.
Answer : A
Answer: A
Question: A box contains 4 red chips and 4 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
Options:
A)1/2
B)4/7
C)7/12
D)2/3
E)7/10
Rationale: Total selection ways: 8C2=8!/4!4!=28
Selecting one blue chip out of two: 4C1=4!/1!3!=4
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (4C1*4C1)/8C2=(4*4)/28=16/28=4/7=B
Answer: B
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2?
Options:
A)12.6.
B)14.4.
C)15.8.
D)16.2.
E)16.4.
Rationale: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2
= 6*0 + 2*7.2 + 8 - 6.2
= 0 +14.4 +1.8
16.2
Answer D
Answer: D
Question: the price of a commodity(in rupees per kilogram) is 100+0.1n, on the nthvday of 2007(n=1,2,,,,,100), and then remains constant. On the other hand, the price of another commodity is 89+0.15n on the nth day of 2007(n=1,2,,,,,,365). On which date in 2007, will the price of these twocommodities be equal????
Options:
A)11th may
B)12th may
C)20th may
D)22th may
E)24th may
Rationale: price of both the commodity cannot be same within 100days( by puttng n=100 in both the price)
price of 1st commodity after 100 days =100+0.1*100= 110
day on which 2nd commodity becomes equal to 1st= 89+0.15n=110
n=140
140th day of 2007 is 20th may
ANSWER:C
Answer: C
Question: At 3.40, the hour hand and the minute hand of a clock form an angle of
Options:
A)120°
B)125°
C)130°
D)135°
E)None
Rationale: Solution
Angle traced by hour hand in 17/2 hrs	= (360/12x17/2 )°
= 255.
Angle traced by min hand in 30 min	= (360/60x30)°
= 180.
Required angle	= (255 - 180)°
=75°
Answer B
Answer: B
Question: The average age of 15 students of a class is 14 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
Options:
A)3years
B)4years
C)5years
D)6years
E)7years
Rationale: Age of the 15th student
=[15 * 14 - (14 * 5 + 16 * 9)]
= (210 - 214) = 4 years.
Answer:B
Answer: B
Question: A train is 320 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)11 seconds
B)38 seconds
C)40 seconds
D)88 seconds
E)36.8 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 320+140 = 460 meter
Time = Distance/speed
= 460 * (2/25) = 36.8 seconds
Answer: E
Answer: E
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. Tee age of the 15th student is?
Options:
A)11 years
B)16 years
C)33 years
D)14 years
E)18 years
Rationale: Age of the 15th student
=[15 * 15 - (14 * 5 + 16 * 9)]
= (225 - 214) = 11 years.
Answer:A
Answer: A
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Options:
A)3 : 1
B)1 : 3
C)1 : 2
D)2 : 1
E)None of these
Rationale: Explanation :
Let speed upstream = x
Then, speed downstream = 2x
Speed in still water = (2x + x)/2 = 3x/2
Speed of the stream = (2x − x)/2 = x/2
Speed in still water : Speed of the stream = (3x/2) (2x/2) = 3 : 1. Answer : Option A
Answer: A
Question: Two numbers are in the ratio of 1 : 2. If 6 be added to both, their ratio changes to 3 : 5. The greater number is
Options:
A)20
B)24
C)28
D)32
E)36
Rationale: Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 6)/(Y + 6) = 3/5
=> X = 12
And Y = 24
ANSWER:B
Answer: B
Question: On flipping 3 coins together what is the outcomes for at least two tail?
Options:
A)1/7
B)3/8
C)3/11
D)4/13
E)5/13
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two heads
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {TTH, HTT, TTT}
3/8
B
Answer: B
Question: If x is 20 percent more than y and y is 60 percent less than z, then x is what percent of z?
Options:
A)500%
B)48%
C)500/3%
D)125%
E)60%
Rationale: Z = 100 ; Y = 40 so X = 48
X as % of Z = 48/100 * 100 => 48%
Answer will be (B)
Answer: B
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
Options:
A)500
B)277
C)222
D)297
E)111
Rationale: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer:A
Answer: A
Question: A ladder 18 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 6 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
Options:
A)12.5
B)15
C)18
D)19
E)25
Rationale: 18^2-6^2=288
it means that the height is equal to 16.9.
since the top of the ladder slips down 4 feet, then the height of the wall =16.9-4=12.9
the bottom =sqrt(18^2-12.9^2)=sqrt(324-166.41)=12.5
ans is A
Answer: A
Question: For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal?
Options:
A) 4%
B) 5%
C) 8%
D) 10%
E) 12%
Rationale: Expected minimum rating = 8
Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 1 + 0 - 1)/10 = -4/10 = -0.4
Current rating is 0.4 less than 8.
Percentage = (0.4/8)*100 = 5%
Answer: B
Answer: B
Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person ?
Options:
A)75 kg
B)95 kg
C)45 kg
D)85 kg
E)25 kg
Rationale: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (75 + 20) kg = 95 kg.
Answer: B
Answer: B
Question: The value of x is to be randomly selected from the integers from 1 to 11, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
Options:
A)5/11
B)4/11
C)3/11
D)2/11
E)1/11
Rationale: y will only be negative for x=2.
(We can check the values from 1 to 11 to be certain.)
P(y is negative) = 1/11
The answer is E.
Answer: E
Question: A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)287m
B)278m
C)400m
D)228m
E)282m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42
= 50/3
3(x + 300)
= 2100 è x
= 400m.
Answer:C
Answer: C
Question: Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to
Options:
A)40
B)80
C)95
D)100
E)120
Rationale: Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively.
Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.
C
Answer: C
Question: One night 40 percent of the female officers on a police force were on duty. If 240 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
Options:
A)90
B)300
C)270
D)500
E)1,000
Rationale: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 240
Number of female officers on duty on that night = 240/2 = 120
(40/100)*F = 120
=>F = 300
Answer B
Answer: B
Question: If 4/a + 5/a + 6/a is an integer, which of the following must also be an integer?
Options:
A)12/a
B)3/a
C)6/a
D)9/a
E)15/a
Rationale: 4/a + 5/a + 6/a
=15/a
Answer E
Answer: E
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)70%
B)20%
C)60%
D)10%
E)80%
Rationale: Explanation:
900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: B
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Options:
A)48
B)12
C)75
D)28
E)91
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.
Option C
Answer: C
Question: If m and n are positive integers, and m=2n and k=9m, then -
Options:
A)k is a factor of m.
B)2m is a factor of k.
C)3m is a factor of k/2.
D)m/2 is a factor of k.
E)k is a factor of m/2.
Rationale: m=2n --> m is even.
k=9m --> m is factor of k, thus m/2 = integer must also be a factor of k.
Answer: D.
Answer: D
Question: The average age of 40 students is 8 years. If the age of teacher is also included , then their average age increases by half a year. What is the age of the teacher?
Options:
A)45 years
B)48.5 years
C)28.5 years
D)26.5 years
E)27.5 years
Rationale: Total age of 40 students = 40*8 = 320
Let the age of the the teacher be x, Then (320+x)/41 = 8+1/2 =8 ½.
320+x =17/2*41 =697/2 = 348.5,
x =348.5-320 = 28.5
ANSWER:C
Answer: C
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 11 members?
Options:
A)110
B)121
C)132
D)144
E)169
Rationale: There are 11 choices for the Chief Minister.
Then there are 10 choices for the Vice Minister.
The total number of ways is 11*10 = 110.
The answer is A.
Answer: A
Question: Two cars namely A and B start simultaneously from a certain place at the speed of 40 kmph and 55 kmph, respectively.The car B reaches the destination 2 hours earlier than A. What is the distance between the starting point and destination?
Options:
A)8 hours 12 minutes
B)6 hours 15 minutes
C)7 hours 20 minutes
D)7 hours 12 minutes
E)None
Rationale: Explanation :
Let the time taken by car A to reach destination is T hours
So, the time taken by car B to reach destination is (T – 2) hours.
S1T1 = S2T2
=> 40(T) = 55 (T – 2)
=> 40T = 55T -110
=> 15T = 110
T = 7 hours 20 minutes
Answer – C
Answer: C
Question: The length of a train and that of a platform are equal. If with a speed of 36 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)299
B)300
C)299
D)750
E)261
Rationale: Speed = [36 * 5/18] m/sec = 10 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 10 => x = 10 * 60 / 2 = 300
Answer: B
Answer: B
Question: When 22 is divided by the positive integer k, the remainder is 2, for how many different values of k is this true?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: When 22 is divided by k, remainder is 2 i.e. there are 2 balls leftover after grouping. so k must be greater than 2.
It also means that 20 is completely divisible by k.
Factors of 20 are 1, 2, 4, 5, 10, 20
Out of these, k can be 4, 5, 10 and 20.
Answer (D)
Answer: D
Question: 7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country.
Options:
A)200
B)300
C)400
D)500
E)600
Rationale: Let x be the total grown quantity of wheat. According to the question
(7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = — 400 million tonnes rice grown
C
Answer: C
Question: In a sequence, each term is obtained by adding 2 to the preceding one. If the sum of the first 20 terms is equal to 140, what is the result of the addition of the first 40 terms?
Options:
A)1020
B)1080
C)1160
D)1240
E)1280
Rationale: a is first term and d = 2 since the preceding number is always greater than the previous one..
Now 20th term is a+19(2).
Sum of n terms is n/2(first term + last term)and here we have to get sum of 20 terms , we get 20/2 ( a + a+38) = 140 ( given sum of 20 terms is 140)
=> 10(2a+38) = 140
=> 2a+38 = 14
=> a = -12
Now to get sum of first 40 terms , we need to get 40th term value i.e. -12+39(2) = 66.
Sum of first 40 terms = 40/2( -12 + 66) = 1080.
Hence option B is correct answer..
Answer: B
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,75,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)80000
B)60000
C)50000
D)70000
E)90000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (175000 - x) respectively. Then,
=1/3 x = 1/2 (175000 - x)
=x/3 + x/2 = 87500
=5x/6 = 87500
=x = 87500 x 6 /5	= 105000
Savings in Public Provident Fund = Rs. (175000 - 105000) = Rs. 70000
Answer is D.
Answer: D
Question: Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 30% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
Options:
A)$20
B)$40
C)$50
D)$70
E)$100
Rationale: Deargoodyear2013,
I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.
Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.
They had this same selling price, $100, before they made the change, and had a profit of 30%, so the manufacturing must have been $70. Answer = (D).
Answer: D
Question: A class has 6 boys and x girls. Average score of boys and girls is 50 and 60 respectively. the average of the whole class is 55, what is the value of x?
Options:
A)5
B)6
C)10
D)12
E)15
Rationale: After you have got : 6(50)+60x/6+x=55
6*50 + 60x = 6*55 + 55x
x=6
Answer is B
Answer: B
Question: If 2x^2 + y^2 = 2xy, then (x - y)^2 =
Options:
A)-x^2
B)3x^2
C)4xy
D)2y^2
E)– y^2
Rationale: (x-y)^2 = x^2 + y^2 - 2xy = x^2 + y^2-2x^2-y^2 = -x^2
Correct option : A
Answer: A
Question: Find the least square number which is exactly divisible by 10,12,15 and 18.
Options:
A)900
B)120
C)103
D)104
E)217
Rationale: L.C.M. of 10, 12, 15, 18 = 180. Now, 180 = 2 * 2 * 3 * 3 *5 = 22 * 32 * 5.
To make it a perfect square, it must be multiplied by 5.
Required number = (22 * 32 * 52) = 900.
ANSWER A 900
Answer: A
Question: George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 15% of the money for taxi fare and buys 15 mangoes. How many oranges can he buy?
Options:
A)25
B)17.5
C)20
D)16
E)12
Rationale: Let the amount of money be 200
Let cost of 1 Orange be 4
Let cost of 1 mango be 5
He decides to retain 15% of 200 = 30 for taxi fare, so he is left with 170
He buys 20 mangoes ( @ 5) so he spends 100
Money left is 70 (170 - 100)
No of oranges he can buy = 70/4 =>17,5
So, George can buy 15 Oranges.
B
Answer: B
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 20% profit?
Options:
A)277
B)960
C)277
D)266
E)768
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 120% of Rs. 640 = 120/100 * 640 = Rs. 768.
Answer: E
Answer: E
Question: In the interior of a forest, a certain number of apes equal to the square of one-fourth of the total number are playing and having great fun. The remaining four apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
Options:
A)48
B)8
C)64
D)80
E)16 or 48
Rationale: Let total number be x
No in the interior = (x/4)^2
No outside = 4
So : x - (x/4)^2=4
x^2-16x+64=0
(x-8)^2=0
So x=8
B
Answer: B
Question: Area of a square is 1/2 hectare. The diagonal of the square is?
Options:
A)250 meter
B)100 meter
C)50√ 2 meter
D)50 meter
E)35 meter
Rationale: Area = 1/2 hectare = 10000 / 2 m2
= 5000 m2
Again Area = 1/2 x (Diagonal)2
So 1/2 x (Diagonal)2 = 5000m2
Diagonal2= 10000
Diagonal = 100
Answer : B
Answer: B
Question: A box contains 9 apples, 8 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: P(choosing a red apple 5 times in a row) = 8/9*7/8*6/7*5/6*4/5 = 4/9 < 0.5
The answer is C.
Answer: C
Question: How much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
Options:
A)40 sec
B)50 sec
C)60 sec
D)70 sec
E)80 sec
Rationale: The distance to be covered = Sum of their lengths = 400 + 300 = 700 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 700/10 = 70 sec.
ANSWER:D
Answer: D
Question: If k is a non-negative integer and 21^k is a divisor of 435,961 then 7^k - k^7 =
Options:
A)0
B)1
C)42
D)118
E)242
Rationale: 4+3+5+9+6+1 = 28, so this number is not divisible by 3 and thus not divisible by 21.
Therefore, k=0
7^k - k^7 =1-0=1
The answer is B.
Answer: B
Question: The Simplastic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
Options:
A)9
B)12
C)36
D)72
E)108
Rationale: The nouns havefixed structureC-V-C-V-C. Now,each Ccan take 3 values (let's say X, Y or Z) andeach Vcan take 2 values (let's say A or E), so there will be 3*2*3*2*3=108 nouns possible.
Answer: E.
It's basically the same if it were how many different 5-digit numbers are possible with the following structure odd-even-odd-even-odd, where odd numbers can be only 1, 3 or 5 and even numbers only 2 and 4.
It's natural to think that a noun can have for example two same vowels (X-A-Y-A-Z) or 3 same consonants (X-A-X-A-X), so if this was not the case then this would be explicitly mentioned.answer is E
Answer: E
Question: What distance will be covered by a city bus moving at 72 kmph in 30 seconds?
Options:
A)200 m
B)300 m
C)600 m
D)500 m
E)400 m
Rationale: 72 kmph = 72 * 5/18 = 20 mps
Dist = Speed * time = 20 * 30 = 600 m.
ANSWER C
Answer: C