divelab/Sys2Bench huggingface dataset:
Question: A fill pipe can fill 1/2 of cistern in 35 minutes. In how many minutes, it can fill 1/2 of the cistern?
Options:
A)20 min
B)25 min
C)30 min
D)35 min
E)40 min
Rationale: Required time = 35*2*1/2 = 20 minutes
Answer is D
Answer: D
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.645 in all. Find the share of B?
Options:
A)134
B)120
C)218
D)140
E)145
Rationale: A+B+C = 645
A = 3B
3B+B+B-25 = 645
5B = 670
B = 134
Answer: A
Answer: A
Question: Kelly invested Rs. 1850 at 82 to obtain an income of Rs. 172, calculate the dividend from his stock.
Options:
A)4.6
B)7.6
C)6.6
D)3.6
E)5.6
Rationale: By investing Rs.1850, income = Rs.172
By investing Rs.82, income = 172Ã—82/1850=7.6
ie, dividend = 7.6%
Answer is B.
Answer: B
Question: If the simple interest on a sum of money for 6 years at 12% per annum is Rs. 700, what is the compound interest on the same sum at the rate and for the same time?
Options:
A)746.77
B)945.77
C)946.77
D)246.77
E)926.77
Rationale: Sum = (700 * 100) / (6 * 12) = Rs. 972.22
C.I. on Rs. Rs. 972.22 for 6 years at 12% = Rs. 1,918.99.
= Rs. 1,918.99 - 972.22 = Rs. 946.77
ANSWER:C
Answer: C
Question: What is the angle between the two hands at 8.20 O'clock?
Options:
A)150 degree
B)120 degree
C)130 degree
D)250 degree
E)320 degree
Rationale: angle=|11/2(min)-30(hrs)|
=|11/2(20)-30(8)|
=|110-240|
=130 deg
ANSWER:C
Answer: C
Question: The fourth proportional to 12, 14 and 12 is?
Options:
A)14
B)66
C)77
D)88
E)99
Rationale: (14*12)/12 = 14
Answer: A
Answer: A
Question: The speed of a boat in still water is 24 kmph. What is the speed of the stream if the boat can cover 64 km downstream or 32 km upstream in the same time?
Options:
A)8 kmph
B)6 kmph
C)7 kmph
D)5 kmph
E)4 kmph
Rationale: X = the speed of the stream
(24 + X) / (24 - X) = 2/1
24+ X = 48 - 2X
3X = 24
X = 8 km/hour
If the speed of the stream is 8km/hour, then the 'downstream' speed of the boat is 24+8 = 32km/hour and the 'upstream' speed of the boat is 24-8 = 16km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x32 = 64km downstream and 2x16 = 32km/hour upstream.
Answer : A
Answer: A
Question: What is the 10th term in this sequence?
3,5,8,15,25,40,67,104,171
Options:
A)273
B)278
C)279
D)377
E)277
Rationale: 3+5 =8 +0 =8
8+5 =13+2 =15
15+8 =23+2 =25
25+15=40+0 =40
40+25=65+2 =67
67+35=102+2 =104
104+67=171+0=171
171+104=275+2=277
so 9th term is 277
ANSWER:E
Answer: E
Question: If -1 < a < 0 < b < 1, which of the following must be less than 0?
I.	a/b
II.	b/a
III.	ab
Options:
A)I only
B)II only
C)III only
D)I,II and III
E)None of the above
Rationale: We could solve this easily using examples.
I is true since a<0, b>0 therefore a/b<0
II is true since a<0, b>0 therefore b/a<0
III is true since a<0, b>0 therefore ab<0
So, the answer is D
Answer: D
Question: A train running at the speed of 90 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150 meter
B)225 meter
C)186 meter
D)288 meter
E)265 meter
Rationale: Speed = 90*(5/18) m/sec
= 25 m/sec
Length of Train (Distance)
= Speed * Time
25 * 9 = 225 meter
Answer:B
Answer: B
Question: Today is Thursday. The day after 50 days will be?
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)Friday
Rationale: Explanation:
50 days = 7 weeks 1 days = 1 odd days
Hence if today is Thursday, After 50 days, it will be = (Thursday + 1 odd days)
= Friday
Answer: Option E
Answer: E
Question: Two articles were sold at Rs. 480 each. On one, he gains 20% and on the other, he loses 12%. How much does he gain or lose in the whole transaction?
Options:
A)0.54%
B)1.54%
C)2.54%
D)3.54%
E)4.54%
Rationale: for the 1st article,cost price
=(100*480)/(100+20)=400
for the 2nd article,cost price
=(100*480)/(100-12)=545.45
total CP=400+545.45=945.45
total SP=480+480=960
so profit=960-945.45=14.55
%gain=(14.55*100)/945.45=1.54%
ANSWER:B
Answer: B
Question: In how many different ways can the letters of the word ‘HOPE’ be arranged ?
Options:
A)40320
B)720
C)120
D)100
E)24
Rationale: E
24
Required number of arrangements = 4! = 24
Answer: E
Question: Three pipes A, B and C can fill a tank in 7 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. How many hours will take C alone to fill the tank?
Options:
A)42/5
B)47/4
C)56/3
D)63/4
E)70/8
Rationale: The rate of A+B+C is 1/7 of the tank per hour.
After 2 hours, the tank is 2/7 full.
The rate of A+B is 5/7 * 1/9 = 5/63 of a tank per hour.
The rate of C is 1/7 - 5/63 = 4/63
C can fill the tank in 63/4 hours.
The answer is D.
Answer: D
Question: In how many ways can a group of 15 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 5 people?
Options:
A)15C5 * 9! *4!
B)15C3 * 8! *3!
C)15C4 * 9! *3!
D)15C2 * 10! *3!
E)16C5 * 10! *4!
Rationale: 10 people can be selected from 15 people in 15C10 ways.
Remaining 5 people can be selected from 5 people in 5C5 ways.
Now, arranging 10 people on a round table = (10-1) ! = 9!
Arranging 5 people on a round table = (5-1) ! = 4!
Hence, total number of ways = 15C10 * 9! * 5C5 * 4!
= 15C5 * 9! * 4!
ANSWER:A
Answer: A
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time will there be 243 million bacteria in the dish?
Options:
A)6: 00 p.m.
B)8: 00 p.m.
C)6: 00 a.m.
D)8: 00 a.m.
E)10: 00 a.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time will there be 243 million bacteria in the dish?
Assume that there are n intervals of 2 hours between 108 million and 243 million.
108 * (1.5)^n = 243
(3/2)^n = 243/108 = 9/4= (3/2)^2
Hence n = 2 intervals.
Each interval is of 2 hours. Therefore, the number of hours = 4
Adding 4 hours to 2 PM, we get 6 PM as the answer.
Option A
Answer: A
Question: An urn contains g green marbles and b blue marbles. If 1 green marbles and 5 blue marbles are added, and then one marble is selected at random from the urn, what is the probability that a blue marble will be drawn?
Options:
A)b/(b+g)
B)(b+5)/(g+3)
C)(b+5)/(b+g+8)
D)(b+5)/(b+g+6)
E)b/(b+g+5)
Rationale: no of fav outcomes i.e. blue MArbles = b+5
Total no of outcomes i.e. total Marbles = (b+5)+(g+1)= b+g+6
probability = (b+5) /(b+g+6)
Answer D
Answer: D
Question: If 60! × 60!/60^n is an integer, what is the largest possible value of n?
Options:
A)1
B)7
C)14
D)28
E)32
Rationale: 60! × 60!/60^n is an integer.
Or 60! × 60!/(6^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 60! = [60/5] + [60/25] = 14
Since there are 2 20!'s, power of 14 in the numerator = 2*14 = 28
Hence the largest value of b for which 60! × 60!/60^n is integer = 28
Correct Option : D
Answer: D
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)8
B)10
C)12
D)15
E)19
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Option E
Answer: E
Question: When 24 is divided by the positive integer c, the remainder is 4. Which of the following statements about c must be true?
I. c is even
II. c is a multiple of 5
III. c is a factor of 20
Options:
A)III only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: 24= m*n + 4
m*n=20
put values of m
m=1 c=20
m=2 c=10
m=4 c=5
I. not true
II. true
III. true
D. correct
Answer: D
Question: A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other ?
Options:
A)9:38pm
B)9:48pm
C)9:58pm
D)9:28pm
E)9:18pm
Rationale: though there is no mention of direction,we hav to consider that both A&B starts from same side.
let at the end of 10hr(i.e at 9pm from 11am),A travelled 40kms in 10hr and B travelled 36kms(1+2+..+8)in 8 hr.
we cant take 11 hr bcoz after 11hr(i.e at 10pm)B has crossed A.
so,A & B are (40-36)=4kms far from each other.
now speed of A=4km/hr & B=9km/hr.
relative speed= 9-4=5km/hr.
so,time taken by them to meet= (4/5)hrs=48min.
so A and B meet At 9:48pm
ANSWER:B
Answer: B
Question: Replace the ? with an approximate value in the following equation? 95.921 + 35.421 × 5.2 + ? = 705.621
Options:
A)791.9
B)783.9
C)793.9
D)973.9
E)733.9
Rationale: 95.921 + 35.421 × 5.2 + ? = 705.621
or, ? = 705.621 – 95.921 + 35.421 × 5.2
? = 705.621 – 95.921 + 184.1892
≈ 793.9
Answer C
Answer: C
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 6 muffins remained. How many guests did Monica plan on?
Options:
A)2.
B)4.
C)5.
D)6.
E)7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 6 = 5x + 2
6x = 5x + 2
x = 2
Answer: A
Answer: A
Question: Which of the following has most number of divisors?
Options:
A)99
B)101
C)176
D)182
E)186
Rationale: Divisors of 99=1,3,9,11,33,99
Divisors of 101=1,101
Divisors of 176=1,2,4,8,11,22,44,88,176
Divisors of 182=1,2,7,13,14,26,91,182
Therefore 176 has most number of divisors.
Option(C)
Answer: C
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Options:
A)8
B)9
C)7
D)6
E)5
Rationale: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%
Answer:A
Answer: A
Question: When the positive integer e is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer f is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of e-f?
Options:
A) 12
B) 24
C) 35
D) 16
E) 30
Rationale: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5e + 3
n = 7f + 4
I will need to check for the smallest such number.
I put f= 1. n = 11. Is it of the form 5e + 3? No.
Put f= 2. n = 18. Is it of the form 5e + 3? Yes.
When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.
Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so your answer is 35.
your answer is C
Answer: C
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 50%?
Options:
A)s.429
B)s.480
C)s.320
D)s.128
E)s.419
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 50% = 50% of 640 = Rs.320
SP = CP - Loss = 640 - 320
= Rs.320
Answer:C
Answer: C
Question: Two persons A and B start moving at each other from point P and Q respectively which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?
Options:
A)1000 Km
B)400 Km
C)800 Km
D)1400 Km
E)2400 Km
Rationale: DETAILED SOLUTION
Total distance travelled by both of them for 22nd meeting = 1400 + 21 x 2 x 1400 = 43 x 1400
Distance travelled by each will be in proportion of their speed:-
Therefore, distance travelled by A = 50/(50 + 20) x 43 x 1400 = 43000 (Note - Always do complicated calculations at last because things cancel out generally)
Now, for every odd multiple of 1400, A will be at Q and for every even multiple of 1400 A will be at P. So, at 42000 Km (1400 x 30, even multiple) A will beat P. So at their 22 meeting, A will be 1000 Km from P, therefore, 400 Km from Q.
CORRECT ANSWER B.
Answer: B
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 20?
Options:
A)A)100
B)B)120
C)C)250
D)D)200
E)E)160
Rationale: Then, 10% of x= 20
(10/100)x = 20
x = (20*100*)/10= 200
Answer is D
Answer: D
Question: A man buys a cycle for Rs.1400 and sells it at a loss of 10%. What is the selling price of the cycle?
Options:
A)Rs.1090
B)Rs.1160
C)Rs.1190
D)Rs.1202
E)NONE
Rationale: Solution
S.P	= 90% of Rs.1400
= Rs.(90/100×1400)
Rs.1260.
Answer CE
Answer: E
Question: If 144/x is an integer and 180/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
Options:
A)I, II, and III
B)I and II only
C)II and III only
D)III only
E)I only
Rationale: The largest possible value of x is 36 (the greatest common factor of 108 and 180), and if x=36 then
D
Answer: D
Question: Two bottles A and B contain diluted ammonium nitric acid. In bottle A, the amount of water is double the amount of acid while in bottle B, the amount of acid is 3 times that of water. How much mixture Should be taken from each bottle in order to prepare 5 litres of diluted sulphuric acid containing equal amount of acid and water?
Options:
A)1, 4
B)3, 2
C)2, 3
D)4, 1
E)1,5
Rationale: A B
Acid water Acid water
1 : 2 3 : 1
Acid=1/3 Acid=3/4
Mixture=Acid:Water=1:1 Required acid=1/2
Now,Required ratio=(1/4):(1/6)=3:2
So the required quantity is 3 and 2 litres respectively.
ANSWER:B
Answer: B
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 5-percent solution?
Options:
A)35
B)22.5
C)27
D)16 2/3
E)15
Rationale: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 5-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 5% of the solution. Set up an inequality and solve for x:
1.5/x = 1/5
x = 7.5
Since you need a 15L solution, you must evaporate 22.5 of the original 50L solution to get a 5% solution.
Answer is B.
Answer: B
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
Options:
A)22887
B)2677
C)2987
D)8925
E)17711
Rationale: Principal = (100 * 4016.25) / (9 * 5)
= Rs. 8925.
Answer:D
Answer: D
Question: The value of x + (xx) when x = 3 is:
Options:
A)A)36
B)B)12
C)C)18
D)D)64
E)E)10
Rationale: x + (xx)
Put the value of x = 2 in the above expression we get,
3 + (33)
= 3 +(3 × 3)
= 3 + (9)
= 3 + 9
= 12
B
Answer: B
Question: A cycle is bought for Rs.850 and sold for Rs.1080, find the gain percent?
Options:
A)22
B)27
C)99
D)88
E)11
Rationale: 850 ---- 180
100 ---- ? => 27%
Answer:B
Answer: B
Question: A reduction of 40% in the price of bananas would enable a man to obtain 66 more for Rs.40, what is reduced price per dozen?
Options:
A)1.91
B)2.91
C)4.91
D)3.91
E)5.91
Rationale: 40*(40/100) = 16 --- 66
? --- 12 => Rs.2.91
Answer: B
Answer: B
Question: A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number Q of tickets sold by the male members of the association
Options:
A)50
B)56
C)58
D)62
E)66
Rationale: Given that, Total average Q sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.
(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C.
Answer: C
Question: 1370 , 1320 , 1070 , -180 ?
Options:
A)-6430
B)-6530
C)-6630
D)-6730
E)-6830
Rationale: 1370,1320,1070,-180,?
1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
ANSWER:A.
Answer: A
Question: If Susan takes 11 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
Options:
A)xy/11
B)660x/y
C)60xy/11
D)xy/660
E)11x/(60y)
Rationale: The answer is E.
She runs x yards in 11x/y seconds =11x/60y minutes.
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.
Options:
A)225 meter
B)200 meter
C)250 meter
D)190 meter
E)180 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter
Answer:B
Answer: B
Question: If t, u, v, w, x, y, and z are seven different prime numbers, which of the following is the smallest possible value of t + u + v + w + x + y + z?
Options:
A)50
B)52
C)54
D)56
E)58
Rationale: The sum of the seven small smallest primes numbers is 2+3+5+7+11+13+17=58.
The answer is E.
Answer: E
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
Options:
A)5%
B)6%
C)2%
D)95%
E)1%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: A
Question: Ratio of two numbers x and y is 2:5. If x is increased by 50% and y is increased by 8 then the new ratio becomes 3:10. what is the ratio 3y:(x+6)
Options:
A)15:8
B)8:15
C)2:5
D)5:2
E)13:6
Rationale: Let:
x = 2n
y = 5n
3n/(5n+5) = 3/10
30n = 3*(5n+5)
n = 1
So, x =2; y=5
3y/(x+6) = 15/8
Answer = A
Answer: A
Question: A boy runs 200 metres in 72 seconds. What is his speed ?
Options:
A)10 km/hr
B)14 km/hr
C)20 km/hr
D)12 km/hr
E)24 km/hr
Rationale: 200/72 * 18/5 = 10 km/hr
ANSWER:A
Answer: A
Question: Operation#is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?
Options:
A)0%
B)10%
C)20%
D)30%
E)40%
Rationale: Any multiple of 10 is even.
Any two-digit prime number is odd.
(even+odd)/2 is not an integer. Thus # does not yield an integer at all.
Therefore P=0.
Answer: A.
Answer: A
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 100 metres?
Options:
A)16 seconds
B)20 seconds
C)14 seconds
D)12 seconds
E)15 seconds
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 100 m = 100/5
= 20 seconds.
Answer: B
Answer: B
Question: How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/4!?
Options:
A)1
B)3
C)5
D)6
E)9
Rationale: 4! = 24
1/100 < 1/24 < 1/10
0.001 < 1/24 < 0.01
So 1/24 has 1 leading zeros
Answer: A
Answer: A
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Options:
A)11
B)77
C)16
D)10
E)88
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer: D
Answer: D
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Options:
A)21 years
B)71 years
C)51 years
D)91 years
E)11 years
Rationale: Explanation:
Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.
Answer: C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is?
Options:
A)5/15
B)5/12
C)5/19
D)5/12
E)5/11
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer: B
Answer: B
Question: Find the odd man out
4,9,16,25,36,42,49
Options:
A)4
B)9
C)16
D)42
E)49
Rationale: 2*2 = 4
3*3=9
4*4=16
5*5=25
6*6=36
7*7=49
ANSWER:D
Answer: D
Question: If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is
Options:
A)18.20
B)18.33
C)18
D)18.3
E)None of these
Rationale: Explanation:
Present worth = Amount - TrueDiscount
= 110 -10 = Rs.100
SI on Rs.100 for a certain time = Rs.10
SI on Rs.100 for doube the time = Rs.20
TrueDiscount on Rs.120 = 120 - 100 = Rs.20
TrueDiscount on Rs.110 = (110x 20/120) = Rs.18.33
Answer: B
Answer: B
Question: A hostel had provisions for 250 men for 28 days. If 50 men left the hostel, how long will the food last at the same rate?
Options:
A)35
B)40
C)50
D)60
E)65
Rationale: A hostel had provisions for 250 men for 28 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 28
250×28=200x
5×28=4x
x=5×7=35
ANSWER A
Answer: A
Question: In a certain province in Japan there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
Options:
A)30
B)105
C)330
D)14!
E)15!
Rationale: Method-1:
Japan has Total Cities = 15 and each city should be connected with every other city
So Total Roads required to connect 1st City with other 14 cities = 14
Now 1st City is connected with all other cities so,
So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13
Now 1st and 2nd Cities are connected with all other cities so,
So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12
......and so on...
Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105=B
Answer: B
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)833 1/4
B)833 1/3
C)833 1/9
D)833 1/2
E)833 1/1
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.Answer: B
Answer: B
Question: The ratio of the volumes of two cubes is 6859 : 1331. What is the ratio of their total surface areas?
Options:
A)1:21
B)12:7
C)1:15
D)21:17
E)13:13
Rationale: Ratio of the sides
= ³√6859 : ³√1331 = 19 : 11
Ratio of surface areas
= 192 : 112 = 12:7
Answer:B
Answer: B
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
Options:
A)761 cm2
B)384 cm2
C)157 cm2
D)276 cm2
E)672 cm2
Rationale: Area of a parallelogram
= base * height
= 24 * 16
= 384 cm2
Answer: B
Answer: B
Question: How much is 90% of 40 is greater than 4/5 of 25?
Options:
A)29
B)776
C)66
D)16
E)99
Rationale: (90/100) * 40 – (4/5) * 25
36 - 20 = 16
Answer: D
Answer: D
Question: (?) + 3699 + 1985 - 2047 = 31111
Options:
A)27488
B)27424
C)27474
D)27784
E)27468
Rationale: C
27474
x + 3699 + 1985 - 2047 = 31111
x + 3699 + 1985 = 31111 + 2047
x + 5684 = 33158
x = 33158 - 5684 = 27474.
Answer: C
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
Options:
A)10
B)20
C)40
D)73
E)64
Rationale: let x pupils in the class
by question
total increase in marks = x/2
so;x/2 = (83 - 63)
x = 2 * 20
40
ANSWER:C
Answer: C
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
Options:
A)288 m
B)704 m
C)898 m
D)556 m
E)465 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m
Answer: B
Answer: B
Question: If f(x)=x^2 and x is a positive integer, which of the following will not be the value of f(f(x))?
Options:
A)1
B)16
C)81
D)256
E)144
Rationale: f(x)=x^2
f(f(x)) = (x^2)^2
=x^4
A. 1 , x=1
B. 16 , x=2
C. 81 , x=3
E. 144
f(x)=12
Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(x)) .
D. 256 , x=4
Answer E
Answer: E