divelab/Sys2Bench huggingface dataset:
Question: A and B participate in a 5000 m bicycle race which is being run on a circular track of 500 m. If the speed of A and B are 20 m/s and 10 m/s respectively, what is the distance covered by A when he passes B for
the seventh time ?
Options:
A)2500
B)2800
C)4000 m
D)Situation is not possible
E)None of these
Rationale: Track length = 500 m
Speed of A and B are 20m/s and 10 m/s respectively
Time taken by them to meet = length/ relative speed = 500/(20-10) 50 sec.
Time taken to meet for the 7th time = 7 *50 =350 sec ……..(1)
Total duration of race = total legth of race/ speed
= 500/20 = 250 sec ……..(2)
From (1) and (2) we can find out that 7th time meeting is not possible.
Answer: D
Answer: D
Question: The function f(K) represents the number of ways that prime numbers can be uniquely summed to form a certain number K such that K = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Lets start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: D
Answer: D
Question: Average age of students of an adult school is 44 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
Options:
A)1200
B)180
C)360
D)240
E)None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 44x + 120*32 = (x + 120)36 ⇒ x = 60
So, Required no. of students after joining the new students
= x + 120 = 180
Answer : B
Answer: B
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7000?
Options:
A)s. 4991
B)s. 5991
C)s. 6001
D)s. 6991
E)s. 7991
Rationale: total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(7000*6)-34009]
= Rs.(42000-34009)
= Rs.7991.
ANSWER:E
Answer: E
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 600. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 615. What is the value of X?
Options:
A)8000
B)6000
C)5000
D)4000
E)3000
Rationale: Simple way to solve this question is to use options.
From SI, we know that X*y=30,000.
Now, put the value of X = 6000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 6000+5% of 6000= 6300.
2nd year, Amount = 6300 + 5% of 6300 =6615
We can see after 2 years Interest = 6615-6000= 615. hence, it satisfies the question. Hence B is the correct answer
Answer: B
Question: If |z|/w = 6,which of the following must be true?
Options:
A)z = -6w
B)z = 6w
C)z^2 = 36w^2
D)z^2 = 36w^3
E)z^3 = 216w^3
Rationale: |z|/w = 6.
|z| = 6w.
Then z = 6w or -6w and so z^2 = 36w^2.
The answer is C.
Answer: C
Question: Find the third proportional to 10 and 30?
Options:
A)10
B)60
C)80
D)90
E)20
Rationale: Formula = Third proportional = (b × b)/a
A = 10 and B = 30
(30 x 30)/ 10 = 900/10= 90
D
Answer: D
Question: A woman has $99999 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her nine children?
Options:
A)2
B)1
C)0
D)3
E)4
Rationale: To find the least amount the woman should add to her saving account to split the money evenly among her 9 children,
she needs to make the total divisible by 9
Simply add the individual digits of the total = 9+9+9+9+9 = 45
45 divided by 9 = 5 so answer is 0
Correct Option : D
Answer: D
Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
Options:
A)75 × 8 ÷ 6
B)98 ÷ 2.5 + 15.2 × 4
C)√225 – 5 × 2(2)
D)76 × 1.5 – 5.5 × 2.6
E)48 × 1.2 + 127.2 ÷ 3
Rationale: Check all options one by one.
(a) 75×8/6=100
(b) 98⁄2.5 + (15.2 × 4) = 100
(c) (15 × 8) – (5 × 4) = 100
(d) (76 × 1.5) – (5.5 × 2.6) = 99.7
(e) (48 × 1.2) + 127.2⁄3 = 100
Answer D
Answer: D
Question: Baby Isabel plays with blocks. Each block is 5.6 inches tall. She has a collection of 38 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
Options:
A)212.8"
B)90.8"
C)206.2"
D)120"
E)151.7"
Rationale: 5.6"*38=212.8". Answer is A.
Answer: A
Question: The sum of the ages of 5 children born at the intervals of years each is 50 years. What is the age of the youngest child?
Options:
A)6 years
B)8 years
C)10 years
D)12 years
E)14 years
Rationale: Let the ages of the children be x, (x + 2), (x + 4), (x + 6) and (x +8) years.
Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 50
5x = 30 => x = 6.
Age of youngest child = x = 6 years.
ANSWER:A
Answer: A
Question: A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
Options:
A)10 years
B)8 years
C)6 years
D)12 years
E)13 years
Rationale: Explanation:
Let the sum be Rs.1 which becomes Rs.2 after 4 years
⇒ 2 = 1(1 + R/100 )4 --- (equation 1)
Let the sum of Rs.1 becomes Rs.8 after n years
⇒ 8 = 1(1 + R/100)n --- (equation 2)
⇒ (2)3 = 1(1+R/100)n
⇒ [1(1+R/100)4]3 = 1(1+R/100)n (âˆµ replaced 2 with the value in equation 1) (1 + R/100)12 = (1+R/100)n
⇒ n = 12
i.e., the sum amounts to 8 times in 12 years
Answer: Option D
Answer: D
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 5 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: To get 40 points as end of season we need another 35 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
Option C=8*3+7*1=31
Option D=9*3+6*1=33
Option E=10*3+5*1=35
hence option E-10
Answer: E
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)12
B)24
C)48
D)60
E)50
Rationale: Answer: Option C
Explanation:
Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
ANSWER C
Answer: C
Question: A cistern which could be filled in 8 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Options:
A)76 hrs
B)99 hrs
C)55 hrs
D)90 hrs
E)40 hrs
Rationale: 1/8 - 1/x = 1/10
=> 40 hrs
Answer: E
Answer: E
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 5 years?
Options:
A)x (1+n/100)^5 - x
B)4x (1+n/100)^4 - x
C)6x (1+n/100)^6 - x
D)2x (1+n/100)^2 - x
E)x (1+n/100)^7 - x
Rationale: Amount after 5 years compounded yearly = x (1+n/100)^5
Thus profit = Final amount - original principle = x (1+n/100)^5 - x . Answer : A
Answer: A
Question: If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
Options:
A)22
B)24
C)26
D)25
E)23
Rationale: Let the number of workers employed to build the wall in 30 hours be y
48 * 15 = 30 * y
(48 *15)/30=y
y=24
Answer:B
Answer: B
Question: Of the 120 passengers on Flight 750, 55% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?
Options:
A)44
B)48
C)50
D)52
E)58
Rationale: Number of passengers on flight = 120
Number of female passengers= .5*120 = 66
Number of passengers in first class = (10/100)* 120 = 12
Number of passengers in coach class = (90/100)* 120 = 108
Number of male passengers in first class = 1/3 * 12 = 4
Number of female passengers in first class = 12-4 = 8
Number of female passengers in coach class = 66 - 8 = 58
Answer E
Answer: E
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
Options:
A)720
B)740
C)760
D)770
E)790
Rationale: Option 'A'
Answer: A
Question: How many factors of 30 are odd numbers greater than 1?
Options:
A)3
B)3
C)5
D)6
E)7
Rationale: prime factors of 30 are 2^1,3^1,5^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,) = (1+1)(1+1) =4
since we need odd divisors other than 1 =>4-1 = 3 odd divisors
B is the answer
Answer: B
Question: 3 + 33 + 333 + 3.33 = ?
Options:
A)324.56
B)372.33
C)436
D)633
E)662
Rationale: 3
+ 33
+ 333
+ 3.33
------
372.33
------
Correct Option is B
Answer: B
Question: 17 times a number gives 187. The number is
Options:
A)11
B)12
C)13.2
D)None
E)Cannot be determined
Rationale: Explanation:
Let the number be 'N'
17×N=187⇒N=11
Correct Option: A
Answer: A
Question: Find the odd man out. 2, 4, 6, 12, 19, 28
Options:
A)12
B)19
C)1
D)3
E)19
Rationale: 19 is an odd number.All other given numbers are even
Answer : Option B
Answer: B
Question: Large amounts of cheques are processed by using
Options:
A)kilobytI
B)kilobyt2
C)kilobyte
D)kilobytK
E)kilobytW
Rationale: Answer: Option 'C'
Answer: C
Question: If 2 persons can do 2 times of a particular work in 2 days, then, 5 persons can do 5 times of that work in?
Options:
A)2 days
B)3 days
C)5 days
D)7 days
E)9 days
Rationale: That is, 1 person can do one time of the work in 2 days.
Therefore, 5 persons can do 5 times work in the same 2 days itself.
A)
Answer: A
Question: In Sam's hanger there are 23 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
Options:
A)1.
B)2
C)3
D)4
E)5
Rationale: Total boxes = 23
Filled with toys = 16
Filled with appliance = 7
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 7 - 3 = 4
Correct Option: D
Answer: D
Question: How many different arrangements of letters are possible if three letters are chosen from the letters A through G and the letters E and A must be among the letters selected?
Options:
A)28
B)30
C)32
D)34
E)36
Rationale: Besides A and E, there are 5 letters and we can choose one of them.
5C1 = 5
Three letters can be arranged in 3! ways.
The number of arrangements is 5*3! = 30
The answer is B.
Answer: B
Question: If (a-6)(b-2) =0, which of the following must be true ?
I. a=6 and b=2
II. if a is not 6, then b=2
III. if a=6, then b is not=2
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: (a-6)(b-2)=0
So either a=6 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Answer: B
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $20. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)180xy
B)180/(xy)
C)20xy
D)20xy/9
E)xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 20 / (xy/9) = 180/(xy).
The answer is B.
Answer: B
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 50 percent of the pack would be outfielder cards?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 50% of toatal Ocards
12-X<.5*12
X<12-6
X<6
X=5
Ans B
Answer: B
Question: The perimeters of two squares are 44 cm and 36 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
Options:
A)76 cm
B)24 cm
C)25.2 cm
D)55 cm
E)34 cm
Rationale: We know perimeter of square = 4(side)
So Side of first square = 44/4 = 11 cm
Side of second square = 36/4 = 9 cm
Area of third Square = 11*11 - 9*9
= 40 cm
So side of third square = 6.3 [because area of square = side*side]
Perimeter = 4*Side = 4*6.3 = 25.2 cm
Answer:C
Answer: C
Question: A 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
Options:
A)1/4
B)2/5
C)1/2
D)3/5
E)2/3
Rationale: you can simply use this formula to avoid confusion:
w1/w2 = (A2 - Aavg)/(Avg - A1)
Here is how you will find the values of A1 an A2.
We have an overall loss (average loss). The average loss is 4 kg when 40 kg alloy is immersed.
This is a loss of (4/40)*100 = 10%.
This is Aavg
The loss of tin is 1.375 kg for every 10 kg.
This means it loses (1.375/10)*100 = 13.75% of its weight in water.
This is A1.
The loss of silver is .375 kg for every 5 kg.
This means it loses (.375/5)* 100 = 7.5% of its weight in water.
This is A2.
Weight of Tin/Weight of Silver = (Silver's loss - Avg loss)/(Avg loss - Tin's loss)
X/Y = (7.5 - 10)/(10 - 13.75) = 2/3
E
Answer: E
Question: How many times in a day, the hands of a clock are straight?
Options:
A)22
B)44
C)48
D)24
E)36
Rationale: The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 'o clock only. Hence the hands point in the opposite directions 22 times in a day.
The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 o'clock). Hence the hands coincide 22 times in a day.
So In 24 hours, the hands come in opposite direction or coincide 44 times.
This is already given as a formula and it's is better to learn the answer by heart as 44
which can save time in competitive exams.(However you should know the theory behind). Answer: Option B
Answer: B
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
A)22
B)77
C)54
D)87
E)21
Rationale: S = 240/16 * 18/5 = 54 kmph.Answer: C
Answer: C
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
Options:
A)0 sq m
B)3 sq m
C)2 sq m
D)6 sq m
E)9 sq m
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
ANSWER:A
Answer: A
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options:
A)3 : 5 : 2
B)3 : 5 : 5
C)6 : 10 : 5
D)3 : 4 : 5
E)4 : 6 : 8
Rationale: Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer: C
Answer: C
Question: A number is divided by 221, the remainder is 64. If the number be divided by 13 then remainder will be
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Let the given number when divided by 119
gives x as quotient and 19 as remainder. Then
Given number = 119x + 19
= 17 x 7x + 17 + 2
= 17 (7x + 1) + 2
so, the required remainder is 2.
ANSWER:B
Answer: B
Question: By investing Rs. 1620 in 8% stock,Michael earns Rs. 135.The stock is then quoted at :
Options:
A)Rs. 80
B)Rs. 96
C)Rs. 106
D)Rs. 108
E)None of these
Rationale: Solution
To earn Rs. 135, investment = Rs. 1620.
To earn Rs. 8, investment = Rs. (1620/135x8) =96
∴ Market value of Rs. 100 stock = Rs. 96.
Answer B
Answer: B
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)7%
B)4%
C)2%
D)1%
E)8%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: B
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 49 times the difference between the two numbers. How many coins did the old man have?
Options:
A) 24
B) 26
C) 30
D) 49
E) 40
Rationale: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 49(x - y) --> x + y = 49.
Answer: D.
Answer: D
Question: What percent of 150 is 40?
Options:
A)0.25%
B)26.67%
C)25%
D)40%
E)250%
Rationale: 150*x /100 = 40
x = 2*40/3
x = 26.67
Ans: B
Answer: B
Question: On January 1, 2001 it was Monday. Which day of the week fall on January 1, 2005?
Options:
A)Saturday
B)Wednesday
C)Monday
D)Tuesday
E)Friday
Rationale: On 31st Dec. 2000 it was Sunday.
Number of odd days from 2001 to 2004=(1 + 1 + 1 + 2) = 5 odd days
31st Dec. 2004, it was Friday
Saturday was the day on 1st Jan. 2005
Answer: A
Answer: A
Question: Raju purchases 550 ml. of milk every day. If the cost of one litter of milk is Rs.44. How much amount will he pay in 45 days?
Options:
A)Rs.1098
B)Rs.1079
C)Rs.1089/-
D)Rs.1099
E)None of these
Rationale: Explanation:
500 ml cost Rs.22
50 ml cost Rs.2.20
:.550 ml cost Rs.24.20
For 44 days the cost of milk = 45 x 24.20
= Rs.1089/-
Answer: Option C
Answer: C
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
Options:
A)157.53
B)157.59
C)157.5
D)157.51
E)157.56
Rationale: (3500*1.5*3)/100 => 157.50
Answer: C
Answer: C
Question: If P and Q are positive integers, P - 3 is divisible by 4 and Q - 1 is divisible by 4, all of the following could be the value of P - Q Except?
Options:
A)1
B)2
C)6
D)18
E)14
Rationale: P-3 = 4Q
=> P = 4Q + 3 = 3,7,11,15,19,23,27,31,35,39
Q-1 = 4P
=> Q = 4P + 1 = 1,5,9,13,17,21,25,29,33,37,41
2=3-1
6=15-9
18=27-9
14=31-17
So , we can see that all the answer choices are possible here except A
Answer: A
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/3%
B)16 7/3%
C)19 2/3%
D)16 2/3%
E)16 4/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: The value of (1-d3) / (1-d) is
Options:
A)> 1 if d > -1
B)>3 if d > 1
C)> 2 if 0 < d < 0.5
D)< 2 if d < -2
E)None
Rationale: Explanation :
Let S = (1 - d3 ) / ( 1 - d ) = ( 1 + d2 + d) .
=> d = 0 then S = 1 .
=> d = 2 then S = 7 .
=> d = 0.1 then S = 1.11 .
=> d = -3 then S = 7 .
Hence, only the option 2 satisfy.
Answer : B
Answer: B
Question: How many multiples of 4 are there between 32 and 252 ?
Options:
A)67
B)64
C)54
D)56
E)60
Rationale: It should be mentioned whether 32 and 252 are inclusive.
If 32 and 252 are inclusive, then the answer is (252-32)/4+1=56.
If 32 and 252 are NOT inclusive, then the answer is (248-36)/4+1=54.
Since OA is C, then we have NOT inclusive case.
Answer: C
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
Options:
A)9:26
B)9:24
C)9:25
D)9:20
E)9:21
Rationale: a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22
=9:25
Answer:C
Answer: C
Question: 40 onions on a scale weigh 7.68 kg. When 5 onions are removed from the scale, the average weight of the 35 onions is 190 grams. What is the average weight (in grams) of the 5 onions which were removed?
Options:
A)200
B)202
C)204
D)206
E)208
Rationale: 35*190=6650.
The other 5 onions weigh a total of 1030 grams.
The average weight is 1030/5 = 206 grams.
The answer is D.
Answer: D
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 3000?
Options:
A)7
B)9
C)11
D)13
E)15
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 < 3000, then the greatest possible length of integer z is 11.
The answer is C.
Answer: C
Question: The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options:
A)20 years
B)21 years
C)22 years
D)23 years
E)24 years
Rationale: Explanation:
Let the average age of the whole team by x years.
11x â€“ (24 + 27) = 9(x -1)
11x â€“ 9x = 42
2x = 42
x = 21.
So, average age of the team is 21 years.
Answer B
Answer: B
Question: The perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
Options:
A)A)72
B)B)828
C)C)729
D)D)75
E)E)35
Rationale: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 60/2 = 35 cm2
Answer: Option D
Answer: D
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)2/215
B)2/131
C)1/216
D)2/217
E)2/319
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: What is the units digit of 17^83 × 13^82 × 11^87?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Cyclicity of 7 is 4 --> 7, 9, 3, 1
Cyclicity of 3 is 4 --> 3, 9, 7, 1
11 raised to any positive power has a units digit 1
17^83 × 13^82 × 11^87 = Units digit of 3 * 9 * 1 = 7
Answer: D
Answer: D
Question: A box contain the number of balls which is as much times greater than 15 as much times lesser than 240.The no. of ball is?
Options:
A)48
B)75
C)60
D)54
E)45
Rationale: Answer
Let the number be x.
x/15=240/x
x^2=240*15=3600
x=√3600=60
Correct Option: C
Answer: C
Question: Compound interest earned on a sum for the second and the third years are Rs.2000 and Rs.2500 respectively. Find the rate of interest?
Options:
A)18% p.a.
B)22% p.a.
C)25% p.a.
D)24% p.a.
E)None of these.
Rationale: Rs.2500 - 2000 = Rs.500 is the interest on Rs.2000 for one year.
Rate of interest = (500/2000) / 100 = 25% p.a
ANSWER:C
Answer: C
Question: 9548+7314=8362=?
Options:
A)8230
B)8410
C)8500
D)8600
E)None of them
Rationale: =(9548+7314)=8362+x
16862=8362+x
x=16862-8362
=8500
Answer is C
Answer: C
Question: 900 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Options:
A)12.88
B)12.6
C)12.55
D)12.21
E)12.27
Rationale: 900*15 = 1100*x
x = 12.27.Answer: E
Answer: E
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Options:
A)9:36
B)9:31
C)9:39
D)9:34
E)9:32
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
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9:31
Answer: B
Answer: B
Question: In the recent, climate conference in New York, out of 700 men, 500 women, 800 children present inside the building premises, 20% of the men, 40% of the women and 10% of the children were Indians. Find the percentage of people who were not Indian?
Options:
A)77%
B)73%
C)79%
D)83%
E)None
Rationale: Solution: Number of Indians men present there = 700*20/100 = 140
Indian women = 500*40/100 = 200
Indian children = 800*10/100 = 80.
Total member present in climate conference = 700+500+800 = 2000
Total Indian = 200+140+80 = 420
Hence, % of Indian present there = 420*100/2000 = 21%
% of people who were not Indian = 100-42 = 79%.
Answer C
Answer: C
Question: Given that x = 2^b – (8^33 + 16^5), which of the following values for b yields the lowest value for |x|?
Options:
A)97
B)98
C)99
D)100
E)119
Rationale: 8^33 + 16^5 = 2^99 + 2^20
Compared to 2^99, the value of 2^20 is negligible.
2^99 - (2^99 +2^20) will minimize the value of |x|.
The answer is C.
Answer: C