divelab/Sys2Bench huggingface dataset:
Question: In a certain circle there are 10 points. What is the number of the triangles connecting 4 points of the 10 points?
Options:
A)80
B)96
C)108
D)120
E)210
Rationale: IMO : E
HERE we have to select 4 points out of 10 points. Order is not important
So the answer will be 10c4 = 210
Answer: E
Question: Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?
Options:
A)5/6
B)2/3
C)1/2
D)5/12
E)1/3
Rationale: 1/3
probability of jim winning is basically the sum of three probabilities:
probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9
probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9
probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9
1/9 + 1/9 + 1/9 = 3/9 = 1/3=E
Answer: E
Question: John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/5 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
Options:
A)59
B)65
C)70
D)77
E)98
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 5 x 60 ) = 12
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 12 x + 20 x + 15 x + 12 x) = 59 x.
For minimum number of pencils x = 1 .
The person should have at least 59 pencils.
A)
Answer: A
Question: A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible?
Options:
A)84
B)40
C)30
D)20
E)12
Rationale: C35∗C34=40
Answer: B.
Answer: B
Question: The product of all the prime numbers less than 22 is closest to which of the following powers of 10?
Options:
A)10^9
B)10^8
C)1*10^7
D)10^6
E)10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
=2.1x10^2*1.3*1.7*1.9
=9.69* 10^6
=1*10^7
C
Answer: C
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 4^a and y = 3^b, which of the following is a possible units digit of xy?
Options:
A)1
B)8
C)5
D)7
E)9
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=4
a=2; X=16
a=3; X=64........ Units digit repeat in a cycle of 4,6,4,6......
Similarly, Finding all values of Y for positive values ofb
b=1; Y=3
b=2; Y= 9
b=3; Y= 27
b=4; Y=81
b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=4 and Y=3: Units digit of XY = 12
When X=4 and Y=9: Units digit of XY = 36
When X=4 and Y=7: Units digit of XY = 28
When X=4 and Y=1: Units digit of XY = 4
Only four possibilities for Units digit of XY i.e. 4, 2, 8 and 6.
Only 8 is given in answer choices, therefore answer is B
Answer: B
Question: What is the remainder if 7^12 is divided by 100?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 7^16 can be written as (7^4)^3
If we divide 7^4 by 100 the reminder is 1
So, (7^4)^3 by 100, the reminder is 1^3 = 1
Answer : A
Answer: A
Question: A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price?
Options:
A)d+5/1.05
B)d/1.05 +5
C)1.05d-5
D)d-5/1.05
E)1.05(p – 5)
Rationale: Let x be the price of the item.
Final price after discount and sales tax = x * (1 - d/100) * 1.05
Let e be the percent discount which would result in the same final price.
Then,
x * (1 - d/100) * 1.05 = x * (1 - e/100)
=> 1.05 - 1.05d/100 = 1 - e/100
=> e/100 = 1.05d/100 - .05
=> e = 1.05d - 5
Hence ,option C is correct.
Answer: C
Question: If a fair die is rolled once, what is the probability that a 3 occurs on at least one roll?
Options:
A)25/36
B)125/216
C)1/6
D)1/36
E)5/6
Rationale: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6) = 1-5/6 = 1/6
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
C is thus the correct answer.
Answer: C
Question: When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
Options:
A)40
B)41
C)42
D)43
E)45
Rationale: Let the age of Usha is 3x then Nisha is x and Asha is 25
Also Usha 34, Nisha y, and Asha 2y.
We know that 3x - 34 = x - 2y = 25 - 2y
Solving above three equations we get x = 9, y = 16
Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40
Answer:A
Answer: A
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 80 of this series?
Options:
A)8990
B)9380
C)9630
D)9960
E)10,240
Rationale: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 80, the sum of the series is:
3(1+2+...+80) + 80(3) =
3(80)(81)/2 + 80(3) =
120*81 + 240 = 9960
The answer is D.
Answer: D
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is "frozen" if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently six spaces behind player B, what is the probability that player B will be frozen after player A rolls?
Options:
A)1/12
B)5/36
C)1/6
D)1/3
E)17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 6 (as A is 6 spaces behind B) = 5 ( (1,5), (2,4), (3,3), (4,2), (5,1) )
So, the probability = 5/36 (Option B)
Answer: B
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball?
Options:
A)12 cm
B)16 cm
C)18 cm
D)20 cm
E)none of the these
Rationale: similar triangle properties..
2/r+6 = 6/r-6
giving r = 12.
Answer: A
Answer: A
Question: What is the difference between the place value and the face value of 9 in the numeral 296827?
Options:
A)None of these
B)89993
C)89991
D)89994
E)89995
Rationale: Explanation:
Place value of 9 = 90000
Face value of 9 = 9
Difference = 9000 - 9 = 89991
Answer: C
Answer: C
Question: A whale goes on a feeding frenzy that lasts for 5 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the third hour?
Options:
A)38
B)47
C)50
D)53
E)93
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 450/5 = 90, so the median is also 90, and that is the amount eaten in the 2nd hour. We need to add 3 to find the total eaten in the next hour, so the answer is 93
option E
Answer: E
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 250 per month. What is his monthly salary?
Options:
A)5000
B)2999
C)2878
D)6250
E)2771
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 â€“ 96 =Rs. 4
100 ------ 4
? --------- 250 => 6250
Answer: D
Answer: D
Question: If the average (arithmetic mean) of seven consecutive integers is k - 2, then the product of the greatest and least integer is
Options:
A)k2 - 9
B)k2 - 2k + 1
C)k2 - 4k - 5
D)k2 + 6k + 9
E)k2 + 4k - 12
Rationale: n = smallest number
n+6 = largest number
(n + n + 6)/2 = k - 2
=> (2n+6)/2 = k - 2
=> n + 3 = k - 2
=> n = k - 5
So Product of n and n+6 = (k-5)(k+1)
= k^2 - 5k + k - 5
= k^2 - 4k - 5
Answer - C
Answer: C
Question: Find the odd man out. 3, 8, 18, 38, 78, 158, 316
Options:
A)38
B)158
C)316
D)8
E)None of these
Rationale: Explanation :
3
3 × 2 + 2 = 8
8 × 2 + 2 = 18
18 × 2 + 2 = 38
38 × 2 + 2 = 78
78 × 2 + 2 = 158
158 × 2 + 2 = 318
Hence, 316 is wrong and 318 should have come in place of that. Answer : Option C
Answer: C
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three (vice presidents)/VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
Options:
A)0.5
B)0.6
C)0.7
D)0.49
E)0.8
Rationale: probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
D
Answer: D
Question: A train 130 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)4
B)7
C)5
D)9
E)8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [130* 3/55] sec = 7 sec
ANSWER:B
Answer: B
Question: An auction house charges a commission of 25% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
Options:
A)$115,000
B)$165,000
C)$215,000
D)$240,000
E)$365,000
Rationale: Say the price of the house was $x, then 0.25*50,000+0.1*(x-50,000)=24,000 --> x=$165,000 (25% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: B.
Answer: B
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
Options:
A)40.4 sec
B)40.5 sec
C)50.4 sec
D)50.5 sec
E)60.4
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
correct Answer: option a
Answer: A
Question: A hall 36m long and 15m broad is to be paved with stones, each measuring 2dm by 5 dm. The number of stones required is:
Options:
A)180
B)1800
C)5400
D)18000
E)1.8
Rationale: Area of the hall= 3600*1500
Area of each stone= (20*50)
Therefore, number of stones= (3600*1500/ 20*50)= 5400
ANSWER:C
Answer: C
Question: A boy has seven trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)88
B)98
C)106
D)108
E)84
Rationale: Explanation:
The boy can select one trouser in seven ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 12 = 84 ways
E)
Answer: E
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:5
C)1:9
D)1:3
E)1:1
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: A
Question: On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 40 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?
Options:
A)33.3%
B)40%
C)50%
D)60%
E)66.6%
Rationale: 0.20P = RT + C
0.4(RT) = no C
=> 0.60(RT) had C
0.20P = 0.60(RT)
RT/P = 1/3=33%
Answer - A
Answer: A
Question: Car Q and Car Y traveled the same 80-mile route. If Car Q took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car Q, how many hours did it take Car Y to travel the route?
Options:
A) 2/3
B) 1
C) 4/3
D) 8/5
E) 3
Rationale: The speed of car Q is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: C
Question: The price of stock increased by 8% last year and decreased by 6% this year. What is the net percentage change in the price of the stock?
Options:
A)0.2%
B)0.8%
C)1.2%
D)1.52%
E)2%
Rationale: (100% + 8%) * (100% - 6%) = 1.08 * 0.94 =1.0152 = 101.52%.
The net percentage change in the price of the stock is (+) 1.52%
The answer is D
Answer: D
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)22
B)28
C)90
D)27
E)23
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15
= Rs.90.
Answer:C
Answer: C
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)11
B)77
C)16
D)10
E)98
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m..Answer: D
Answer: D
Question: Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1500
Options:
A)30
B)70
C)210
D)300
E)150
Rationale: 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.
100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.
Then we want to know what is the largest possible GCF of x and 2100.
Well 1500 = 3 *5 * 10 * 10
We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.
We know x has one factor of 3, but not two factors --- that takes the 3.
We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other
No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.
3*5*10 = 150
If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 2100.
E
Answer: E
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/6
B)3/2
C)3/4
D)3/1
E)3/6
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y
= 23 x + 23 y
==> 4 x = 6 y ==> x/y
= 3/2.
Answer: B
Answer: B
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 14 and 15. The larger of the two numbers is:
Options:
A)338
B)278
C)345
D)231
E)121
Rationale: Clearly, the numbers are (23 * 14) and (23 * 15). Larger number
= (23 * 15) = 345.
Answer: C
Answer: C
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 126, what is the common ratio of the G.P?
Options:
A)3
B)1/3
C)2
D)5
E)1/5
Rationale: 126=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
126=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
126=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
125=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
125=r^3
r=5
D
Answer: D
Question: A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Ten employees have done just two courses and only one made ​​the three courses. How many employees have no training?
Options:
A)A)0
B)B)9
C)C)10
D)D)11
E)E)26
Rationale: Total employees=50
studied accounting=22
studied finance=15
studied marketing=14
10 employees have been double counted and one employee has been counted thrice.
Therefore employees who have received training=22+15+14-10-(2*1)
=51-12
=39
Employees with no training
=50-39
=11
Ans=D
Answer: D
Question: A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men ?
Options:
A)72
B)68
C)74
D)82
E)69
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 8 people in this case.
Where K = the total number of elements to select, 4 people in this case.
The total number of combinations is therefore:
8!/((8-4)!4!) = 70
However, one of these combinations are not valid since they have all members of men
The correct answer is 70-1 = 69.Ans E
Answer: E
Question: A train covers a certain distance at a speed of 320kmph in 6 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of
Options:
A)1152km/hr
B)1120km/hr
C)1650km/hr
D)1750km/hr
E)1850km/hr
Rationale: Explanation:
Distance = 320Ã—6 = 1920km
Required speed = (1920Ã— 3/5) = 1152km/hr
Answer: Option A
Answer: A
Question: Thirty percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are non-science majors if 40% of the class are men?
Options:
A)2%
B)5%
C)28%
D)30%
E)95%
Rationale: 3/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have - 0.3 * 60 = 18
[Non-Science-Women] will have - 42
[Science-Men] will have = 20-18 = 2
[Non-Science-men] will have - 38
S0 38/40 * 100 = 95%
Answer - E
Answer: E
Question: The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes?
Options:
A)1:7
B)1:3
C)1:8
D)1:1
E)1:2
Rationale: 1:8
Answer: C
Answer: C
Question: How many integers are there between 42 and 97, inclusive?
Options:
A)51
B)55
C)56
D)57
E)58
Rationale: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (97 - 42) + 1 =56
Option C
Answer: C
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 20 miles per hour and the rest of the distance at an average speed of 80 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip?
Options:
A)(180-x)/2
B)(x+60)/4
C)(300-x)/5
D)600/(115-x)
E)8,000/(400-4x)
Rationale: E....
X% traveeled at 80 mph
100-X% traveeled at 20 mph
total timt taken = x/80 +(100-x)/20 = (400-4x)/80
Total distance = x+(100-x) = 100
Av speed = Tot Dis/Time Taken which is E
Answer: E
Question: Which of the following describes all values of x for which 2–x^2 >= 0?
Options:
A) x >= 1
B) x <= –1
C) 0 <= x <= 2
D) x <= –1 or x >= 1
E) –2 <= x <= 2
Rationale: Which of the following describes all values of x for which 2–x^2 >= 0?
(A) x >= 1
Plugged in 2. 2–(3)^2 >= 0 -7>=0? NO. Wrong
(B) x <= –1
Plugged in -3. 2–(-3)^2 >= 0 -7>=0? NO. Wrong
(C) 0 <= x <= 2
Plugged in 0, 1, and 2. All of them work. But E is better because it describes all the values of x
(D) x <= –1 or x >= 1
A and B answer this. Wrong.
(E) –2 <= x <= 2
X is a positive or negative fraction or a zero.
x = -2 x = 2 x = 0
Plug all of them. They work.
Answer is E.
Answer: E
Question: A man buys an item at Rs. 800 and sells it at the loss of 20 percent. Then what is the selling price of that item
Options:
A)Rs. 640
B)Rs. 760
C)Rs. 860
D)Rs. 960
E)None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 800
= 80/100 * 800
= 640
Option A
Answer: A
Question: A freight elevator can carry a maximum load of 1200 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
Options:
A)25
B)85
C)190
D)215
E)210
Rationale: The average of existing 2 package is (150 + 280)/2 = 430/2 = 215
Remaining allowed weight = 1200 - 200 - 430 = 570
.
allowed per package = 570 / 3 = 190
So difference in average of existing and allowable = 215 - 190 = 25
Hence A
Answer: A
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)5/7
B)5/9
C)5/1
D)5/2
E)5/5
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability
= (5 * 4)/⁹C₂ = 20/36 = 5/9
Answer:B
Answer: B
Question: Sujit incurred a loss of 45% on selling an article for Rs.3410/-. What was the cost price of the article?
Options:
A)Rs.6200/-
B)Rs.5080/-
C)Rs.6250/-
D)Rs.6750/-
E)None of these
Rationale: Explanation:
45% loss means SP of Rs.3410/- is 55% of CP
:. CP = 3410x100/55 = Rs.6200/-
Answer: Option A
Answer: A
Question: Find the least number must be subtracted from 5474827 so that remaining no.is divisible by 12?
Options:
A)3
B)5
C)4
D)7
E)2
Rationale: On dividing 5474827 by 12 we get the remainder 7, so 7 should be subtracted
D
Answer: D
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 7 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
Options:
A)2.5 hours
B)4.5 hours
C)5.5 hours
D)1.5 hour
E)None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 7 hours, Tank A and B can effectively fill 1⁄12 × 7 = 7/12 of the tank.
Time taken to fill the remaining 1−(7/12) = 5/12 of the tank = (5/12)/(1/6) = 2.5 hours. Answer : Option A
Answer: A