divelab/Sys2Bench huggingface dataset:
Question: There are X girls in a class, and their average height is P inches. In the same class, there are Y boys with an average height of Q inches. What is the average height of all the students in the class?
Options:
A)(X + Y)/(M + N)
B)(M + N)/(X + Y)
C)(XM + YN)/(M + N)
D)(XP + YQ)/(X + Y)
E)MN/XY
Rationale: Total height = XP+YQ
No of students = X+Y
Avg = (XP+YQ)/(X+Y)
Answer is D
Answer: D
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.2, 0.1, and 0.7 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
Options:
A)0.061
B)0.12
C)0.218
D)0.216
E)0.941
Rationale: The probability that eachdoesn'thit is: 0.8, 0.9, and 0.3. When we have multiple independent events, we multiply the probabilities:
.8*.9*.3 = 0.216.
Option: D
Answer: D
Question: A and B together have Sterling 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Options:
A)Sterling 460
B)Sterling 484
C)Sterling 550
D)Sterling 664
E)None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1210 x 2/5) = Sterling 484.
Answer: Option B
Answer: B
Question: What is the units digit of (63^4)(41^7)(99^9)?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: The units digit of 63^4 is the units digit of 3^4 which is 1.
The units digit of 41^7 is the units digit of 1^7 which is 1.
The units digit of 99^9 is the units digit of 9^9 which is 9.
Note the pattern: 9^1 = 9, 9^2 = 81, 9^3 = 729,...
The units digit alternates between 9 and 1.
The units digit of 1*1*9 is 9.
The answer is E.
Answer: E
Question: How many factors does 35^2 have?
Options:
A)2
B)8
C)24
D)25
E)26
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*4 = 24
Answer C.
Answer: C
Question: If the cost price of 24 chocolates is equal to the selling price of 16 chocolates, the gain percent is :
Options:
A)24%
B)8%
C)50%
D)40%
E)None of these
Rationale: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 16 chocolates = Rs. 16;
S.P. of 16 chocolates =Rs. 24.
.'. Gain% = 8*100/16 = 50%
Answer : C
Answer: C
Question: Company C sells a line of 25 products with an average retail price of $1,400. If none of these products sells for less than $420, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
Options:
A)16000
B)11400
C)13200
D)15400
E)16800
Rationale: The average price of 25 products is $1,400 means that the total price of 25 products is 25*1,200=$35,000.
Next, since exactly 10 of the products sell for less than $1,000, then let's make these 10 items to be at $420 each (min possible).
Now, the remaining 14 items cannot be priced less than $1,000, thus the minimum possible price of each of these 14 items is $1,000.
Thus the minimum possible value of 24 products is 10*420+14*1,000=$18,200.
Therefore, the greatest possible selling price of the most expensive product is $35,000-$18,200=$16,800.
Answer: E
Answer: E
Question: A volume of 11248 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
Options:
A)2812
B)8231
C)2734
D)4222
E)4254
Rationale: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 11248l can be kept in (11248/4) hemispheres
ans.2812
ANSWER:A
Answer: A
Question: A train 200m long passes a standing man in 15 seconds. What is the speed of the train?
Options:
A)30km/hr
B)36km/hr
C)48km/hr
D)50km/hr
E)32km/hr
Rationale: Speed of the train = 200/15* 18/5 = 48km/hr
Answer is C
Answer: C
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 5 shirts each of them then average number of shirt each of them now has
Options:
A)65
B)63
C)62
D)64
E)61
Rationale: Required average
= Old average + New average
= 60 + 5 = 65
answer :A
Answer: A
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options:
A)2 : 1
B)1 : 2
C)1 : 1
D)4 : 3
E)None of these
Rationale: Explanation :
5% of A + 4% of B = (2/3)(6% of A + 8% of B)
(5A/100) + (4B/100) = (2/3)((6A/100) + (8B/100))
⇒ 5A + 4B = (2/3)(6A + 8B)
⇒ 15A + 12B = 12A + 16B
⇒ 3A = 4B
⇒ A/B = 4/3
⇒ A:B = 4:3
Answer : Option D
Answer: D
Question: A tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A) 5.12%
B) 6.12%
C) 7.12%
D) 8.12%
E) 9.12%
Rationale: We start with 6,500 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 6,500 = 325 gallons of sodium chloride.
When 2,500 gallons of water evaporate we are left with 4,000 gallons of solution. From here we can determine what percent of the 4,000 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(325/4,000) x 100 = ?
0.0812 x 100 = ?
= 8.12%
Answer is D.
Answer: D
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Options:
A)399
B)266
C)150
D)277
E)281
Rationale: 1/2 * 15 * 20 = 150
Answer:C
Answer: C
Question: A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
Options:
A)15
B)66
C)77
D)8
E)54
Rationale: One days's work of A, B and C = 1/90 + 1/30 + 1/45
= (1 + 3 + 2)/90 = 1/15
A, B and C together can do the work in 15 days.
Answer: A
Answer: A
Question: A car has a 20-gallon fuel to travel 500 miles.At this rate, how many gallons of fuel are needed for a 1000 mile car ?
Options:
A)10
B)30
C)20
D)40
E)50
Rationale: Number of gallons of fuel per mile = 500 /20 = 25 gallons per mile
Number of gallons of fuel for a 1000 mile car = 1000/25 = 40
ANSWER:D
Answer: D
Question: What is the area of square field whose side of length 15 m?
Options:
A)225
B)662
C)772
D)882
E)21
Rationale: 15 * 15
= 225 sq m
Answer:A
Answer: A
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 3 years. What is the sum?
Options:
A)122762
B)132877
C)122882
D)133875
E)132887
Rationale: Principal = (100 * 4016.25) / (1 * 3)
= Rs.133875.
Answer:D
Answer: D
Question: A man can buy a new house in 4 years with all of his earnings. But he spend the same amount in household expenses in 8 years and for savings in 12 years. How many time needed for buying the house?
Options:
A)12
B)20
C)30
D)15
E)24
Rationale: His savings in 1 year = 1/4 - (1/8+ 1/12) = 1/24
He can buy a new house in 24 years
ANSWER:E
Answer: E
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Options:
A)1.44%
B)1.74%
C)1.94%
D)2.44%
E)1.47%
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 %
= 1.44%
Answer:A
Answer: A
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent. Overall he make a.
Options:
A)228
B)288
C)27
D)200
E)280
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 11/100) = 8000 + 880
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 880 = Rs. 280
As this is positive, an overall profit of Rs. 280 was made.Answer:E
Answer: E
Question: Two cyclists are running on a circular track of 500m.They start from the same point A at the same time.If they meet for the first time at a point 100 m from A, which of the following could be the possible ratio of their speeds?
Options:
A)1:4
B)2:3
C)3:5
D)5:7
E)7:11
Rationale: well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 100m away from the starting point. This distance between their first meeting can be less than 500 in only two circumstance.
1) if both are travelling in the same direction and one of them has been given a head start say by few meters.
2) or if both are travelling in the opposite direction.
now since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 2:3.
Why?? here is a solution
As here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)
now one of them has covered 100m, therefore other must have covered 400m, therefore ratio of their speeds/velocities will be 1:4
A
Answer: A
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Options:
A)5:3
B)3:5
C)1:5
D)5:1
E)None of them
Rationale: Let 40% of A = 2/3 B
Then, 40A/100= 2B/3
= 2A/5 = 2B/3
= A/B = (2/3) x (5/2)= 5/3
Therefore, A : B = 5 : 3.
Answer is A.
Answer: A
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)152
B)150
C)289
D)369
E)287
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:B
Answer: B
Question: The sum of two numbers is 65 and their product is 1050. What will be the sum of their reciprocals?
Options:
A)(11/140)
B)(11/210)
C)(35/4)
D)(75/8)
E)None
Rationale: Solution
x+y=65 xy=1050 1/x+1/y=x+y/xy 65/1050 = (11/210).
Answer B
Answer: B
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
Options:
A)5 km/hr
B)7 km/hr
C)9 km/hr
D)2 km/hr
E)1 km/hr
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A
Answer: A
Question: Find the third proportional to 2 and 8?
Options:
A)10
B)32
C)36
D)19
E)20
Rationale: Formula = Third proportional = (b × b)/a
A = 2 and B = 8
(8 x 8 )/ 2 = 64/2 = 32
B
Answer: B
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
Options:
A)54
B)432
C)864
D)2,916
E)148,824
Rationale: We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*4C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A).
9C1*4C1*8C1*3C1=864.
Answer: C.
Answer: C
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
Options:
A)38
B)43
C)46
D)49
E)52
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
C
Answer: C
Question: If a positive integer n, divided by 5 has a remainder 2, which of the following must be true
I. n is odd
II. n+1 cannot be a prime number
III. (n+2) divided by 7 has remainder 2
Options:
A)None
B)I only
C)I and II only
D)II and III only
E)I, II and III
Rationale: n can be written as :
n = 5k+2. Thus, taking k=0, we have n=2.
I.n=2,even.False
II.2+1=3, is a prime. False.
III.n+2 = 4,4 divided by 7 leaves a remainder of 4. False.
ANSWER:A
Answer: A
Question: Buffalo gives 4 liter milk, cow gives (1/2) liter milk and goat gives 1/4 liter milk. you have to get 20 liter milk by 20 animals.what is the number of cows?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Assume number of respective animals are x,y,z.
x+y+z=20---(1) as the total number of animal has to be 20
Amt of milk will be 4x+(1/2)y+(1/4)z=20---(2)
Solving equation 1 and 2 we get
15x+y=60 ----(3)
Since buffalo gives 4litre and total milk is 20, x < 5
But from eq 3, x cannot be more than 4;
Further if x=1 or 2; y>20... Not possible, since total animal is 20
Thus, x=3, y=15, z=2
15cows
ANSWER:D
Answer: D
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Options:
A)50 KM
B)60 KM
C)40 KM
D)55 KM
E)120 KM
Rationale: Let the actual distance travelled be x km.
Then,x/10	=(x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km.
ANSWER A
Answer: A
Question: The total weight of six nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
Options:
A)0.18 oz.
B)0.5 oz.
C)1.8 oz.
D)5 oz.
E)1.2 oz
Rationale: Average = Total/Number of items
= 7/6 = 1.2.
Hence, E
Answer: E
Question: A quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs,
also QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the approx area of pqrs
Options:
A)6root(3)
B)12root(3)
C)9root(3)
D)18root(3)
E)12root(3)
Rationale: Lets take, QR=PS= a m and RS=b m, So, PQ=3b m
now if are of a square is 36 sqm, then perimeter is 24
now perimeter of the inscribed quadrilateral is 4b+2a= 24
so, 2b+a=12
from this we can get set of solutions like (a,b)= (6,3), (8,2), (10,2)
Now, formula for area of inscribed quadrilater is root{(s-a)(s-b)(s-c)(s-d)}
Here s= 12
now by trial and error method we can get the solution
appprox area is 18root(3)
ANSWER:D
Answer: D
Question: A man starts from B to K, another starts from K to B, at the same time. After passing each other they complete their journeys in 3.33 and 4.80 hours respectively. Find the speed of the second man if the speed of the first is 12 km/ hr
Options:
A)12 kms/hr
B)10 kms/hr
C)14 kms/hr
D)Data inadequate
E)none
Rationale: 12:x=sqrt(288):sqrt(199.8)
12:x=17:14
x=168/17 ~10km/hr
ANSWER:B
Answer: B
Question: Eight children — A, B, C, D, E, F, G, and H — are going to sit in eight chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?
Options:
A)2520
B)5040
C)10,080
D)20,160
E)40,320
Rationale: The number of ways to seat 8 people is 8! = 40,320.
Child C will sit to the left of Child D in exactly half of these arrangements.
The total number of possible arrangements is 40,320/2 = 20,160
The answer is D.
Answer: D
Question: If the ratio of x to y is 1 to 5, then (y-x)/(x+y)?
Options:
A)-7/3
B)-3/7
C)2/3
D)1
E)2/6
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 1 to 5 means
(x/y)=(1/5)
Cross-multiply
1x = 5y
x = (1/5)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (1/5)*y) / ((1/5)*y + y)
= ((4/5)*y) / ((6/5)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(4/5) / (6/5)
= (4/5) * (6/7)
The 5s cancel each other out, and you are left with 4/6 to 2/3.
Answer: C
Question: A train speeds past a pole in 15 sec and a platform 110 m long in 25 sec, its length is?
Options:
A)165
B)150
C)988
D)177
E)171
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 110)/25 = x/15 => x = 165 m.
Answer: A
Answer: A
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
Options:
A)7 years
B)5 years
C)2 years
D)4 years
E)9 years
Rationale: 4 years
Answer: D
Answer: D
Question: (112 x 54) = ?
Options:
A)67000
B)70000
C)76500
D)77200
E)85200
Rationale: Explanation:
(112 x 54) = 112 x(10/2)4=112 X10 4 /2 4 =1120000/16 =70000
ANSWER IS B
Answer: B
Question: In a company ones salary increases 6/5 times in every year. After 4 year of joining average salary is 1342. Then what's the starting salary of the company?
Options:
A)900
B)1000
C)1100
D)1200
E)1300
Rationale: Let x be initial salary.
After one year it becomes 6/5*x
4 months salary is
x+6/5x +6/5*6/5x+ 6/5*6/5*6/5x + 6/5*6/5*6/5*6/5x =1342*4
By solving we get x =1000
ANSWER:B
Answer: B
Question: There are 5 questions in a question paper. In an examination 5% students answer all questions and 5% answered none. 50% of the rest answered 3 questions and 20% answered 2 questions and 300 answered only 1 question. How many students appeared for the test?
Options:
A)1400
B)1500
C)1600
D)1700
E)1800
Rationale: Let total no.of students be x
x=(x*5/100)+(x*5/100)+(x*50/100)+(x*20/100)+300
100x=(5*x)+(5*x)+(50*x)+(20*x)+30000
100x=80x+30000
20x=30000
x=1500
ANSWER:B
Answer: B
Question: The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?
Options:
A)375
B)2570
C)2800
D)3315
E)None of these
Rationale: Explanation:
Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. Of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cm. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315
ANSWER: D
Answer: D
Question: If 0.5% of A =95 paise, then the value of A is ?
Options:
A)Rs. 190
B)Rs. 17
C)Rs. 1.70
D)Rs. 4.25
E)None
Rationale: Answer
∵ 0.5/100 of A = 95/100
∴ A = Rs. (95 / 0.5) = Rs. 190
Correct Option: A
Answer: A
Question: Look at this series: 83, 80, 85, 82, 87, 84, ... What number should come next?
Options:
A)89
B)95
C)85
D)83
E)80
Rationale: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option A
Answer: A
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
Options:
A)3/105
B)3/103
C)1/108
D)2/113
E)2/115
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: C
Question: The value of (10^7-10^2)/(10^6-10^3) is closest to which of the following?
Options:
A)1
B)10
C)10^2
D)10^3
E)10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^7 - 10^2
10^7 is HUGE compared to 10^2.
So 10^7 - 10^2 is very close to 10^7 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^6 is HUGE compared to 10^3.
So 10^6 - 10^3 is very close to 10^6.
So we have:
10^7/10^6
or 10^(7-6) = 10.
Choose B.
Answer: B
Question: In Town X, 64 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)25%
C)32%
D)34%
E)52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 42 are employed males, hence 22% are employed females.
(employed females)/(total employed people)=22/64=34%
Answer: D.
Answer: D
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'7" tall, which of the following is the median height of the children?
Options:
A)2'2"
B)2'7"
C)3'3"
D)3'4"
E)4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'7"+2'7")/2 = 2'7"
Ans:Option B
Answer: B
Question: How many times digit 6 is used while writing numbers from 80 to 1000?
Options:
A)648
B)300
C)252
D)225
E)26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 225. Hence D.
Answer: D
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
Options:
A)25600.24
B)25600.28
C)25600.17
D)25600.28
E)25600.22
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer: A
Answer: A
Question: A bag consists of 30 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
Options:
A)5/6
B)2/4
C)1/4
D)1/8
E)1/16
Rationale: bag consists of 20 marbles, of which 5 are blue, 9 are red
remainder are white. So, white = 30 - 5 - 9 = 16.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 9/30+16/30 = 25/30 = 5/6
Hence, answer will be A.
Answer: A
Question: If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
Options:
A)55/601
B)601/55
C)11/120
D)120/11
E)120/13
Rationale: given a+b=55,hcm and lcm is 5 and 120
axb=lcmx hcf
600=120x5
1/a+1/b=a+b/ab=>55/600=>11/120
ANSWER:C
Answer: C
Question: An electric pump can fill a tank in 10 hours. Because of a leak in the tank, it took 20 hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
Options:
A)10hours
B)12hours
C)20hours
D)5hours
E)15hours
Rationale: Work done by the leak in 1 hour = 1/10 - 1/20 = 1/20
The leak will empty the tank in 20hours
Answer is C
Answer: C
Question: There are 7 players in a bowling team with an average weight of 76 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
Options:
A)78 Kg.
B)70 Kg.
C)75 Kg.
D)70 Kg.
E)72 Kg.
Rationale: The New average will be= (76*7+110+60)/9= 78 kgs
A is the answer
Answer: A
Question: A fair coin is tossed repeatedly. If heads appears on first 7 tosses what is the probability that tail appears on the next two tosses?
Options:
A)1/6
B)1/5
C)1/3
D)1/4
E)1/6
Rationale: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
Answer: D
Question: Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 42 years. What is Molly's age right now?
Options:
A)24
B)27
C)30
D)33
E)36
Rationale: Now, Sandy is 42 - 6 = 36
Molly's age is (3/4) * 36 = 27
The answer is B.
Answer: B