divelab/Sys2Bench huggingface dataset:
Question: A cab driver 5 days income was $300, $150, $750, $200 , $600. Then his average income is?
Options:
A)$350
B)$375
C)$400
D)$425
E)$450
Rationale: avg = sum of observations/number of observations
avg income=(300+150+750+200+600)/5 = 400
Answer is C
Answer: C
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)2898
B)277
C)500
D)297
E)435
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: C
Answer: C
Question: Assume the equation U = mgh. If m is quadrupled and h is halved, by what factor does U change?
Options:
A)3
B)2
C)4
D)1/2
E)16
Rationale: The equation is U = mgh.
If m is quadrupled and h is halved, the equation becomes:
U = (4m)*g*(h/2)
U = 2mgh
Initially U was mgh and now it is 2mgh, therefore U increases by a factor of 2.
Answer = B = 2
Answer: B
Question: 3, 7, 15, 31, 63, ?
Options:
A)89
B)127
C)142
D)158
E)168
Rationale: Each number in the series is the preceding number multiplied by 2 and then increased by 1.
Answer : B.
Answer: B
Question: The probability that event B occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event A will occur?
Options:
A)0.05
B)0.45
C)0.15
D)0.5
E)0.55
Rationale: P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(A) - 0.25
P(A) = 0.45
Ans : B
Answer: B
Question: There are 7 magazines lying on a table; 4 are fashion magazines and the other 3 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
Options:
A)1/2
B)7/8
C)32/35
D)11/12
E)13/14
Rationale: answer is B
Total probability=8C3=48
4C3 +4C2*4C1+4C1*4C2=4+24+24=42
therefore the probability that at least one of the fashion magazines will be selected=42/48=7/8
B
Answer: B
Question: Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 4 hours. How long would it take Taimour to paint the fence alone?
Options:
A)6 hours
B)8 hours
C)12 hours
D)24 hours
E)32 hours
Rationale: I believe the answer is C. Please see below for explanation.
if Jamshid can paint a dence in 50 percent less time then Taimour we can infer the following rate J = 2T
if working together they can do the job in 8 hours we can infer 1 = 2T+T * 4 => 1/12
Working alone Taimour can do the job in 1 = 1/12 * hours => 12
Answer C
Answer: C
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent R of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
Options:
A)9%
B)11%
C)15%
D)25%
E)90%
Rationale: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is R= .25/ 1 *100 = 25% D is the answer.
Answer: D
Question: Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 40 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 40 minutes, for how many kilometers total did she hike east?
Options:
A)3.625
B)3.5
C)3
D)3.04
E)4
Rationale: Set up two R x T =D cases.
1. 1/12 km/ min x T = 2.75
from which T= 33 mins.
We know total journey time now is 40 +33 =73.
The rate is the same ie 1/12km/min.
set up second R x T =D case.
1/12 km/min x 73 = 6.08 km
Now the total journey would be halved as distance would be same in each direction. 6.08/2 =3.04
D.
Answer: D
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 32 percent of the total votes?
Options:
A)10%
B)12.5%
C)15%
D)17.5%
E)20%
Rationale: There were 80% of the votes remaining and he needed 12%/80% = 3/20 = 15%
The answer is C.
Answer: C
Question: If DREAM is coded as 78026 and CHILD is coded as 53417,how can LEADER be coded ?
Options:
A)102078
B)102708
C)102087
D)102780
E)102790
Rationale: from given two words L=1 E=0 A=2 D=7 E=0 and R=8
ANSWER:B
Answer: B
Question: A number when divided by 4, gives 40 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 3
Options:
A)A)1
B)B)3
C)C)4
D)D)6
E)E)7
Rationale: Explanation:
P ÷ 4 = 40
=> P = 40 * 4 =160
P / 3 = 160/ 3 = 53, remainder = 1
Answer: Option A
Answer: A
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)6
C)8
D)9
E)6
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer:A
Answer: A
Question: The salary of a person was reduced by 28%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
Options:
A)10%
B)15%
C)20%
D)25%
E)38.9%
Rationale: Let the original salary be $100
new salary = $72
increase on 72 = 28
increase on 100 = [(28/72)100]% = 38.9%
Answer is E
Answer: E
Question: In honor of the year 2014, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
Options:
A)18
B)36
C)42
D)55
E)56
Rationale: All options other than 'D' are factors of 2014. Hence, 'D' is the answer
Answer: D
Question: The ratio of Gomati’s and Rashmi’s ages is 3 : 5 respectively. After ten years this ratio will become 2 : 3. What is Rashmi’s age in years?
Options:
A)50
B)40
C)60
D)Cannot be determined
E)None of these
Rationale: Quicker Method : After 10 years, the ratio of Gomati and Rashmi’s ages is 2 : 3. We can also write 2 : 3 as 4 : 6. Now, difference in the ratio is I in both the cases.
Therefore, 1 = 10
∴ 5 → 5 × 10 = 50 years.
Answer A
Answer: A
Question: a man leaves office daily at 7 pm, a driver with car comes from his home to pick up him from office and bring back home.one day he gets free at 5:30 pm....,instead of waiting for car ,he starts walking towards his home,on the way he meets the car and returns home by car,he reaches home 20 minutes earlier than usual. In how much time does he reach home usually ?
Options:
A)1 hr and 20 mins
B)1 hr and 30 mins
C)1 hr and 40 mins
D)1 hr and 10 mins
E)1 hr and 50 mins
Rationale: Since the car has met the person 20 minutes before hand, it has actually saved 10 mins of journey (to and fro)
since the man has started 1.30 hrs before and car has met him 10 mins before actual time he takes to reach daily is 1 hr and 20 mins
ANSWER:A
Answer: A
Question: How many positive integers I less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
Options:
A)19
B)18
C)17
D)16
E)15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: E
Question: In Richie's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
Options:
A)43.0
B)45.5
C)46.0
D)49.0
E)50.0
Rationale: In Richie's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=A
Answer: A
Question: Souju's age is 1/4th of her father's age. Souju's father's age will be twice Tharak's age after
10 years. If Tharak's eight birthdays was celebrated two years before, then what is Souju's present age.
Options:
A)6.5
B)7.5
C)8.5
D)8
E)9
Rationale: tharak's present age =8+2=10
souju's father's age after 10 years =2(10+10)=40
souju's father's present age =40−10=30
tharak's present age =1/4 *30=7.5
ANSWER:B
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)150
B)781
C)767
D)277
E)266
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: A
Answer: A
Question: Price of a book increases 15% successively (2times) what is the new price of the book more compared to that of the old price:
Options:
A)32.25%
B)23.34%
C)36%
D)39%
E)29%
Rationale: New price is 1.15*1.15*old price = 1.3225 *old price
Increase in price = 0.3225 * old price
% increase = 100* 0.3225 * old price /old price = 32.25 %
ANSWER:A
Answer: A
Question: A is 16th position and 29th from down of the people who passed. 5 failed , 6 didn't give . how many boys are there in the class?
Options:
A)52
B)53
C)54
D)55
E)56
Rationale: A is 16th position, means = 15 + A
29th from down, means = A + 28
Total passed = A + 15 + 28 = 44
Total failed = 5
Didn't give = 6
Therefore, total boys = 44 + 5 + 6 = 55
ANSWER:D
Answer: D
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Options:
A)2 : 3
B)4 : 3
C)6 : 7
D)9 : 16
E)None of these
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
Answer B
Answer: B
Question: 9 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
Options:
A)1:2
B)1:3
C)2:1
D)2:5
E)None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 9x + 2y = 4(x+y)
=> 5x = 2y
=> x/y = 2/5
=> x:y = 2:5
Option D
Answer: D
Question: The speed of a car is 90 km in the first hour and 42 km in the second hour. What is the average speed of the car?
Options:
A)89 kmph
B)92 kmph
C)75 kmph
D)65 kmph
E)66 kmph
Rationale: S = (90 + 42)/2 = 66 kmph
E
Answer: E
Question: How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 12, without any of the digits repeating?
Options:
A)100
B)98
C)81
D)96
E)72
Rationale: 0,1,2,3,4,5
One digit will have to remain out for all 5 digit numbers;
if 0 is out; Leftover digits will be 1,2,3,4,5 = Sum(1,2,3,4,5)=15. Ignore
if 1 is out; Leftover digits will be 0,2,3,4,5 = Sum(0,2,3,4,5)=14. Ignore
if 3 is out; Leftover digits will be 0,1,2,4,5 = Sum(0,1,2,4,5)=12.
4*4! = 4*24 = 96
if 4 is out; Leftover digits will be 0,1,2,3,5 = Sum(0,1,2,3,5)=11. Ignore
if 5 is out; Leftover digits will be 0,1,2,3,4 = Sum(0,1,2,3,4)=10. Ignore
Total count of numbers divisible by 12 = 96
Ans:D
Answer: D
Question: 6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
Options:
A)30
B)21
C)18
D)15
E)10
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 6(6-1)/2 = 6*5/2 = 30/2 = 15
=> the answer is D(15)
Answer: D
Question: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
Options:
A)10
B)5
C)15
D)20
E)25
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.
Answer is D.
Answer: D
Question: Which of the following correctly lists the data sets in order of greatest to least standard deviation?
I. 4, 12, 15, 17, 19, 25
II. 42, 42, 42, 42, 42, 42
III. 57, 58, 59, 50, 51, 52
Options:
A)II, I, III
B)I, III, II
C)I, II, III
D)II, III, I
E)III, II, I
Rationale: out of three given sets,
II has all numbers same, so it has zero standard deviation hence it is Least
only answer choices C and D have II in least position.
Out of I ans III
III has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in I,numbers are spread widely hence std deviation should be more than III
hence order should be II, III, I
IMO C
Answer: C
Question: If Rs. 782 be divided into three parts, proportional to 1/2:2/3 :3/4, then the first part is:
Options:
A)202
B)201
C)205
D)206
E)204
Rationale: Given ratio = 1/2: 2/3:3/4
= 6 : 8 : 9.
Therefore, 1st part = Rs. (782 x 6/23)= Rs. 204.
Answer is E.
Answer: E
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, 2X + 3Y + 3Z = 5Y + 11. What is the value of Z?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
2X + 3Y + 3Z = 5Y + 11
2Z+4+3Z+3+3Z = 5Z+5+11
3Z = 9
Z = 3
The answer is B.
Answer: B
Question: The population of a town increased from 1,75,000 to 2,97,500 in a decade. The average percent increase of population per year is
Options:
A)4.37%
B)5%
C)6%
D)8.75%
E)7%
Rationale: Solution
Increase in 10 years	= (297500 - 175000)
= 122500
Increase%	= (122500/175000Ã—100)%
= 70%.
Required average	= (70/10)%
= 7%.
Answer E
Answer: E
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1600 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140
B)99
C)88
D)160
E)12
Rationale: Given that the area of the square = 1600 sq.units
=> Side of square = √1600 = 40 units
The radius of the circle = side of the square = 40 units Length of the rectangle = 2/5 * 40 = 16 units
Given that breadth = 10 units
Area of the rectangle = lb = 16 * 10 = 160 sq.units
Answer: D
Answer: D
Question: If a tap could fill entire tank in 20 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 16 hrs without leakage
Options:
A)12hrs
B)24hrs
C)36hrs
D)80hrs
E)52hrs
Rationale: time take to fill[withleakage] =20hrs so workdone in 1hr=1/20
time tkae to fill[without leakage]=16hrs so workdone in 1hr=1/16
if u subtract both u'll get time taken by leakage to empty...
1/20-1/16=1/80 so 80hrs
ANSWER:D
Answer: D
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
Options:
A)2
B)8
C)1
D)6
E)5
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 20 km in 4 hours.
But he took 10 hours.
He would have saved 10 – 4 = 6 hours.
Answer: D
Answer: D
Question: Look at this series: 544, 509, 474, 439, 404, 369 ... What number should come next?
Options:
A)334
B)408
C)306
D)507
E)404
Rationale: 334
This is a simple subtraction series. Each number is 35 less than the previous number.
A
Answer: A
Question: The cost of type 1 rice is Rs 15 per Kg and type 2 rice
is Rs 20 per Kg. If both type1 and type 2 are mixed in the
ratio of 2:3,then the price per Kg of the mixed variety
of rice is?
Options:
A)15
B)17
C)19
D)18
E)16
Rationale: Let the price of the mixed variety be Rs x per Kg.
Cost of 1 Kg of type 1 rice Rs 15 Cost of 1 Kg of type 2 rice Rs 20
Mean Price Rs x
20-x x-15
(20-x) /( x-15) = 2/3
=> 60-3x = 2x-30
5x = 90=>x=18.
ANSWER : D 18
Answer: D
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
Options:
A)3% decrease
B)5% decrease
C)9% decrease
D)4% decrease
E)8% decrease
Rationale: (30 * 30)/100 = 9% decrease
Answer:C:
Answer: C
Question: A money lender lent Rs. 1000 at 4% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
Options:
A)3.2
B)3.75
C)4
D)4.25
E)4.5
Rationale: (1000xtx4/100) + (1400xtx5/100) = 350 â†’ t =3.2 answer A
Answer: A
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x + 4, y + 4, z + 4 ?
Options:
A)4d
B)d
C)5d
D)d+4
E)d+16
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 4 is added in each term of set {x, y, z} then the new set {x+4, y+4, z+4} will remain same as the previous standard deviation i.e. d
Answer: B
Answer: B
Question: A batsman makes a score of 100 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
Options:
A)40
B)50
C)62
D)45
E)56
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+100 = 11x
x = 100-50 = 50
Answer is B
Answer: B
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges= 40 percent of the remainder the cost, how much less would 2 machines of type A cost than 1 machine of type B?
Options:
A)$10,000
B)$11,200
C)$12,000
D)$12,800
E)$13,200
Rationale: 1 machine of type B will cost: 20% down payment of 50,000 = 10,000 plus remaining sum (50,000-10,000=40,000) with 40% of finance charges 40,000*1.4=56,000 --> 10,000+56,000=66,000;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000 plus remaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 66,000 - 52,800 = 13,200.
Answer: E.
Answer: E
Question: If simple interest on a certain sum of money for 8 years at 4% per annum is same as the simple interest on Rs. 560 for 8 years at the rate of 12% per annum then the sum of money is
Options:
A)Rs.1820
B)Rs.1040
C)Rs.1120
D)Rs.1680
E)None of these
Rationale: Explanation:
Let the sum of money be x
then
(x × 4 × 8)/100 = (560 × 12 × 8)/100
x × 4 × 8 = 560 × 12 × 8
x × 4 = 560 × 12x = 560 × 3 = 1680
Answer: Option D
Answer: D
Question: The average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for tour is:
Options:
A)5
B)10
C)20
D)30
E)40
Rationale: Explanation :
Let the initial number of persons be x. Then,
=> 16x + 20 x 15 -15.5 (x + 20)
=> 0.5x = 10
=> x = 20
Answer : C
Answer: C
Question: A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?
Options:
A)8
B)7
C)5
D)2
E)1
Rationale: 70 * (10/100) = 7
Wine Water
87 1/2% 12 1/2%
87 1/2% ------- 63
12 1/2% -------? => 9-7=2
Answer: D
Answer: D
Question: Which of the following are roots of an equation (x^-2)-(x^-1)-30=0
Options:
A)1/5 and -1/6
B)-1/5 and 1/6
C)1/5 and 1/6
D)-1/5 and -1/6
E)-5/2 and -1/6
Rationale: Given: (x^-2) - (x^-1) - 30 = 0
Rewrite as: 1/(x²) - 1/x - 30 = 0
Remove fractions by multiplying both sides by x² to get: 1 - 1x - 30x² = 0
Rearrange to get: 30x² + x - 1 = 0
Factor to get: (5x + 1)(6x - 1) = 0
So, EITHER 5x + 1 OR 6x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 6x - 1 = 0, then x = 1/6
So, the roots (solutions) are -1/5 and 1/6
The answer is B.
Answer: B
Question: A drink vendor has 80 liters of Mazza, 144 liters of Pepsi, and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.
So, the number of liters in each can = HCF of 80,144 and 368 = 16 liters.
Now, number of cans of Maaza = 80/16 = 5
Number of cans of Pepsi = 144/16 = 9
Number of cans of Sprite = 368/16 = 23
Thus, the total number of cans required = 5 + 9 + 23 = 37 Answer: C
Answer: C
Question: Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?
Options:
A)100m
B)75m
C)120m
D)50m
E)70m
Rationale: since both trains move in same direction so:
average speed=50-32=18kmph=5mps
speeed=length of train /time
length of train=5*15=75m
ANSWER:B
Answer: B
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
Options:
A)39, 30
B)41, 32
C)42, 33
D)43, 34
E)42, 34
Rationale: Let their marks be (x + 9) and x.
Then, x + 9 = 56/100(x + 9 + x)
25(x + 9) = 14(2x + 9)
3x = 99
x = 33
So, their marks are 42 and 33.
answer :C
Answer: C
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 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)21
B)88
C)40
D)99
E)22
Rationale: Relative speed = 60 + 30 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 *1/25 = 40 sec
Answer: C
Answer: C
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of n?
Options:
A)11
B)12
C)15
D)18
E)22
Rationale: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, n = m + 1(Michael) = 12
option B
Answer: B
Question: Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was six times as old as Sam. How old is Jim now?
Options:
A)30
B)34
C)38
D)42
E)46
Rationale: J = 2F = 2(S+9) = 2S+18
J-6 = 6*(S-6)
(2S+18)-6 = 6S-36
S = 12 and so J = 42
The answer is D.
Answer: D
Question: The average of 11 numbers is 9.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
Options:
A)71.5
B)11.5
C)81.5
D)11.5
E)22.5
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 9.9 x 11] = 22.5.
Answer: E
Answer: E