divelab/Sys2Bench huggingface dataset:
Question: What is the maximum number of pieces of birthday cake of size 4” by 4” that can be cut from a cake 20” by 20”?
Options:
A)5
B)10
C)16
D)20
E)25
Rationale: Each length =20" each piece =4"
Cake could be divided to maximum of 25 pieces
Answer: E
Answer: E
Question: How many ways are there to split a group of 4 girls into two groups of 2 girls each? (The order of the groups does not matter)
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: the combination is 4C2 /2
= 4!/2!*2! *2 = 3
E
Answer: E
Question: Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2
Options:
A)26
B)22
C)25
D)27
E)29
Rationale: (4)^11x (7)^5 x (11)^2
= (2 x 2)^11 x (7)^5 x (11)^2
= 2^11 x 2^11 x7^5x 11^2
= 2^22 x 7^5 x11^2
Total number of prime factors = (22 + 5 + 2) = 29.
Answer is E.
Answer: E
Question: A certain restaurant offers 8 different curry, 5 different main courses, 6 different ice creams. If customers choose one salad, one main course and two different ice creams for their meal, how many different meals are possible?
Options:
A)120
B)240
C)480
D)500
E)600
Rationale: MAGOOSHOFFICIAL SOLUTION:
To count the number of curry, we have to count the possibilities for the three components, and then, according to the Fundamental Counting Principle, we multiply. For more on the FCP, see this blog.
For salads, there are 8 possibilities. Done.
For main courses, there are 5 different possibilities. Done.
For ice creams, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can use the shortcut, nC2 = (n*(n-1))/2.
6C2 = (6*5)/2 = 15
So, there are 15 combinations of two different desserts.
For the number of meals, we multiply 8*5*15. We know 8*5 = 40. Then, we need 40*15. Well, 4*15 = 60, so 40*15 must be 600.
Answer = (E)
Answer: E
Question: In a certain corporation, there are 300 male employees and 150 female employees. It is known that 40% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
Options:
A)1/2
B)2/3
C)3/5
D)7/10
E)11/15
Rationale: P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.4*300/450 = 120/450 = 4/15
The sum of the probabilities is 9/15 = 3/5
The answer is C.
Answer: C
Question: A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)40
B)55
C)60
D)79
E)80
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 10) km/hr.
x - 10 = 45 => x = 55 km/hr.
Answer: Option B
Answer: B
Question: A began business with 12000 and is joined afterwards by B with 72000. When did B join, if the profits at the end of the year are divided equally?
Options:
A)8 months
B)9 months
C)10 months
D)7 months
E)None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 12000 : (12 – x) × 72000
or 12 : 6(12 – x)
Since profit is equally divided so
12 =6(12 – x) or x = 10. Thus B joined after 10 months.
Answer C
Answer: C
Question: A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?
Options:
A)1200
B)1260
C)1301
D)1340
E)1400
Rationale: sol. let the new sp be Rsx.then
(100-loss%) : (1st sp)=(100+gain%) (2nd sp)
{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.
Option B
Answer: B
Question: The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?
Options:
A)100 %
B)200%
C)300%
D)600%
E)None of these
Rationale: Explanation:
Let the salaries of A, B, C be x, 2x and 3x respectively.
Then,2x + 3x = 6000 => x = 1200.
A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.
Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.
Answer: B
Answer: B
Question: A certain number of persons can finish a piece of work in 100 days. If there were 10 persons less, it would take 10 more days finish the work. How many persons were there originally?
Options:
A)90
B)100
C)110
D)120
E)130
Rationale: Explanation:
Assume that x persons can finish a piece of work in 100 days
Also it is given that (x−10) persons can finish a piece of work in 110 days (∵ 100 + 10 = 110)
More persons, less days(indirect proportion)
Hence we can write as(persons) x : (x−10) :: 110 : 100
⇒100x=110(x−10)
⇒100x=110x−1100
⇒10x=1100
⇒x=1100/10=110
Answer: Option C
Answer: C
Question: In how many ways can a team 16 be chosen out of a batch of 20 players?
Options:
A)4845
B)6852
C)3125
D)5846
E)7846
Rationale: Required number of ways= 20C16= 20C(20-16) = 20C4
= (20*19*18*17)/(4*3*2*1)
= 4845.
ANSWER:A
Answer: A
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in meterr?
Options:
A)40 m
B)60 m
C)65 m
D)70 m
E)80 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: Two trains run in opposite directions on a circular track. Train Q travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?
Options:
A)3
B)6
C)9
D)18
E)22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train Q be X, thus that covered by the train B will be 12*3.14-X
dQ = X dB = 12*3.14 - X
Times taken by A and B are
tQ= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of Q and B: totalSpeed = 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tQ =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5.
Answer: B
Question: Complete the numerical series by replacing the question mark with the correct numbers.
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
9+5+5 = ??????
Options:
A)454584
B)454585
C)454586
D)454587
E)None
Rationale: Solution:
454585
Explanation:
Number is formed as (numA*numB)(numB*numC)(numC*numA)
Following the formular, 1st row will be like
5+3+2 => 5*3 3*2 2*5 => 151022
Simillarly
(9*5)(9*5)(9*5+9*5-5) => 454585
Answer B
Answer: B
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
Options:
A)5/1
B)5/9
C)5/8
D)5/6
E)5/2
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 =5/9.
Answer:B
Answer: B
Question: If 12 machine can finish a job in 40 days, then how many more machines would be needed to finish the job in one -fourth less time?
Options:
A)a. 4
B)b. 8
C)c. 10
D)d. 12
E)e. 16
Rationale: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 12 machines (identical ones, I assume) work simultaneously for 40 days, they will do a total of 12*40 machine-days of work. So the job requires 12*40 days of machine work in total. We instead want the job done in 1/4 less time, so in 30 days. So we'll need 12*40/30 = 16 machines, or 4 additional machines.
A
Answer: A
Question: In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?
Options:
A)$2.4 million
B)$2.9 million
C)$3.0 million
D)$3.1 million
E)$3.6 million
Rationale: Let the number of pairs of shoes sold in 1985 = N
let price per pair of shoe sold in 1985 = P
In 1986,number of pairs of shoes sold decreased by 20 % = .8N
Price per pair increased by 20% = 1.2P
Company's revenue from sale of shoes in 1986 = 3 million$
=> .8N * 1.2 P = 3
=>.96 NP = 3
=> NP = 3/.96 = 3.125 million $
Answer D
Answer: D
Question: If E is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)E(E+1)(E-4)
B)N(N+2)(N-1)
C)N(N+3)(N-5)
D)N(N+4)(N-2)
E)N(N+5)(N-6)
Rationale: Now take E = 3k , E = 3k+1 E = 3k+2..put in all the choices. If by putting all the values of E we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: A
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)76 m
B)178 m
C)235 m
D)187 m
E)176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2
=> 2(140 + x)= 750 => x = 235 m.
Answer: C
Answer: C
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 45 true?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Answer B
(a+b)(a-b)=45
3cases For (a+b), (a-b)
45, 1
15, 3
9, 5
Answer B
Answer: B
Question: Miguel is 50 years old. He is 5 years older than thrice his son’s age. Find the age of his son.
Options:
A)11years
B)12years
C)13years
D)14years
E)15years
Rationale: sons age=x
50-3x=5
x=15years
ANSWER:E
Answer: E
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth.The percentage of decrease in area is :
Options:
A)13%
B)14%
C)18%
D)20%
E)28%
Rationale: Let original length =x and original breadth =y.
Decrease in area =xy-(80/100*x*90/100*y)=(xy-18/25*xy)=7/25*xy.
Decrease% = (7/25*xy*1/xy*100)%=28%.
Answer is E
Answer: E
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)3000
B)1230
C)2000
D)5600
E)3400
Rationale: C
C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
Answer: C
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)1/25
B)2/21
C)5/26
D)3/41
E)1/115
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: C
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?
Options:
A)777
B)500
C)789
D)776
E)881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
Answer B
Answer: B
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)8/3
B)2
C)8/5
D)5/8
E)5/3
Rationale: Distance traveled by Eddy = 450 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 450/3 = 150 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 150/75 = 2
Answer B
Answer: B
Question: What is x if x + 2y = 10 and y = 3?
Options:
A)10
B)8
C)6
D)4
E)2
Rationale: Substitute y by 3 in x + 2y = 10
x + 2(3) = 10
x + 6 = 10
If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10.
x = 4
correct answer is D) 4
Answer: D
Question: A factory has a fixed cost of $35,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
Options:
A)9,000
B)14,000
C)18,000
D)22,500
E)27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =35000
no of items required = 35000/2.5 = 14000
Ans B
Answer: B
Question: A deer is standing 60 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 15 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?
Options:
A)125
B)135
C)145
D)155
E)165
Rationale: Let x be the length of the tunnel.
When the deer runs 60 meters west, the train goes 600 meters to a point 15 meters from the west entrance of the tunnel.
When the deer runs east, the deer runs x-60 meters while the train goes x + 600 + 15 meters.
x + 600 + 15 = 10(x-60)
9x = 1215
x = 135 meters
The answer is B.
Answer: B
Question: The triplicate ratio of 1:4 is?
Options:
A)1:64
B)1:62
C)1:34
D)3:64
E)5:64
Rationale: 1^3: 4^3 = 1:64
ANSWER:A
Answer: A
Question: Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
Options:
A)188
B)100
C)177
D)268
E)266
Rationale: Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 100 min.
AnswerB
Answer: B
Question: There are 3 questions in a question paper. If the questions have 4,3 and 2 solutions respectively, find the total number of solutions
Options:
A)24
B)25
C)30
D)40
E)54
Rationale: Here question 1 has 4 solutions, question 2 has 3 solutions and question 3 has 2 solutions.
=> By the multiplication (counting) rule,
Total number of solutions=4Ã—3Ã—2==4Ã—3Ã—2= 24
ANSWER A
Answer: A
Question: ram draws a card randomly among card 1-23 and keep it back.then sam draws a card among those.what is the prob than sam has drawn a card greatr than ram?
Options:
A)11/23
B)12/23
C)13/23
D)14/23
E)15/23
Rationale: Sum of probability of drowing a card greater than drawn by ram is (22/23)+(21/23)+.....(1/23)=253/23
but probability for choosing 1 card out of 23 is 1/23
therefore total probability is (253/23)*(1/23)=(11/23)
ANSWER:A
Answer: A
Question: Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together ?
Options:
A)100/11 min past 8
B)100/11 min past 9
C)100/11 min past 2
D)100/11 min past 1
E)100/11 min past 5
Rationale: Explanation:
In this type of problems the formulae is
x is replaced by the first interval of given time Here i.e 8
= min
Therefore the hands will be in the same straight line but not
together at min.past 8.
Answer: A) 100/11 min past 8
Answer: A
Question: A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)87
C)26
D)21
E)44
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:E
Answer: E
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
Options:
A)Rs.287
B)Rs.429
C)Rs.480
D)Rs.412
E)Rs.482
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:C
Answer: C
Question: How many three letter words are formed using the letters of the word TIME?
Options:
A)12
B)14
C)18
D)24
E)61
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer:D
Answer: D
Question: If chemistry book page and math book page ratio is 6:5.A child tore 25 page from chemistry book and 15 page from Math book.Now,ratio becomes 1:1.so,tell the initial no. of pages of chemistry.
Options:
A)50
B)60
C)70
D)80
E)40
Rationale: Chemistry pages=6x,Math pages=5x
6x-25/5x-15=1/1
6x-25=5x-15,6x-5x=10,x=10
chemistry pages=6x=60pages
answer B
Answer: B
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
Options:
A)12
B)16
C)24
D)48
E)50
Rationale: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
answer :D
Answer: D
Question: By selling 20 pencils for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?
Options:
A)8.56
B)10.75
C)14.5
D)16.5
E)11.4
Rationale: 70% --- 20
130% --- ?
70/130 * 20 = 10.75
Answer: B
Answer: B
Question: On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out
sand-dunes, 1 has treasure and only 2 out of 5 sand dunes formed have lucky coupons. Find
the probability that the blown-out sand dune will contain both the things.
Options:
A)2/25
B)4/75
C)7/75
D)3/5
E)4/5
Rationale: Probabilty of sand dune blown out = 2/3
Probabilty that it has treasure = 1/5
Probability that it has lucky coupon = 2/5
total probability = 2/3 * 1/5 * 2/5 = 4/75
ANSWER:B
Answer: B
Question: A car manufacturer sold 500 mini vans at $10000 each, 200 hatchbacks at $8000 each, and 220 sports utility vehicles at $18000 each. what percentage of the company's revenue is from the sale of sports utility vehicles?
Options:
A)27.5%
B)50.4%
C)37.5%
D)29.7%
E)39.5%
Rationale: Correct Answer: C
The company's total revenue from mini vans=500* $10000=$5 000 000
The company's total revenue from hatchbacks=200*$8000=$1 600 000
The company's total revenue from sports utility vehicles=220*$18000=$3 960 000
The combined total of all sales=$10560000
Therefore % of sports utility vehicles sales=3 960 000/10560000*100= 37.5%
Answer: C
Question: A number x is 6 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)83.3%
C)80.5%
D)81%
E)1%
Rationale: Say y=1 and x=6.
Then y=1 is less than x=6 by (6-1)/6*100=5/6*100=83.3%.
Answer: B.
Answer: B
Question: Rahul and Sham together can complete a task in 35 days, but Rahul alone can complete same work in 60 days. Calculate in how many days Sham can complete this work ?
Options:
A)84 days
B)82 days
C)76 days
D)68 days
E)60 days
Rationale: Explanation:
As Rahul and Sham together can finish work in 35 days.
1 days work of Rahul and Sham is 1/35
Rahul can alone complete this work in 60 days,
So, Rahul one day work is 1/60
Clearly, Sham one day work will be = (Rahul and Sham one day work) - (Rahul one day work)
=1/35-1/60
=1/84
Hence Sham will complete the given work in 84 days.
ANSWER IS A
Answer: A
Question: 7 teams compete in a track competition. If there are 12 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 3(max wins) x 4 = 12 (4 teams win three events)
The answer is B.
Answer: B
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)40 days
B)20 days
C)30 days
D)60 days
E)40 days
Rationale: C
30 days
C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)54
B)90
C)64
D)92
E)98
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 16 sec. What is the length of the platform?
Options:
A)287 m
B)431.25 m
C)267 m
D)287.25 m
E)656 m
Rationale: Speed = 300/16 = 75/4 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 75/4
=> x = 731.25 m
Answer:B (431.25)
Answer: B
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: A
Question: Ritesh and Co. generated revenue of Rs. 1,250 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
Options:
A)12.5%
B)20%
C)25%
D)50%
E)None of these
Rationale: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,250 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1250 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1250.
=>10,000.
Hence, the total revenue by end of 2007 is Rs. 10,000. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/10000)×100.
=>25%.
Answer : C
Answer: C
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream?
Options:
A)15
B)17
C)14
D)18
E)16
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 51/3 = 17 kmph.
Answer:B
Answer: B
Question: If a, b, and c are integer and ab + c is odd, which of the must be true?
I. a + c is odd
II. b + c is odd
III. abc is even
Options:
A)I only
B)II only
C)III only
D)I and III only
E)II and III only
Rationale: Personally I'd approach this question in another way.
ab+c=odd, means:
1. ab=even (which means that at least one of them is even) and c=odd
OR:
2. ab=odd (which means that both are odd) and c=even
We can see that in both cases at least one is even thus option III (abc=even) is always true.
Now, for I: if c=odd(case 1) and a=odd(so b=even) then a+c=even≠odd, so this option is not always true.
Exactly the same for option II: if c=odd (case 1) and b=odd (so a=even) then b+c=even≠odd, so this option is not always true.
Answer: C (III only).
Answer: C
Question: A number is missing from the number series below.
Can you find it ?
84, 155, 258, 399 ,?, 819.
Options:
A)275
B)350
C)399
D)584
E)449
Rationale: D
The missing number is 584.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
258 = 6^3 + 6^2 + 6
399 = 7^3 + 7^2 + 7
819 = 9^3 + 9^2 + 9
Thus,
584 = 8^3 + 8^2 + 8
Answer: D
Question: What is the lowest positive integer that is divisible by 8 through 11, inclusive?
Options:
A)999
B)7811
C)6555
D)9200
E)7920
Rationale: The integer should be divisible by: 8, 9, 10 and 11. The least common multiple of these integers is LCM=8*9*10*11=7920
Answer: E
Answer: E
Question: The sum of two numbers is 24 and their product is 148. Find the sum of the squares of that numbers.
Options:
A)250
B)280
C)230
D)290
E)250
Rationale: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=24ab=148 So, 24^2=a^2+b^2+2*148576=a^2+b^2+296a^2+b^2=280Ans B
Answer: B