divelab/Sys2Bench huggingface dataset:
Question: The average age of a class of 42 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)45 Years
B)46 Years
C)59 Years
D)52 Years
E)54 Years
Rationale: Total age of students is 42X16 = 672 Years Total age inclusive of teacher = 43X (16+1) = 731 So, Teacher's age is 731-672= 59 Yrs There is a shortcut for these type of problems Teacher's age is 16+(43X1) = 59 Years Answer : C
Answer: C
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is
Options:
A)Rs.9471
B)Rs.12,628
C)Rs.18,040
D)Rs.12,228
E)None
Rationale: Solution
Ratio of their shares	=(35000Ã—8):(42000Ã—10)
= 2 : 3.
Suganya's share	= Rs.(31570 Ã—2/5)
= Rs.12228.
Answer D
Answer: D
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be.
Options:
A)60 km/h
B)55 km/h
C)40 km/h
D)70 km/h
E)80 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph
Answer : A.
Answer: A
Question: A train 650 m long is running at a speed of 117 km/hr. In what time will it pass a bridge 325 m long?
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Speed = 117 * 5/18 = 65/2 m/sec
Total distance covered = 650 + 325 = 975 m
Required time = 975 * 2/65 = 30 sec
Answer: A
Answer: A
Question: Find the value of ( 0.75 * 0.75 * 0.75 - 0.001 ) / ( 0.75 * 0.75 - 0.075 + 0.01)
Options:
A)0.845
B)1.908
C)2.312
D)0.001
E)0.002
Rationale: (0.75*0.75*0.75-0.001)=0.75^3 -0.1^3
0.75*0.75-0.075+0.01=0.75^2-0.1^2
a^3-b^3=(a+b)(a^2-ab+b^2)
so after cancellation remainning term is (a+b) i.e 0.75+0.1=0.85
nearly to 0.845
ANSWER:A
Answer: A
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
Options:
A)9 years
B)29 years
C)18 years
D)19 years
E)17 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 34 * 3 = 196 - 75 - 102 = 19 years.
ANSWER:D
Answer: D
Question: A train speeds past a pole in 25 seconds and a platform 150 m long in 30 seconds. Its length is?
Options:
A)23
B)22
C)21
D)30
E)19
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 25 => y = x/25
(x + 150) / 30 = x / 25
x = 30 m.
Answer:D
Answer: D
Question: Two trains are moving in opposite directions with speed of 150 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
Options:
A)56
B)48
C)47
D)30
E)25
Rationale: Explanation:
Relative speed = 150+90 = 240 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/240 hr = 1/120 hr = 3600/120 seconds = 30 seconds
Answer: Option D
Answer: D
Question: LCM of 2/7,3/14 and 5/3is
Options:
A)45
B)35
C)30
D)25
E)None
Rationale: Explanation:
LCM of numerators /HCF of denominators= LCM of 2, 3, 5/HCFof7,14,3 = 30/1=30
Correct Option: C
Answer: C
Question: A man can do a piece of work in 5days, but with the help of his son, he can finish it in 4days. In what time can the son do it alone?
Options:
A)5
B)5 1/2
C)7 1/2
D)6
E)20
Rationale: Son's 1day work = 1/4 - 1/5 = 1/20
Son alone can do the work in 20days = 20 days
Answer is E
Answer: E
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.13000 after a year?
Options:
A)3630
B)3900
C)8828
D)2387
E)2813
Rationale: 6300:4200:10500
3:2:5
3/10 * 13000 = 3900
Answer: B
Answer: B
Question: An error 1% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options:
A)2.01
B)30.1
C)3.01
D)25.01
E)4.05
Rationale: Explanation:
100 cm is read as 101 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (101 × 101)cm2= 10609
(A2 - A1) = 10201-10000 = 201
=> 201/10000*100 =2.01
Answer : A
Answer: A
Question: If the cost price is 81% of selling price then what is the profit percentage.
Options:
A)22.45
B)23.45
C)32.45
D)23.54
E)23.55
Rationale: selling price=Rs100 : then cost price=Rs 81:profit =Rs 19.
Profit={(19/81)*100}%=23.45%
Answer is B.
Answer: B
Question: Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
Options:
A)1/7
B)1/6
C)1/5
D)1/2
E)1/3
Rationale: Suppose the portion of her salary that she saved is X
and the remaining portion is Y
X+Y= total take home salary
given, 12X = 6Y
or 2X = Y
Total take-home salary= X+ 2X= 3X
hence, she saved 1/3-rd portion of her take home salary
E
Answer: E
Question: On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 800 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
Options:
A)$5
B)$15
C)$23
D)$100
E)$105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
500(1.10)^2 = 500(1.21) = 605
and Lana would have
800(1.05)^2 = 800(1.1025) = 882
Thus, Tim earned 105 dollars, while Lana earned 82 dollars
The difference is $23 and the answer is C.
Answer: C
Question: John completes a piece of work in 320 days, Rose completes the same work in 480 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)190
B)192
C)194
D)196
E)198
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 320 × 480/800 = 192 days
Answer is B
Answer: B
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
A)20
B)18
C)12
D)14
E)15
Rationale: A's 2 day's work = 1/20 x 2 = 1/10
(A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 1/10
Work done in 3 days = A's 2 day's work + (A + B + C)'s 1 day's work
Work done in 3 days = 1/10 + 1/10
Now, work is done in 3 days = 2/10 = 1/5
So, 1/5 cork is done in 3 days.
So, work will be done in (3 x 5) = 15 days.
So, correct answer is E
Answer: E
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 23?
Options:
A)101
B)187
C)191
D)201
E)264
Rationale: ok, not sure if this is the best explanation, but here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 23 = t 3 + 3 + 4 + 5 + 6....+ 22
the 3 + 4 + 5 + ... + 22 sequence is equal the sequence 1 + 2 + ... + 22, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 22 sequence is equal to n*(n+1)/2 with n being 22, so equal to 22 * 23 / 2 = 253
so :
t 23 = t 3 + 253 - 3
t 23 = 14 + 253- 3 = 253 + 11 = 264, hence answer E
Answer: E
Question: Out of seven models, all of different heights, five models will be chosen to pose for a photograph. If the five models are to stand in a line from shortest to tallest, and the fourth-tallest and sixth-tallest models cannot be adjacent, how many different arrangements of five models are possible?
Options:
A)6
B)11
C)17
D)72
E)210
Rationale: Total no. of ways "5 models can be selected from 7" = 7C5 = 21.
Fourth tallest and Sixth tallest can never stand adjacent to each other. Also, all selected models will be lined up from shortest to tallest.
Hence, we have to pull out the no. of ways 4 & 6 stand adjacent to each other from the above total, i.e = 21.
The following will be the way in which 4 & 6 stand close to each other.
1 2 3 4 6
1 2 4 6 7
1 3 4 6 7
2 3 4 6 7
So, the answer will be 21-4 = 17 ways.
ANS:C
Answer: C
Question: Two pipes A and B can separately fill a tank in 10 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
Options:
A)450
B)540
C)542
D)829
E)279
Rationale: 1/10 + 1/15 - 1/x = 1/15
x = 10
10 * 45 = 450
Answer: A
Answer: A
Question: A rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If 6 people choose their seats at random, what is probability that person P directly faces person Q?
Options:
A)1/5
B)1/8
C)2/7
D)5/6
E)3/5
Rationale: Person P will be seated somewhere at the table.
Each of the other 5 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/5.
The answer is A.
Answer: A
Question: In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
Options:
A)1:4
B)1:3
C)2:3
D)3:4
E)None of these
Rationale: Explanation:
33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: B
Answer: B
Question: Of 30 applicants for a job, 11 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
Options:
A)14
B)13
C)8
D)7
E)5
Rationale: C. 8
30 - 3 = 27
27 - 11 - 18 = -8
Then 8 are in the intersection between 4 years experience and degree.
Answer C
Answer: C
Question: How many multiples of 2 are there between 10 and 100(both are inclusive)?
Options:
A)2
B)7
C)6
D)46
E)3
Rationale: the answer is (100-10)/2+1=46
Answer is D
Answer: D
Question: If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is
Options:
A)a) 407
B)b) 518
C)c) 519
D)d) 521
E)e) 525
Rationale: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 8 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 4th and 5th numbers in the set). This means that numbers 4 and 5 in this set are 413 and 415. Because we know that number 4 is 413, we know that the smallest number is 3 odd numbers below this, which means that it is 3*2 = 6 below this (every odd number is every other number). Therefore 413-6 = 407, answer choice A
Answer: A
Question: If N = 2^0.15 and N^b = 32, b must equal
Options:
A)3/80
B)3/5
C)4
D)100/3
E)80/3
Rationale: 15/100 = 3/20
N = 2 ^ 3/20
N^b = 2^5
(2^3/20)^b = 2^5
b = 100/3
Answer: D
Answer: D
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone?
Options:
A)87
B)26
C)48
D)37
E)20
Rationale: π * 12 * 4
= 48
Answer:C
Answer: C
Question: Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?
Options:
A)0
B)1/10
C)1/7
D)1/4
E)1/3
Rationale: You know how to solve for Total number of people who can use at least one machine:
Total = n(A) + n(B) - n(A and B)
Total people who can use at least one machine = 17 + 18 - 15 = 20
So all 20 people know how to use at least one machine. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to use any machine.
Answer A
Answer: A
Question: A CAR HAS RUNS 10000 MILES USING 5 TYRES INTERCHANGABLY TO HAVE A EQUAL WORNOUT BY ALL TYRES HOW MANY MILES EACH TYRE SHOULD HAVE RUN?
Options:
A)7000 miles.
B)8000 miles.
C)9000 miles.
D)6000 miles.
E)5000 miles.
Rationale: Total distance traveled by all the tires is 4*10000= 40000 miles.(since only 4 tires can be active at a time.
To make an equal run, Distance traveled by each tire is 40000/5 = 8000 miles.
ANSWER:B
Answer: B
Question: A person buys an article at Rs.800. At what price should he sell the article so as to make a profit of 35%?
Options:
A)600
B)277
C)269
D)261
E)1080
Rationale: Cost price = Rs.800
profit = 35% of 800 = Rs.280
Selling price = Cost price + Profit
= 800 + 280 = 1080
Answer: E
Answer: E
Question: A train covers a distance at a speed of 240kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of?
Options:
A)516
B)840
C)560
D)720
E)920
Rationale: Distance = 240*5 = 1200km
Required speed = 1200*3/5 = 720 km/hr
Answer is D
Answer: D
Question: Calculate how many ways a woman who has 4 bags and 5 books can put the books in her bag?
Options:
A)1034
B)1025
C)1024
D)1025
E)1324
Rationale: First book can be put in 4 ways, similarly second, third ,forth and fifth books also can be put in 4 ways.
So total number of ways = 4 x 4 x 4 x 4 x 4 = 1024
C
Answer: C
Question: Two pipes P and Q can fill a tank in 4 hours and 5 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
Options:
A)4 hours 20 min
B)5 hours 49 min
C)3 hours 50 min
D)3 hours 22 min
E)2 hours 13 min
Rationale: Explanation:
Part filled by P in 1 hour = 1/4
Part filled by Q in 1 hour = 1/5
Part filled by (P + Q) in 1 hour = ( 1/4 + 1/5) = (9/20)
Time taken to fill the tank is (20/9) = 20/9*60 = 133 mins = 2 hrs 13 mins
ANSWER E
Answer: E
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.74 km
B)5.78 km
C)5.76 km
D)5.79 km
E)5.29 km
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Answer: C
Question: What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage?
Options:
A)99.6
B)95.2
C)97.5
D)98.25
E)None of these
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-5+1/5
95.2
Thus the CP is Rs 95.2.
ANSWER B
Answer: B
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 900 gm and 750 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?
Options:
A)3.84
B)1.75
C)3.36
D)2.72
E)None of these
Rationale: Here's how I did it. My notes from reading the problem were:
1L A = 900 gm
1L B = 850 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Eachpartis 4/5 of a liter.
So if we have 3 parts A, we have 900*3*(4/5) = 2160
If we have 2 parts B, we have 750*2*(4/5) = 1200
2160 + 1200 = 3360
Solving for units gives us 3.36
So the answer is C
Answer: C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)16 km/hr
B)56 km/hr
C)43 km/hr
D)50 km/hr
E)87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45
==> x
= 50 km/hr.
Answer:D
Answer: D
Question: If 5^k + 5^k = (5^9)^(5^9) - 5^k, then k = ?
Options:
A) 5^11 - 1
B) 11/2
C) 242
D) 3^10
E) 3^11 - 1
Rationale: 5^k + 5^k = (5^9)^5^9 - 5^k
5*(5^k) = 5 ^ (25 * 5^9 ) = 5^(5^2 * 5^9) = 5^(5^11)
5^k+1 = 5^(5^11)
So k+1 = 5^11
So k = 5^11 -1
Answer is A
Answer: A
Question: The cash realised on selling a 14% stock is Rs.107.25, brokerage being 1/4% is?
Options:
A)366
B)107
C)102
D)192
E)122
Rationale: Cash realised= Rs. (107.25 - 0.25)
= Rs. 107.
Answer: B
Answer: B
Question: An employer pays Rs.20 for each day a worker works and for fests Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal?
Options:
A)40
B)30
C)70
D)20
E)10
Rationale: Suppose a worker remained ideal for x days then he worked for 60-x days
20*(60-x)-3x=280
1200-23x=280
23x=920
x=40
Answer is A.
Answer: A
Question: A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
Options:
A)104
B)140
C)200
D)150
E)250
Rationale: 624/6 = 104 kmph
ANSWER A
Answer: A
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x – 16
(x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30
Answer: Option D
Answer: D
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/8 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
Options:
A)9.6
B)12.4
C)16.2
D)18.3
E)21.5
Rationale: Machine K works at a rate of 1/24 of the units per hour.
The rate of K + M together is 7/8 * 1/6 = 7/48 of the units per hour.
The rate of machine M is 7/48 - 2/48 = 5/48.
It would have taken machine M a total time of 9.6 hours.
The answer is A.
Answer: A
Question: The number 219 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers?
Options:
A)20
B)21
C)19
D)17
E)15
Rationale: sum of the squares of 3 different positive integers = 219
13^2 + 7^2 + 1^2 = 219
now,
sum of these 3 different integers = 13 + 7 + 1 = 21
Ans - B
Answer: B
Question: Griffin has a bag of marbles that contains 7 black marbles and 5 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be black?
Options:
A)4/15
B)5/22
C)6/35
D)7/44
E)8/55
Rationale: P(3 black marbles) = 7/12*6/11*5/10 = 7/44
The answer is D.
Answer: D
Question: A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds
Options:
A)5 sec
B)6 sec
C)7 sec
D)8 sec
E)9 sec
Rationale: Explanation:
Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 100/(50/3) = (100 ×(3/50)) sec =6 sec
Answer: Option B
Answer: B
Question: A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 181 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
Options:
A)6564
B)7372
C)8281
D)9331
E)can not be determined
Rationale: Let the side for growing cabbages this year be X ft. Thus the area is X^2.
Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.
The area would have increased by 181 sq ft as each cabbage takes 1 sq ft space.
X^2 - Y^2 = 181
(X + Y)(X - Y) = 181
181 is a prime number and thus it will be (91+90)*(91-90).
Thus X = 91 and Y = 90
X^2 = 91^2 = 8281
The answer is C.
Answer: C
Question: Given that 2x + 15 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
Options:
A)-4 and -1
B)-5 and 4
C)-4 and 1
D)-2 and 5
E)2 and 5
Rationale: 2x + 15 > 5
i.e 2x >5-15
i.e. 2x > -10
i.e. x > -5
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -5 < x < 4
Answer: Option B
Answer: B
Question: Difference between the length &breadth of a rectangle is 15 m. If its perimeter is 90 m, then its area is??
Options:
A)2000 m^2
B)2340 m^2
C)450 m^2
D)2556 m^2
E)2534 m^2
Rationale: We have: (l - b) = 15 and 2(l + b) = 90 or (l + b) = 45
so 2 l = 60 = > l = 30 & b = 15
Area = 30 * 15 = 450 m^2
Answer : C
Answer: C
Question: During a Thanksgiving weekend, a car rental company rented seven-tenths of the vehicles with it including three fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
Options:
A)20%
B)30%
C)40%
D)60%
E)25%
Rationale: 60% of the vehicles are 4WDs:
60 are 4WDs and 40 are not.
Seven-tenths (70%) of the vehicles were rented:
70 rented and 30 not.
Three fifths of the 4WDs were rented:
3/5*60 = 36 4WDs were rented and 24 not.
So, out of 30 vehicles that were not rented 24 were 4WDs and 6 not: 6/30 = 20%.
Answer: A.
Answer: A
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 93, what is the value of x?
Options:
A)95
B)91
C)102
D)101
E)85
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 93
x = 91
Answer : B
Answer: B
Question: Find the missing number. 1, 4, 9, 16, 25, 36, 49, (....)
Options:
A)80
B)67
C)64
D)85
E)96
Rationale: The series is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, ...
Hence, next term = 8^2 = 64
Answer is C
Answer: C
Question: A rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. What is the largest size of the tile which could be used for the purpose ?
Options:
A)14 cms
B)21 cms
C)42 cms
D)None of these
E)Cannot be determined
Rationale: Solution
Largest size of the tile .
H.C.F of 378 cm and 525 cm = 21 cms.
Answer B
Answer: B
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)22
B)28
C)25
D)82
E)34
Rationale: M = 20
S = 5
DS = 20 + 5 = 20.Answer:C
Answer: C
Question: A University library checks out books for a 5-week period, but allows them to be renewed up to 6 times. What is the Maximum no.of Weeks the library will allow a book to be checked out?
Options:
A)35
B)36
C)37
D)39
E)41
Rationale: Library checkout is 5 week period and can be renewed 6 times. So he can keep for a maximum of 8 weeks.
when he is allotted the book
0-5 weeks (1st renew)
5-10 weeks (2nd renew)
10-15 weeks (3rd renew)
15-20 weeks (4th renew)
20-25 weeks (5th renew)
25-30 weeks (6th renew)- maximum renew
after that,
30-35 (submission)
So 35 weeks is maximum.
ANSWER:A
Answer: A
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many Q hours does it currently take Anne to clean the house on her own?
Options:
A)6
B)7
C)8
D)12
E)14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to Q=1/3 (As the work is completed in Q=3 hours)
Solving these 2 equations we can find B as 12
So, D
Answer: D
Question: An bus covers a certain distance at aspeed of 100 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
Options:
A)560 km/h
B)567 km/h
C)300 km/h
D)723 km/h
E)720 km/h
Rationale: Distance = (100 x 5) = 500 km.
Speed = Distance/Time
Speed = 500/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 500 x 3/5 km/hr = 300 km/hr.
C
Answer: C