divelab/Sys2Bench huggingface dataset:
Question: A Mango costs Rs 25 each and a apple costs Rs. 21 each. If I spend Rs 71 on total what is the number of mango I purchased?
Options:
A)4
B)6
C)2
D)10
E)8
Rationale: 2 * 25+ 21 = 71
Answer : 2
Option : C
Answer: C
Question: 1/2 is what percent of 1/3
Options:
A)150%
B)200%
C)250%
D)300%
E)None of these
Rationale: Explanation:
1/2/1/3 * 100 = 1/2 * 3/1 * 100 = 150 %
Option A
Answer: A
Question: If 18 men take 15 days to to complete a job, in how many days can 24 men finish that work?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Ans. 10 days
Answer: A
Question: A box contains four gold coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
Options:
A)4/5
B)3/5
C)2/5
D)1/5
E)3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
A
A
Answer: A
Question: a making a cube with dimension 5*5*5 using 1*1*1 cubes.what is the number of cubes needed to make hollow cube looking of the same shape.
Options:
A)98
B)99
C)100
D)101
E)102
Rationale: 125 1*1*1 small cubes=5*5*5 cubes
because hallow in inner we don't have 3*3*3 cubes
so 125-27=98 cubes required
ANSWER:A
Answer: A
Question: A can finish a piece of work in 5 days. B can do it in 25 days. They work together for four days and then A goes away. In how many days will B finish the work?
Options:
A)3 days
B)1 day
C)2 days
D)4 days
E)5 days
Rationale: 4/5 + (4 + x)/25 = 1 => x = 1 day
Answer: B
Answer: B
Question: In a 20 litre mixture ratio of milk and water is 3:1.how much milk should added so that mixture ratio Become 4:1?
Options:
A)3
B)2
C)8
D)6
E)5
Rationale: Amount of milk=20×3/4=15 litre and water= 5 litre
Let x litre milk to be added
Then 15+x/5=4/1=15+x=20,x=5
Answer E
Answer: E
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,4) and (t,-7). What is the least possible value of the slope of line L?
Options:
A)6
B)2
C)-2
D)-6
E)-5.5
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-7-4)/(4-2) = -5.5
IMO option E is correct answer.
Answer: E
Question: Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65 cm
Options:
A)45cm
B)255cm
C)244cm
D)55cm
E)280cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1575 cm, 1125cm, 765cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 255.
Option B
Answer: B
Question: 12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. If Mohan further sells the shares at a premium of Rs. 11 each, find his gain in the transaction.
Options:
A)75000
B)76000
C)77000
D)74000
E)70000
Rationale: Face value of each share = Rs.20
Market value of each share = Rs.25
Number of shares = 12500
Amount required to purchase the shares = 12500 × 25 = 312500
Mohan further sells the shares at a premium of Rs. 11 each
ie, Mohan further sells the shares at Rs.(20+11) = Rs.31 per share
total amount he gets by selling all the shares = 12500 × 31 = 387500
His gain = 387500 - 312500 = Rs.75000
Answer is A.
Answer: A
Question: In a box of 7 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
Options:
A)1/2
B)1/5
C)2/3
D)2/7
E)1/7
Rationale: First, there are 5C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 7C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 5C3/7C3=10/35 = 2/7
Answer is D
Answer: D
Question: Two trains of length 100 m and 300 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)70/7 sec
B)80/7 sec
C)40/7 sec
D)100/7 sec
E)90/7 sec
Rationale: D
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 300)/35
= 500/35 = 100/7 sec.
Answer: D
Question: Machine Q and machine B are each used to manufacture 660 sprockets. It takes machine Q 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine Q. How many sprockets per hour does machine Q produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: [Reveal]Spoiler:
TimeB: 660/x
TimeQ: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeQ
660/100+10 => 660/110 = 6=A
Answer: A
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)27 2/23 %
B)33 1/3 %
C)30%
D)19%
E)29%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
ANSWER:B
Answer: B
Question: For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 15 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?
Options:
A)3/20 candles
B)1/2 candles
C)1 1/3 candles
D)2 candles
E)3 candles
Rationale: ANS = 3/10
S= 60k/d^2
At 2 feet
15 = 60k/4 so k = 1
At 20 feet
S = 60 *1/20^2 = 3/20
A
Answer: A
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ?
Options:
A)137
B)262
C)119
D)122
E)152
Rationale: Number of words which can be formed
= 5! - 1 = 120 - 1 = 119.
Answer:C
Answer: C
Question: Express a speed of 126 kmph in meters per second?
Options:
A)10 mps
B)35 mps
C)26 mps
D)97 mps
E)16 mps
Rationale: 126 * 5/18
= 35 mps
Answer:B
Answer: B
Question: Which number need to add to 859622 to get a number exactly divisible by 456?
Options:
A)658909
B)353565
C)757345
D)454664
E)859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: E
Question: A student chose a number, multiplied it by 2, then subtracted 200 from the result and got 110. What was the number he chose?
Options:
A)168
B)100
C)155
D)160
E)200
Rationale: Solution:
Let x be the number he chose, then
2*x*200 =110
2x=310
x=155
correct answer C
Answer: C
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 4136 cm is?
Options:
A)22
B)28
C)17
D)12
E)47
Rationale: 2 * 22/7 * 14 * x = 4136 => x = 47
Answer: E
Answer: E
Question: An airplane covers 50 miles in 1/5 hours. How many miles can the airplane cover in 5 hours?
Options:
A)800
B)600
C)1250
D)950
E)1000
Rationale: divide 5 by 1/5
=5 ÷ 1/5
=5/1 ÷ 1/5
=5/1*5/1
=25.
Then, multiply 50 by 25 to get 1250
In 5 hours, the airplane will cover 1250 miles
Answer is C.
Answer: C
Question: We made a down payment of $80 and borrowed the balance on a new cello which cost $500. The balance with interest was paid in 23 monthly payments of $19 each and a final payment of $4. The amount of interest paid was what percent of the amount borrowed?
Options:
A)3.5%
B)4%
C)4.5%
D)5%
E)5.5%
Rationale: We borrowed $420.
To pay back this loan, we paid 23*$19 + $4=$441.
The interest was $441-$420=$21.
The percentage was $21/$420=0.05=5%.
The answer is D.
Answer: D
Question: Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
Options:
A)2367
B)2456
C)2799
D)3334
E)3458
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: D
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 20 cm?
Options:
A)827 cm2
B)380 cm2
C)285 cm2
D)178 cm2
E)176 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (20)
= 380 cm2
Answer:B
Answer: B
Question: If [[x]] = x^2 + 2x + 4, what is the value of [[5]]?
Options:
A)39
B)9
C)15
D)19
E)25
Rationale: These functions questions might look intimidating, but they just test your knowledge about how well you can substitute values
[[x]] = x^2 + 2x + 4
[[5]] = 5^2 + 2*5 + 4 = 39. Option A
Answer: A
Question: Rahul put his timepiece on the table in such a way that at 6 P.M. hour hand points to North. In which direction the minute hand will point at 9.15 P.M. ?
Options:
A)233
B)37
C)27
D)West
E)271
Rationale: Explanation:
At 9.15 P.M., the minute hand will point towards west.
Answer: D) West
Answer: D
Question: The average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg. What might be the weight of the new girl?
Options:
A)85 kg
B)90 kg
C)80 kg
D)75 kg
E)70 kg
Rationale: Total weight increased = 20 x 2 kg = 40 kg.
Weight of new person = 40 + 40 kg =80 kg
Answer : C
Answer: C
Question: The sum of all two digit numbers divisible by 6 is
Options:
A)910
B)510
C)710
D)610
E)810
Rationale: Required numbers are 12,18,24 . . . . . 96
This is an A.P. in which a=12,d=6 and l=96.
Let the number of terms in it be n.Then t=96
So a+(n-1)d=96.
12+(n-1)*6=96,
12+6n-6=96
6+6n=96
6n=96-6
n = 90/6
then n=15.
Required sum
=n/2(a+l)
=15/2(12+96)
=810
Answer is E.
Answer: E
Question: there is a circle of radius 5.what is the area of the biggest rectangle that can be cut out of this circle ?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: biggest rectangle would be a square,whose diagonal is 10(5+5)
if side of square is a, 100=a^2+a^2=2a^2
so area of square=a^2=100/2=50
ANSWER:A
Answer: A
Question: An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2
meteres
Options:
A)1200
B)2400
C)1400
D)2500
E)3500
Rationale: Explanation:
It means that 0.08% of x = 2
=>(8100×100×x)=2=>x=2×100×1008=>x=2500
Answer: Option D
Answer: D
Question: Jim bought edging to go around a circular garden with a radius of 3 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
Options:
A)28.84' additional edging
B)48.84' additional edging
C)38.84' additional edging
D)18.84' additional edging
E)58.84' additional edging
Rationale: (2)3.14 x 3 = 18.84' circumference of small garden
2 x 3 = 6' diameter of small garden
3.14 x 12 = 37.68' circumference of garden with
doubled diameter
37.68 - 18.84 = 18.84' additional edging needed
In real life this would probably be rounded to 19 or 20 feet.
correct answer D
Answer: D
Question: Two numbers have a H.C.F of 14 and a product of two numbers is 2562. Find the L.C.M of the two numbers?
Options:
A)140
B)150
C)160
D)170
E)183
Rationale: L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 2562/14 = 183.
ANSWER:E
Answer: E
Question: Exactly 3/5 of the people in the room are under the age of 21, and exactly 5/13 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Options:
A)21
B)35
C)39
D)60
E)42
Rationale: The total number of the people in the room must be a multiple of both 5 and 14 (in order 3/5 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 5 and 14, which is 70.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.
Therefore there are 3/5*70=42 people in the room under the age of 21.
Answer: E.
Answer: E
Question: 5% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Options:
A)2988
B)2776
C)4400
D)4675
E)881
Rationale: X * (95/100) * (80/100) = 3553
X = 4675
Answer:D
Answer: D
Question: If the sum of the first n positive integers is S, what is the sum of the first n positive integers divisible by 5, in terms of S ?
Options:
A) S/2
B) S
C) 2S
D) 2S + 2
E) 5S
Rationale: Answer is E
Given sum of 1 2 3.....n = S
sum of 5 , 10 , 15 ....5n = 5[sum(1 2 3....n) ] = 5S
Answer: E
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Options:
A)7527
B)7652
C)5550
D)6363
E)8272
Rationale: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year
= 66600/12 = 5550.
Answer: C
Answer: C
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Options:
A)Rs.20
B)Rs.30
C)Rs.40
D)Rs.25
E)Rs.28
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
ANSWER:C
Answer: C
Question: a person travels from his house to office from 09:00am to 11:00 am and covers a distence of 13.4km. find the average speed of the person.
Options:
A)20.1km/h
B)20.5km/h
C)26.8km/h
D)22.1km/h
E)20.9km/h
Rationale: time=11:00-09:00=2 hour
distance=13.4km
speed=13.4*2=26.8 km/h
ANSWER:C
Answer: C
Question: How many Books each of Volume 150 meter cube can be packed into a crate of volume 3000 meter cube?
Options:
A)cannot be determined
B)20
C)25
D)30
E)35
Rationale: Gud question with a simple concept.
In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.
In above with volume given , we can come up with different shapes, so we cant know the answer
For ex :3000 m3 can be 300*10 or 30*100 or just 3000*1 we don't know , so we cant calculate
Answer : A
Answer: A
Question: If the average (arithmetic mean) of the four numbers 23, 15, 32, and (N + 1) is 50, then N =
Options:
A) 19
B) 20
C)121
D)122
E) 129
Rationale: 23+15+32+N+1= 50 x 4 = 200
=>N +71 = 200
=>N=129
Answer E
Answer: E
Question: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $130. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
Options:
A)$21
B)$27
C)$31
D)$61
E)It cannot be determined
Rationale: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:
3B+7S+C=130
4B+10S+C=164.5
Subtracting the first equation from the second gives us B+3S=34.5
Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=61. In any case, there is no necessity to know each item's price, just the sum.
Answer: D
Answer: D
Question: A sum of money lent out at S.I. amounts to a total of $480 after 2 years and to $680 after a further period of 5 years. What was the initial sum of money that was invested?
Options:
A)$360
B)$380
C)$400
D)$420
E)$440
Rationale: S.I for 5 years = $680 - $480 = $200
The S.I. is $40/year
S.I. for 2 years = $80
Principal = $480 - $80 = $400
The answer is C.
Answer: C
Question: The HCF of two numbers is 52 and the other two factors of their LCM are 11 and 12. What is the largest number.
Options:
A)624
B)450
C)480
D)504
E)555
Rationale: Explanation:
HCF of the two numbers = 52
HCF will be always a factor of LCM
52 is factor of LCM
other two factors are 11 & 12
Then the numbers are (52 *11) and (52 x 12)
= 572 and 624
Answer: Option A
Answer: A
Question: A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio:
Options:
A)31 : 44
B)31 : 27
C)16 : 15
D)35 : 44
E)35 :27
Rationale: n case of stock1, if he invest Rs.105, he will get a dividend of Rs.12 (assume face value = 100)
In case of stock2, if he invest Rs.88, he will get a dividend of Rs.8 (assume face value = 100)
ie, if he invest Rs.(88*12)/8, he will get a dividend of Rs.12
Required ratio = 105 : (88 × 12)/8 = 105 : (11 × 12) = 35 : (11 × 4) = 35 : 44
Answer : Option D
Answer: D
Question: A train covered a certain distance at a uniform speed. If the train had been 6 km/hr faster, it would have taken 4 hour less than the scheduled time. And, if the train were slower by 6 km/hr, the train would have taken 6 hr more than the scheduled time. The length of the journey is:
Options:
A)720 km
B)700 km
C)740 km
D)600 km
E)None of these
Rationale: Explanation :
Let the length of the journey be d km and the speed of train be S km/hr.
Then,
=>d/(S+6)=t−4. ---------------(i)
=>d/(S−6)=t+6. ---------------(ii)
Subtracting the (i) equation from(ii), we get :-
=>d/(S−6)−d/(S+6)=10 --------------(iii)
Since, Time=Distance/Speed.
From (i) , (ii) and (iii), w get :-
S=30 and d = 720 km.
Answer : A
Answer: A
Question: Of the five numbers in a sequence, the first term is 15,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
Options:
A)9,375
B)9,750
C)9,975
D)9,984
E)14,976
Rationale: 1st number= 15,000
2nd number = 20% of 15,000= 3000
3rd number= 20% of 3000= 600
4th number = 20% of 600= 120
5th number= 20% of 120= 24
Range = 15,000-24= 14976
E is the answer
Answer: E
Question: How many seconds will a 550 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)12 sec
B)30 sec
C)33 sec
D)16 sec
E)18 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 550 * 3/50
= 33 sec.
Answer: C
Answer: C
Question: A survey was sent to 80 customers, 12 of whom responded. Then the survey was redesigned and sent to another 63 customers, 10 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
Options:
A)2%
B)5%
C)14%
D)28%
E)63%
Rationale: Rate of first survey = 12/80
Rate of second survey = 10/63
% Response rate increase (10/63-12/80)/(12/80) = 5%
Answer is B = 5%
Answer: B
Question: A train 120 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)7.2 sec
B)9.3 sec
C)12 sec
D)15.2 sec
E)18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 120 m at 50/3 m / sec = 120 *3/ 50 sec = 7.2 sec
Answer : 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)4
C)7
D)8
E)9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer:A
Answer: A
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 90) square inches. What is the perimeter of the photograph, in inches?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+8)(y+8)=M and so (2) xy + 8x + 8y + 64 = M+90
Let's subtract equation (1) from equation (2).
6x + 6y + 60 = 90
2x + 2y = 10, which is the perimeter of the photograph.
The answer is A.
Answer: A
Question: Mandrake has to choose 4 from 20 people. There are 3 girls, 5 boys , 12 children. What is total probability that he will choose 1G , 2B , 1C?
Options:
A)1/27
B)2/27
C)3/7
D)4/7
E)5/7
Rationale: (3C1 * 5C2 * 12C1)/ 20C4 = 3*10*12/4845= 360/4845=2/27
ANSWER:B
Answer: B
Question: Compute the perimeter of a square with area 36.
Options:
A)24
B)27
C)25
D)26
E)29
Rationale: If the length of the square is s, then s2 = 36 so s = 6. The perimeter is therefore
4s = 24 .
correct answer A
Answer: A
Question: A teacher gave the same test to three history classes: U, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Options:
A)74
B)75
C)76
D)77
E)78
Rationale: Ans : B (75)
lets say class U indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class U is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = U+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Answer: B
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?
Options:
A)7 meters
B)9 meters
C)8 meters
D)5 meters
E)3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 12,0000 m : C is the circumference
C = 5 meters
correct answer D
Answer: D
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5676, 6336
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: B
Question: 15 tennis players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
Options:
A)190
B)200
C)210
D)220
E)225
Rationale: 15 th player can play with remaining 14 members two times = 2*14=28
14 th " remaining 13= 2*13=26
2*(1+2+3+4+......+14)=2(14)(14+1)/2=210
ANSWER:C
Answer: C
Question: If f(x) = 4x − √x and g(x) = x^2, what is f(g(5))?
Options:
A)-4
B)8
C)16
D)32
E)95
Rationale: g(x) = x²
g(5) = 5² = 25
So, f(g(5)) = f(25)
f(x) = 4x − √x
So, f(25) = 4(25) − √25
= 100 - 5
= 95
= E
Answer: E
Question: The public library has exactly 2 floors. It has 1/2 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
Options:
A)1/4
B)5/14
C)12/17
D)9/14
E)5/6
Rationale: Lẹt x bé thế nó of shelves and ý bé thế nó of books per shelf on first floor.
Now no of shelves on 2nd floor = (1/2)*x
no of books per shelf on 2nd floor = (5/6) * y
Số total no books on first floor = xy and total no of books on 2nd floor = (1/2)*x*(5/6)*y = (5/12)*xý
fraction of library books on first floor = (xý)/(xý + (5/12)*xý)
=1 / (1+(5/12))
=12/17
Số C
Answer: C
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)78 sec
B)89 sec
C)27 sec
D)24 sec
E)12 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10
= 89 sec.
Answer:B
Answer: B
Question: Two-third of a positive number and 49/216 of its reciprocal are equal. The number is:
Options:
A)5/12
B)7/12
C)25/144
D)144/25
E)146/25
Rationale: Let the number be x. Then,
2/3 x = 49/216 * 1/x
x2 = 49/216 * 3/2 = 49/144
x = 7/12
ANSWER:B
Answer: B