divelab/Sys2Bench huggingface dataset:
Question: In a certain supermarket, a triangular display of cans is arranged in 9 rows, numbered 1 through 9 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 120 cans in the entire display, how many cans are in the six row?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Let x be the number of cans in row 1.
The total number of cans is x + (x+3) + ... + (x+24) =
9x + 3(1+2+...+8) =
9x + 3(8)(9)/2 =
9x + 108
Since the total is less than 120, x must equal 1.
The number of cans in the 6th row is 1 + 3(5) = 16
The answer is C.
Answer: C
Question: If the height of a cone is increased by 100% then its volume is increased by?
Options:
A)200%
B)300%
C)100%
D)500%
E)350%
Rationale: Height of=>100%
so increased by 100%
ANSWER C
Answer: C
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 135. What is that number?
Options:
A)12
B)29
C)20
D)15
E)99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 135
6x + 15 = 135
6x = 120
x = 20
ANSWER:C
Answer: C
Question: If M = s% of t and N = t% of s, then which of the following is true?
Options:
A)M is equal to N
B)M is smaller than N
C)M is greater than N
D)none of these
E)Cannot be determined
Rationale: Explanation :
Solution: s% of t = (s/100 * t)
=> (t/100 * s) = t% of s
=> M = N
Answer : A
Answer: A
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)7
C)6
D)5
E)2
Rationale: 2x * x = 128 => x= 8
Answer: A
Answer: A
Question: Distance between 2 places A and B is given. A man P starts from place A at 9 pm and another man Q goes from B at 10pm . Speed of Q is double of that of P. Both cover 1/4 dist in the same time interval. then A travels the entire dist in time
Options:
A)8hrs
B)9hrs
C)10hrs
D)11hrs
E)12hrs
Rationale: let speed of p and q are x, 2x
time taken by A to cover 1/4 distance =t
x*t = 2x*(t-1)
t=2 for 1/4 of total distance
A travels the entire dist in time 2*4=8hrs
ANSWER:A
Answer: A
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)1:99
C)1:95
D)1:12
E)1:11
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x
=1:96.
Answer:A
Answer: A
Question: In the game of Dubblefud, red chips, blue chips and green chips are each worth 1,2 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 15, 000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: this is equivalent to :-
x * 2y * 5z = 15000
y
= z (given)
x * 2y * 5y = 15000
x * y^2 = 15000/10
2x * y^2 = 1500
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 30 as
2* 30 * y^2 =1500
y^2 = 25
y =5
Number of red chips = 30 hence C
Answer: C
Question: Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?
Options:
A)58 kg
B)60 kg
C)64 kg
D)70 kg
E)None
Rationale: Sol.
For 9 kg Zinc, mixture melted = (9+11) kg.
For 28.8 kg Zinc, mixture, melted = [20/9 x 28.8] kg
= 64 kg.
Answer C
Answer: C
Question: If x+y=10, x-y=18, for integers of x and y, x=?
Options:
A)14
B)15
C)25
D)13
E)42
Rationale: x+y =10
x-y = 18
2x = 28
x = 14
Answer is A
Answer: A
Question: (1^2+2^2+3^2+.....+7^2)=?
Options:
A)330
B)345
C)365
D)140
E)None of them
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=7
=(1/6x7x8x15)
=140
Answer is D.
Answer: D
Question: What is the area of an equilateral triangle whose one side length is 50?
Options:
A)225√3
B)325√3
C)425√3
D)525√3
E)625√3
Rationale: -> -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(50^2)/4=625√3 and the answer is E.
Answer: E
Question: Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
Options:
A)1/6
B)1/4
C)2/3
D)3/4
E)11/12
Rationale: So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/3*1/4=11/12.
Answer: E.
Answer: E
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab?
Options:
A)10
B)12
C)14
D)17
E)18
Rationale: 2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10
A)
Answer: A
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.210 only. Menâ€™s wages are?
Options:
A)6Rs
B)2Rs
C)4Rs
D)9Rs
E)14Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 210 Rs.
5M + 5M + 5M ----- 210 Rs.
15M ------ 210 Rs. => 1M = 14Rs.
Answer: E
Answer: E
Question: a man can row 20 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
Options:
A)13 km/hr.
B)6 km/hr.
C)9 km/hr.
D)15 km/hr.
E)10 km/hr.
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=20 or x=10.
Rate upstream=10 km/hr,rate downstream=30 km/hr.
Hence,rate of stream=1/2(30-10)km/hr=10 km/hr.
Answer is E.
Answer: E
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order R? (1 cubic meter = 1,000 liters)
Options:
A)92
B)90
C)82
D)78
E)75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
R=12.5*6 = 75.E
Answer: E
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 22 gallons of ethanol, how many gallons of fuel A were added?
Options:
A)160
B)150
C)250
D)80
E)50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 22 gallons then 0.12A+0.16(200-A)=22 --> A=250.
Answer: C.
Answer: C
Question: A certain team has 16 members, including Joey. A three-member relay team will be selected as follows: one of the 16 members is to be chosen at random to run first, one of the remaining 15 members is to be chosen at random to run second, and one of the remaining 14 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Options:
A)1/4
B)2/5
C)1/6
D)2/7
E)1/8
Rationale: Each member has an equal probability to run second (1/16) or third (1/16).
The probability that Joey runs second or third is 1/16 + 1/16 = 1/8
The answer is E.
Answer: E
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 780. The number of hares in the zoo is?
Options:
A)190
B)199
C)77
D)66
E)221
Rationale: 200*2 = 400
780
-----
380
1----2
?----380 = 190
Answer:A
Answer: A
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
Options:
A)90
B)99
C)97
D)95
E)65
Rationale: 30 * 33/2 = 5/2 * 2 * x => x = 99
ANSWER B
Answer: B
Question: A boy has five trousers and 15 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)75 ways
B)87 ways
C)66 ways
D)108 ways
E)21 ways
Rationale: Explanation:
The boy can select one trouser in five ways.
The boy can select one shirt in 15 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 15 = 75 ways.
Answer: A
Answer: A
Question: Three candidates contested an election and received 1000, 2000 and 4000votes respectively. What percentage of the total votes did the winning candidate got?
Options:
A)30%
B)50%
C)57%
D)62%
E)75%
Rationale: Total number of votes polled = (1000 + 2000 + 4000) = 7000
Required percentage = 4000/7000 * 100 = 57% (approximately)
Answer: Option C
Answer: C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 120 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
Options:
A)3
B)4
C)6
D)8
E)10
Rationale: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 2 hours to travel 240 km, so C leaves 6 hours after A.
The answer is C.
Answer: C
Question: How many positive integers less than 27 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
Options:
A)27
B)25
C)24
D)20
E)22
Rationale: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}
3 odd multiples of 5: {5, 15, 25}
11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+3+11-1=22.
Answer: E.
Answer: E
Question: Including Cara and Dan, there are five members on the board of directors for a company. If the board is to be split up into a three-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
Options:
A)2/3
B)1/2
C)1/3
D)2/4
E)2/5
Rationale: The number of possible subcommittees with Cara is 4C2=6.
The number of possible subcommittees with Cara and Dan is 3C1=3.
The fraction of Cara's subcommittees which include Dan is 3/6=1/2.
The answer is B.
Answer: B
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
Options:
A)Rs. 3932
B)Rs. 3972
C)Rs. 3372
D)Rs. 3942
E)Rs. 3772
Rationale: Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
Answer: Option C
Answer: C
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)19%
C)68%
D)19%
E)38%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: A
Question: Two pipes A and B can fill a tank in 15 min and 27 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)14 min 19 sec
B)14 min 42 sec
C)18 min 24 sec
D)14 min 40 sec
E)14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/27
1/27 : 8/15 :: 1 ; x
x = 8/15 * 1 * 27 = 14 2/5 min = 14 min 24 sec.
The tank will be full in (4 min. + 14 min. 24 sec) = 18 min 24 sec.Answer: C
Answer: C
Question: Lake A has a duck population of 30 females and 35 males. Lake B’s duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
Options:
A)144
B)105
C)78
D)51
E)36
Rationale: Lake A has a duck population of 30 females and 35 males --> the ratio is F:M = 30:35 = 6:7.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 6:7.
C
Answer: C
Question: Which of the following numbers is between 2⁄5 and 1⁄4?
Options:
A).45
B).35
C).23
D).22
E).20
Rationale: Isn't it B?
2/5 = .40
1/4 = .25
The only answer between that is B, .35.
Answer: B
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is ?
Options:
A)14 years 8 months
B)15 years
C)16 years 4 months years
D)17 years 10 months years
E)None
Rationale: Answer
Total decrease
= ( 20 X 2 ) months
= 3 years 4 month
∴ Age of the new boy
= ( 18 years ) – ( 3 years 4 months)
= 14 years 8 month
Correct Option: A
Answer: A
Question: If d is the mean of x, y, and z, what is the mean x - 5, y - 5, z - 5 ?
Options:
A)d
B)3d
C)15d
D)d - 5
E)d + 15
Rationale: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case mean will decrease by 5, as we are subtracting 5 from each term in a set --> Mean =d - 5.
Answer: D.
Answer: D
Question: Yearly subscription to professional magazines cost a company $940.00. To Make a 30% cut in the magazine budget, how much less must be spent?
Options:
A)654
B)655
C)656
D)657
E)658
Rationale: total cost 940
940*30/100=282
so the cut in amount is 282
the less amount to be spend is 940-282=658
ANSWER:E
Answer: E
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)180
B)270
C)360
D)500
E)550
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
ANSWER B
Answer: B
Question: what is the remainder when 45820 is divided by 45
Options:
A)8
B)15
C)25
D)10
E)5
Rationale: 45820 / 45
45820 / 9*5
9164 / 9 => rem = 2
we have cancelled it by 5
reqd remainder = 5*2 = 10
ANSWER:D
Answer: D
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 6 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$10,494
C)$10,500
D)$11,500
E)$12,705
Rationale: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10494. So the answer is (B).
Answer: B
Question: A, B and C enter into a partnership by investing Rs. 15000, Rs.21000 and Rs.27000 respectively. At the end of 8 months, B receives Rs.1260 as his share. Find the share of A.
Options:
A)Rs. 600
B)Rs. 1620
C)Rs. 1080
D)Rs. 900
E)None of these
Rationale: Explanation:
Ratio of capital of A, B and C
= 15000 : 21000 : 27000
= 5 : 7 : 9
Let the total profit be Rs. x.
Then, B's share = Rs. 7x/21 = Rs. x/3
But x/3 = 1260
=> x = 3780
Hence, the total profit = Rs. 3780
A's share = Rs.[(5/21) × 3780] = Rs. 900
Answer: Option D
Answer: D
Question: If two pipes function simultaneously, the reservoir will be filled in 12 days.One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir.
Options:
A)53 hours
B)13 hours
C)30 hours
D)43 hours
E)45 hours
Rationale: If two pipes function simultaneously, the reservoir will be filled in 12 hours ( not days).One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir.
Then one pipe will fill tank in 20 hrs and second in 30 hrs when opened alone.
ANSWER:C
Answer: C
Question: Megala bought an electric drill at 85% of the regular price.
She paid $850 for the drill. What was the regular price?
Options:
A)$1000
B)$1869
C)$3869
D)$5869
E)$4869
Rationale: Regular price = 850/85*100 = 1000
Answer : A
Answer: A
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Options:
A)34299
B)28789
C)15000
D)28999
E)15022
Rationale: Answer: C) Rs.15000
Answer: C
Question: What is the Compound Interest on Rs.8500 at 7.5% p.a. compounded half-yearly for 2 1/2 years.
Options:
A)1409.85
B)1717.85
C)1427.85
D)2717.85
E)1817.85
Rationale: Compound interest : A = P(1 + r/n)nt
A = 10,217.85
C.I. >> 10,217.85 - 8500 >> Rs. 1717.85
Answer:B
Answer: B
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 4 industrial stocks, 5 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
A)12
B)19
C)60
D)180
E)720
Rationale: 4C3 * 5C2 * 3C2 = 4*60*3 = 720.
Answer: E.
Answer: E
Question: Find the odd man out
3,12, 24,48, 56, 96
Options:
A)48
B)8
C)16
D)56
E)2
Rationale: 3*2 = 6
6*2 =12
12*2=24
24*2=48
48*2=96
ANSWER:D
Answer: D
Question: Two bullet train s 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Options:
A)15.8 sec.
B)12.6 sec.
C)11.8 sec.
D)10.8 sec.
E)08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 210) m = 350 m.
Required time = 350x9/250 = 54/5 = 12.6 sec.
ANSWER B
Answer: B
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A & B leaves after 2 days simultaneously from the beginning. How long will work lost?
Options:
A)14 1/3
B)10 1/3
C)11 1/3
D)12 1/3
E)13 1/3
Rationale: 2/10 + 2/15 + x/20 = 1
x = 40/3 = 13 1/3
Answer: E
Answer: E
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 65 unique alphanumeric case sensitive characters.
Options:
A)63^4
B)62^5
C)62(62^4)
D)66(65^4)
E)63(62^6)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 65^4 + 65^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=65^4(1+ 65)
=65^4 * 66
Answer D
Answer: D
Question: 155 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Options:
A)12 liters
B)62 liters
C)41 liters
D)50 liters
E)34 liters
Rationale: Milk = 3/5 * 155 = 93 liters
Water = 62 liters
93 : (62+P) = 3:4
186 + 3P = 372 => P = 62
62 liters of water are to be added for the ratio become 3:4.
Answer:B
Answer: B
Question: Let a be a positive integer. If q is divisible by 2^a and q is also divisible by 3^(2a), then it is possible that q is NOT divisible by
Options:
A)6
B)3 × 2^a
C)2 × 3^(2a)
D)6^a
E)6^(2a)
Rationale: Since, q is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1
Only for E, 6^(2a) doesn't satisfy, if a = 1 and q=18, it is not divisible by 6^2 (i.e 36)
Hence answer is E
Answer: E
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 55% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
Options:
A) 7/12
B) 1/4
C) 1/2
D) 7/24
E) 17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
C
Answer: C
Question: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is
Options:
A)2 mph
B)2.5 mph
C)3 mph
D)4 mph
E)None
Rationale: Solution
Speed downstreams	=(10 + x)mph.
Speed upstreams	=(10 - x)mph.
= 18 kmph.
36/(10-x) - 36/(10+x)	= 90/60
= 72x ×60
= 90(100 - x²)
x²+48x+100= 0.
x= 2mph.
Answer A
Answer: A
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Options:
A)22 1/9 kmph
B)22 8/2 kmph
C)22 1/8 kmph
D)22 1/2 kmph
E)22 1/4 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 21/2 kmph
Answer:D
Answer: D
Question: Find the value of 10 + 2 â€¢ (8 â€“ 3)
Options:
A)25
B)13
C)17
D)20
E)15
Rationale: 10 + 2 â€¢ (8 â€“ 3)
= 10 + 2 (5)
= 10 + 2 *5
= 10 + 10
= 20
correct answer D
Answer: D
Question: A person crosses a 300 m long street in 4 minutes. What is his speed in km per hour?
Options:
A)1.6
B)4.5
C)8.2
D)6.5
E)2.9
Rationale: distance = 300 meter
time = 4 minutes = 4 x 60 seconds = 240 seconds
Speed = distance/time=300/240=1.25 m/s=1.25Ã—18/5 km/hr=4.5 km/hr
Answer :B
Answer: B
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Dinesh get lockers with the numbers 100, 400, 150, and 420, respectively, who is the most popular student?
Options:
A)Baskar
B)They have equal popularity
C)Dinesh
D)Raja
E)Kamal
Rationale: Distinct prime factors of 100 (Raja) : 2,5
Distinct prime factors of 400 (Kamal): 2 and 5.
Distinct prime factors of 150 (Baskar): 2,3, and 5
Distinct prime factors of 420 (Dinesh): 2,3,5 and 7.
So most popular student - Dinesh
Answer C
Answer: C
Question: The radius of a wheel is 25.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)724 m
B)798.3 m
C)287 m
D)278 m
E)927 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 25.4 = 79829 cm
= 798.3 m
Answer:B
Answer: B
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
Options:
A)6Rs
B)2Rs
C)4Rs
D)9Rs
E)3Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer: A
Answer: A
Question: Two brothers took the exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of Y/X ?
Options:
A)3
B)2.
C)1/2.
D)1/3.
E)There isn't enough data to answer the question
Rationale: X-Y = (X+Y)/2
2 X - 2 Y = X + Y
X = 3 Y
Y/X = 1/3
D is the answer.
Answer: D
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
Options:
A)10 and 50
B)12 and 18
C)24 and 64
D)21 and 63
E)22 and 44
Rationale: 64 has only the prime 2 (64=2^6) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Answer: C
Question: Rahul went to a shop and bought things worth Rs. 28, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Rs 15
B)Rs 12.10
C)Rs 22.70
D)Rs 26.80
E)None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 28 - 5 - 0.30
=22.70
Answer : C
Answer: C