divelab/Sys2Bench huggingface dataset:
Question: Before the regime change, the National Museum regularly displayed only one third of the artifacts in its collection; the other two thirds were kept in storage. The National Museum’s curator estimates that one seventh to one fifth of the artifacts in the museum’s collection disappeared during the regime change. If the National Museum now wishes to display the same number of artifacts as it did before the regime change, and if none of the missing artifacts are recovered, then the museum will keep in storage:
Options:
A)4/5 to 6/7 of artifacts in collection
B)9/14 to 13/20
C)3/5 to 5/7
D)7/12 to 11/18
E)7/18 to 5/12
Rationale: let T be total number of artifacts initially.
stolen (1/7)T to (1/5)T
left (6/7)T to (4/5)T = new total
1/3 for display T/3
storage (6/7)T -T/3 to (4/5)- T/3
11/21 T to 7T/15
so storage to new total = (11T/21) / (6T/7) to (7T/15) / (4T/5)
i.e 11/18 to 7/12
Answer is D.
Answer: D
Question: A CAN FINISH A WORK IN 18 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
Options:
A)5
B)5 1/2
C)6
D)8
E)NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (18*1/3)=6 DAYS.
CORRECT OPTION:C
Answer: C
Question: Of a certain group of 100 people, 40 graduated from High School L, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School L, did not graduate from College Y, and do not live in City Z ?
Options:
A) 5
B) 15
C) 35
D) 65
E) 85
Rationale: 1. l+y+z+ly+yz+lz+lyz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Answer: C
Question: There are two shelves A and B.The number of books in shelf A is 50 more than in shelf B..Then 20 books are removed from each shelf..Then the number of books in shelf A is twice the number of books in shelf..what are the number of books in shelf A originally?
Options:
A)100
B)120
C)140
D)160
E)180
Rationale: books in a=50+x and b=x when 20 are removed 50+x-20=2(x-20) therefore x=70 and no of buks in A initially=50+70=120
ANSWER:B
Answer: B
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat?
Options:
A)6
B)12
C)14
D)16
E)28
Rationale: Equate the fat:
0.1x + 0.4*8 = 0.2(x + 8) --> x = 16.
Answer: D.
Answer: D
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)11
B)10
C)17
D)16
E)15
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.Answer: B
Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)27 7/7 m
B)27 9/7 m
C)27 6/9 m
D)27 7/9 m
E)27 7/1 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train
= 50/9 * 5 = 250/9
= 27 7/9 m.
Answer:D
Answer: D
Question: At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
Options:
A)62
B)171
C)475
D)513
E)684
Rationale: Total automobile instalment credit = 57*3 = 171
Total consumer instalment credit =171∗100/36=475;Answer = C. 475
Answer: C
Question: 150 metres long yard, 11 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)10
B)15
C)14
D)16
E)17
Rationale: 11 trees have 10 gaps between them,
Required distance (150/10) = 15
B
Answer: B
Question: Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.
Options:
A)15
B)30
C)18
D)12
E)25
Rationale: Sol. Height of the triangle = [(13) 2- (12) 2](1/2) cm = (25)(1/2) cm = 5 cm.
Its area = (1/2)* Base * Height = ((1/2)*12 * 5) cm^2 = 30 cm^2.
Ans: B
Answer: B
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 14 lighbulbs, how many different samples can be chosen?
Options:
A)6
B)24
C)36
D)66
E)91
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
14!/2!(14-2)!
14!/2!*12!
14*13/2*1
=91
E
Answer: E
Question: A man sold 20 articles for $50 and gained 20%. How many articles should he sell for $90 to incur a loss 20%?
Options:
A)45
B)36
C)40
D)54
E)48
Rationale: Production cost per article: $50*(100%-20%) / 20 = $2.0
Required production costs for a loss of 20%: $90*(100% + 20%) = $108
Number of articles to be sold for $108 to incur a 20% loss: $108 / $2.0 = 54
Thus, solution D is correct.
Answer: D
Question: When 3 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
Options:
A)1
B)2
C)8
D)31
E)30
Rationale: Total outcome is 2^3 = 8
Favourable cases = H_ H
The second place can be occupied by either H or T
There are 2^1 =2 ways that can be done.
Hence, the correct option is B
Answer: B
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
Options:
A)299
B)2676
C)150
D)288
E)166
Rationale: 1/2 * 15 * 20 = 150
Answer:C
Answer: C
Question: T is 10% S. S is 5% of U. How are T and U related?
Options:
A)T is 50% of U
B)T and U are equal
C)T is 500% of U
D)T is 5% of U
E)T is 55% of U
Rationale: If...
T=.1S
S=.5U
Then...
T/.1=.5U
Multiply both sides by .1
T=5U
T is 500% of U
The answer is C
Answer: C
Question: In a board game, a stack of 42 cards, 8 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
Options:
A)1/8
B)1/5
C)1/4
D)4/21
E)3/14
Rationale: After 2 cards have been selected, there are 40 cards remaining.
P(third card has a picture of fruit) = 8/40 = 1/5
The answer is B.
Answer: B
Question: The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is
Options:
A)Rs.920
B)Rs.940
C)Rs.880
D)Rs.900
E)Rs.930
Rationale: This can be done much easier.
Price of 45 apples and 60 oranges = Rs.1350
Price of 15 apples and 20 oranges = Rs.1350/3 = Rs.450 (∵ Divided LHS and RHS by 15)
Price of 30 apples and 40 oranges = Rs.450 × 2 = Rs.900 (∵ Multiplied LHS and RHS by 2)
ANSWER:D
Answer: D
Question: In how many ways can a cricket eleven be chosen out of a batch
of 15 players.
Options:
A)1302
B)1365
C)1205
D)1064
E)1265
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
ANSWER B 1365
Answer: B
Question: Excluding stoppages, the average speed of a bus is 80 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
Options:
A)15 min
B)18 min
C)16 min
D)20 min
E)30 min
Rationale: In 1hr, the bus covers 80 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (80 - 40) km i.e 40 km at 80 km/hr.
stoppage time = 40/80 hrs
= 30 min
Answer: E
Answer: E
Question: 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)1/5
B)1/3
C)2/7
D)3/5
E)3/11
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B
Answer: B
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
Options:
A)10
B)76
C)88
D)55
E)12
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Answer: A
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)265 m
B)755 m
C)245 m
D)127 m
E)156 m
Rationale: Speed = (45 * 5/18) m/sec
= (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2
==> 2(130 + X) = 750
==> X
= 245 m.
Answer:C
Answer: C
Question: Find the L.C.M of 40,60,800
Options:
A)2600
B)1200
C)800
D)2400
E)4800
Rationale: 40=2^3*5 60=2^2*3*5 800=2^5*5^2
L.C.M=2^5*3*5^2=2400
Answer=(D)
Answer: D
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)7m
B)4m
C)9m
D)2m
E)5m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6
=2m.
Answer:D
Answer: D
Question: In 2010, Arman’s birthday was on a Thursday. What day of the week was it 68 days after his birthday?
Options:
A)Tuesday
B)Friday
C)Saturday
D)Sunday
E)Monday
Rationale: Day of week after 68 days after Arman's birthday = 7*9 + 5
Saturday as the period will have 9 weeks and 5 days .
The 5 days in the end will be Friday - Saturday - Sunday- Monday- Tuesday
Answer A
Answer: A
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400?
Options:
A)2000
B)1900
C)2888
D)2777
E)2671
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74
=> 1900
Answer:B
Answer: B
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 86 minutes, then the slower pipe alone will be able to fill the tank in
Options:
A)81 min
B)108 min
C)144 min
D)192 min
E)None
Rationale: Solution
Let the slower pipe alone fill the tank in x minutes.
Then, faster pipes will fill it in x/3 minutes.
Therefore, 1/x + 3/x	= 1/36
‹=› 4/x = 1/36
‹=› x= 144 min.
Answer C
Answer: C
Question: A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?
Options:
A)15 minutes
B)25 minutes
C)1 hour 15 minutes
D)1 hour 40 minutes
E)4 hours 30 minutes
Rationale: Trains depart from X at 6/7/8/9 and reach Y at 7:45/8:45/9:45 etc
Trains depart from Y at 9/9:30/10/10:30 etc. This means a minimum wait of 15 mins is required at Y.
They arrive at Z at 11:20/11:50/12:20/12:50. They depart from Z at 8/8:45/9:30/10:15/11/11:45/12:30 and so on. Note that if she arrives at Z at 20 mins past the hour, she will need to wait for at least 10 mins for 12:30/3:30 etc train. If she arrives at 50 mins past the hour, again she needs to wait for at least 10 mins to take the 2 o clock train. So anyway 10 mins at Z is a given.
So minimum she will need to wait for 15+10 = 25 mins.
This works out if she takes 8 o clock train from X, reaches Y at 9:45, takes 10 o clock train from Y and reaches Z at 12:20 and takes 12:30 train from Z.
Answer (B)
Answer: B
Question: What is the greatest positive integer x such that 3^x is a factor of 9^8?
Options:
A)5
B)9
C)16
D)20
E)30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^8?
9^8 = (3^2)^8 = 3^16
C. 16
Answer: C
Question: Two pipes C and D can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)A)1/8
B)B)1/3
C)C)1/9
D)D)1/2
E)E)1/4
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer:B
Answer: B
Question: In the manufacture of a certain product, 6 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
Options:
A)0.125%
B)0.24%
C)0.8%
D)1.25%
E)2.0%
Rationale: Percent of defective produced = 6%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(6/100)*100%
= (24/10000)*100%
= (24/100)%
= .24 %
Answer B
Answer: B
Question: Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 36, what is the measure of side XY?
Options:
A)4
B)4√2
C)12
D)8√2
E)Cannot be determined from the information provided
Rationale: ans C ..12..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=36 or yz=3*\sqrt{2}..
therefore hyp=xy=12
Answer: C
Question: A man has some hens and cows. If the number of heads be 42 and the number of feet equals 124, then the number of hens will be
Options:
A)22
B)24
C)26
D)20
E)28
Rationale: Explanation :
Let number of hens = h and number of cows = c
number of heads = 42
=> h + c = 42 ---(Equation 1)
number of feet = 124
=> 2h + 4c = 124
=> h + 2c = 62 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 62 - 42
=> c = 20
Substituting the value of c in Equation 1, we get
h + 22 = 42
=> h = 42 - 20 = 22
i.e., number of hens = 22
Answer : A
Answer: A
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Options:
A)482
B)197
C)267
D)216
E)270
Rationale: 20000(11/10)4 - 20000(6/5)2
= 482
Answer:A
Answer: A
Question: The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the 15th term in the sequence?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below
02,07,22,67, 202, 607, 1822, 5467...
Observe the last two digits of the sequence which have the cyclicity of4and the last two digits repeat in the order {02, 07, 22, 67}
Also 15th Term =4*3 +3
i.e. 15th Terms will have same Last two digits as 3rd term of the sequence = 22
i.e. Sum of lat two digits of 15th Term = 2+2 = 4
A
Answer: A
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.5
C)12.6
D)12.2
E)12.1
Rationale: 1000*15 = 1200*x
x = 12.5
Answer: C
Answer: C
Question: in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 8 people all together .how many people can sit in a bus?
Options:
A)52
B)49
C)95
D)88
E)89
Rationale: Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 8
Total People can seat= 81+8=89
ANSWER:E
Answer: E
Question: If y is a positive integer, which of the following could NOT be the square of y?
Options:
A) 5,228,644
B) 5,224,169
C) 4,989,696
D) 4,985,225
E) 4,998,752
Rationale: A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
Answer: E
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.70000?
Options:
A)6620
B)3277
C)2688
D)2998
E)23170
Rationale: A = 70000(11/10)3
= 93170
= 70000
----------
23170
Answer:E
Answer: E
Question: A sock drawer contains four socks, each one a different solid color. The colors of the socks are red, orange, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
Options:
A)12
B)15
C)6
D)36
E)42
Rationale: Since here order of socks is not important then we'll have 4C2 i.e. 6 combinations.
Answer : C
Answer: C
Question: There are a total of 100 jars on the shelf. Small jars hold 3 liters and large jars hold 5 liters. The jars can hold a total of 376 liters. How many small jars are on the shelf?
Options:
A)49
B)53
C)56
D)59
E)62
Rationale: Let S be the number of small jars and let L be the number of large jars.
S + L = 100.
L = 100 - S.
3S + 5L = 376.
3S + 5(100-S)= 376.
-2S+500=376.
2S = 124.
S = 62.
The answer is E.
Answer: E
Question: A cylindrical can has a radius of 4 centimeters and a height of 18 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
Options:
A)16 pi
B)64 pi
C)96 pi
D)144 pi
E)576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*4*18=144 pi
Answer is D.
Answer: D
Question: Robert's salary was increased by 50% and subsequently decreased by 10%. how much percentage does he gain?
Options:
A)15%
B)20%
C)10%
D)25%
E)30%
Rationale: let original salary be $100
increased salary = 10% of (150% of $100) = (10/100)*(150/100)*100 = $15
increase = 15%
correct option is A
Answer: A
Question: Find the average of all prime numbers between 40 and 80.
Options:
A)59.4
B)56
C)39.8
D)44.9
E)None
Rationale: Sol.
There are five prime numbers between 40 and 80.
They are 41, 43, 47, 53, 59, 61, 67, 71, 73, 79
âˆ´ Required average = [41+ 43+ 47+ 53+ 59+ 61+67+ 71+73+ 79 / 10] = 594/ 10 = 59.4
Answer A
Answer: A
Question: list of salaries of 5 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000
Options:
A)$28,000
B)$28,500
C)$30,200
D)$30,800
E)$35,500
Rationale: Ordering the data from least to greatest, we get:
$29,000, $31,000, $35,500, $40,000, $43,000
Since there is an odd number of items in the data set, we compute the median by taking the middle number
The median salary is $35,500.
Answer : E
Answer: E
Question: One fourth of a solution that was 13% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
Options:
A)25%
B)34%
C)22%
D)18%
E)8.5%
Rationale: consider total solution to be 100 liters and in this case you'll have: 75*0.13+25*x=100*0.16 --> x=0.25.
Answer: A.
Answer: A
Question: Find the smallest number of five digits exactly divisible by 24,48,64 and 88.
Options:
A)11952
B)11852
C)11752
D)11652
E)11552
Rationale: Smallest number of five digits is 10000.
Required number must be divisible by L.C.M. of 24,48,64,88 i.e 2012,
On dividing 10000 by 2012,we get 60 as remainder.
Therefore, Required number = 10000 +( 2012 â€“ 60 ) = 11952.
Answer is A.
Answer: A
Question: A student travels from his house to school at 10 km/hr and reaches school 2 hours late. The next day he travels 18 km/hr and reaches school 1 hour early. What is the distance between his house and the school?
Options:
A)65.0
B)67.5
C)70.0
D)72.5
E)75.0
Rationale: Let x be the distance from his house to the school.
x/10 = x/18 + 3
9x = 5x + 270
4x = 270
x = 67.5 km
The answer is B.
Answer: B
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $38 of gas?
Options:
A)212
B)256
C)304
D)372
E)460
Rationale: 38/4 = 9.5 gallons
9.5*32 = 304 miles
The answer is C.
Answer: C
Question: Arjun sold an ipod for Rs 17,940 with a discount of 8% and gained 19.6%. If no discount is allowed, then what will be his gain per cent?
Options:
A)30%
B)26.4%
C)24.8%
D)25.8%
E)None of these
Rationale: S.P = Rs 17,940
Discount = 8%
Market price = (17940 x 100)/ (100 - 8)
Rs 19,500
Gain = 19.6%
C.P = 17940 x 100/100 + 19.6 = Rs 15,000
If no discount is allowed on the Market price then S.P = Rs 19,500
Therefore, Gain % = (4500/15000 ) x 100 = 30 %
ANSWER:A
Answer: A
Question: A bag contains ten marbles of the same size: 3 are identical green marbles, 2 are identical red marbles, and the other 5 are five distinct colors. If 5 marbles are selected at random, how many distinct combinations Z of five marbles could be drawn?
Options:
A) 41
B) 51
C) 62
D) 72
E) 82
Rationale: there will be different cases, which we will take one by one..
1)case 1 when all five colours are different-7c5=21..
2)case 2 when three different colours and 2 of same type=6c3*2=30..
3)case 3 when two different colours and 3 of same type=6c2=15..
4)case 4 when one different colours and 2 of two different colors=5c1*4!/2!2!=15...
5)case 4 when 3 of one type and 2 of other colour=1...
total Z-82 ans E
Answer: E
Question: How many seconds will a 600 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)20
B)30
C)36
D)50
E)60
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 = 600 * 3/50 = 36 sec.
Answer: Option C
Answer: C
Question: Choose the missing terms out of the given alternatives.
AZ, BY, ?
Options:
A)EF
B)GH
C)ED
D)DW
E)CX
Rationale: E
CX
The first letter moves one step forward. The second letter moves one step backward.
Answer is E
Answer: E
Question: If X,Y is 25%,35% smaller than Z then how much percentage is Y greater than X?
Options:
A)13 1/2%
B)13 1/4%
C)13 1/3%
D)12 1/2%
E)14 1/2%
Rationale: Explanation:
X = 75 %
Y = 65 %
Z = 100 %
X-Y/X * 100 = 10/75 * 100 = 13 1/3 % greater than X
Answer: Option C
Answer: C
Question: A bike traveled 127 miles in 5 hours 11 minutes. What was the average speed of the bike in miles per hour?
Options:
A)24.50 miles / hour
B)25.6 miles / hour
C)25.9 miles / hour
D)29.1 miles / hour
E)30 miles / hour
Rationale: We first convert the time of 5 hours 11 minutes in minutes
5 hours 11 minutes = 5* 60 + 11 =311 minutes
Average speed S is given by distance / time. Hence
S = 127 miles / 311 minutes = 0.408 mile / minute
= 24.50 miles / hour
correct answer A
Answer: A
Question: If m,s,and t are positive real numbers such that m(s+t) = 152, s(t+m) =162 , and t(m+s) = 170, then mst is
Options:
A)a) 672
B)b) 688
C)c) 704
D)d) 720
E)e) 750
Rationale: ms+mt = 152 --------------------------------------1)
st+sm = 162---------------------------------------2)
mt+ts = 170---------------------------------------3)
Re-writing equation 3 as follows:
mt+ts = 162 + 8
mt+ts = st+sm + 8
mt = sm + 8 ............... (4)
Adding (1)(4)
2mt = 160
mt = 80
mst has to be multiple of 80, only 720 fits in
Answer = D
Answer: D