MU-NLPC/Calc-aqua_rat huggingface dataset:
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)	Choose one.
A) 92  B) 90  C) 82  D) 78  E) 75

Solution: 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 = 75.75
Answer: E
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?  Choose the correct choice:	A) 160	B) 150	C) 250	D) 80	E) 50

Solution: 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: 250.
Answer: C
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? Choose the correct choice from the following answers:
A) 1/4
B) 2/5
C) 1/6
D) 2/7
E) 1/8

Solution: 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 1/8.
Answer: E
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?	Choose one
A) 190 B) 199 C) 77 D) 66 E) 221

Solution: 200*2= 
200*2 = 400
400   780   -----   380   1----2   ?----380= 190   190nswer:190
Answer: A
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?  Choose the correct choice from the following choices
A) 90	B) 99	C) 97	D) 95	E) 65

Solution: 30 * 33/2 = 5/2 * 2 * x => x = 99   ANSWER 99
Answer: B
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

Solution: 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= 
  5 * 15 = 75
75 ways.   75 waysnswer: 75 ways
Answer: A
Three candidates contested an election and received 1000, 2000 and 4000votes respectively. What percentage of the total votes did the winning candidate got?
Choose the correct choice from the following options.
A) 30%  B) 50%  C) 57%  D) 62%  E) 75%

Solution: Total number of votes polled = (1000 + 2000 + 4000)= 
(1000 + 2000 + 4000) = 7_000
7000   Required percentage= 4000/7000 * 100 = 57% (approximately)   Answer: Option 57%
Answer: C
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?  Choose the correct choice from the following answers:  A) 3  B) 4  C) 6  D) 8  E) 10

Solution: 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 6.
Answer: C
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? Choose the most appropriate option:
A) 27
B) 25
C) 24
D) 20
E) 22

Solution: 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= 
 9+3+11-1 = 22
22.   Answer: 22.
Answer: E
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? Choose the most appropriate option.
A) 2/3  B) 1/2  C) 1/3  D) 2/4  E) 2/5

Solution: 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 1/2.
Answer: B
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?
Choose the correct choice from the following.
A) Rs. 3932  B) Rs. 3972  C) Rs. 3372  D) Rs. 3942  E) Rs. 3772

Solution: Explanation:   Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.   R = (100 * 60)/(100 * 6)= 
(100 * 60)/(100 * 6) = 10
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 Rs. 3372
Answer: C
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Select the correct option:
A) 18%
B) 19%
C) 68%
D) 19%
E) 38%

Solution: 1500 ---- 270   100 ---- ? => 18%   18%nswer:18%
Answer: A
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?  Choose the correct answer:	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

Solution: :   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: 18 min 24 sec
Answer: C
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

Solution: 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.   78
Answer: C
Which of the following numbers is between 2⁄5 and 1⁄4? Choose the correct choice from the following choices
A) .45  B) .35  C) .23  D) .22  E) .20

Solution: Isn't it .35?    2/5= 
 2/5 = 2/5 = around 0.4
.40   1/4= 
1/4 = 1/4 = around 0.25
.25   The only answer between that is .35, .35.
Answer: B
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

Solution: 14 years 8 monthsnswer   Total decrease   = ( 20 X 2 ) months   = 3 years 4 month   ∴ 14 years 8 monthsge of the new boy   = ( 18 years ) – ( 3 years 4 months)   = 14 years 8 month   Correct Option: 14 years 8 months
Answer: A
If d is the mean of x, y, and z, what is the mean x - 5, y - 5, z - 5 ?
Choose one:
A) d
B) 3d
C) 15d
D) d - 5
E) d + 15

Solution: 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 - 5.
Answer: D
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?
Choose the correct option: A) 654 B) 655 C) 656 D) 657 E) 658

Solution: total cost 940   940*30/100= 
940*30/100 = 282
282   so the cut in amount is 282   the less amount to be spend is  940-282= 
 940-282 = 658
658   ANSW658R:658
Answer: E
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? Pick:  A) 180  B) 270  C) 360  D) 500  E) 550

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 870= 
9/29 * 870 = 270
270   ANSWER 270
Answer: B
what is the remainder when 45820 is divided by 45  Choose the correct choice from the following choices.
A) 8 B) 15 C) 25 D) 10 E) 5

Solution: 45820 / 45   45820 / 9*5   9164 / 9 => rem = 2   we have cancelled it by 5   reqd remainder = 5*2= 
5*2 = 10
10   ANSWER:10
Answer: D
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?  Choose the correct choice from the following answers.
A) $10,350	B) $10,494	C) $10,500	D) $11,500	E) $12,705

Solution: 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 ($10,494).
Answer: B
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. Choose the correct choice from the following options:
A) Rs. 600  B) Rs. 1620  C) Rs. 1080  D) Rs. 900  E) None of these

Solution: 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 Rs. 900
Answer: D
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.	Choose the correct choice from the following
A) 53 hours
B) 13 hours
C) 30 hours
D) 43 hours
E) 45 hours

Solution: 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:30 hours
Answer: C
Megala bought an electric drill at 85% of the regular price.
She paid $850 for the drill. What was the regular price?	Choose the correct answer
A) $1000	B) $1869	C) $3869	D) $5869	E) $4869

Solution: Regular price = 850/85*100= 
850/85*100 = 1_000
1000   $1000nswer : $1000
Answer: A
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:  Choose the correct option.
A) 34299	B) 28789	C) 15000	D) 28999	E) 15022

Solution: Answer: 15000) Rs.15000
Answer: C
What is the Compound Interest on Rs.8500 at 7.5% p.a. compounded half-yearly for 2 1/2 years.	Choose the correct choice from the following answers
A) 1409.85  B) 1717.85  C) 1427.85  D) 2717.85  E) 1817.85

Solution: Compound interest : A = P(1 + r/n)nt   A = 10,217.85   C.I. >> 10,217.85 - 8500 >> Rs. 1717.85   Answer:1717.85
Answer: B
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?
--	Choose one
A) 12
B) 19
C) 60
D) 180
E) 720

Solution: 4C3 * 5C2 * 3C2 = 4*60*3= 
4*60*3 = 720
720.   Answer: 720.
Answer: E
Find the odd man out
3,12, 24,48, 56, 96	Choose one:
A) 48
B) 8
C) 16
D) 56
E) 2

Solution: 3*2= 
3*2 = 6
6   6*2= 
6*2 = 12
12   12*2= 
12*2 = 24
24   24*2= 
24*2 = 48
48   48*2= 
48*2 = 96
96   ANSWER:56
Answer: D
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:  Choose the correct choice from the following answers:  A) 15.8 sec.  B) 12.6 sec.  C) 11.8 sec.  D) 10.8 sec.  E) 08.8 sec.

Solution: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.   Distance covered in crossing each other = (140 + 210)= 
(140 + 210) = 350
350 m.   Required time= 350x9/250 = 54/5 = 12.6 sec.   ANSWER 12.6 sec.
Answer: B
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?	Choose the correct choice from the following choices.
A) 14 1/3 B) 10 1/3 C) 11 1/3 D) 12 1/3 E) 13 1/3

Solution: 2/10 + 2/15 + x/20 = 1   x = 40/3 = 13 1/3   Answer: 13 1/3
Answer: E
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.
Pick one.
A) 63^4	B) 62^5	C) 62(62^4)	D) 66(65^4)	E) 63(62^6)

Solution: 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 66(65^4)
Answer: D
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?	Choose the correct choice
A) 12 liters  B) 62 liters  C) 41 liters  D) 50 liters  E) 34 liters

Solution: Milk = 3/5 * 155= 
3/5 * 155 = 93
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:62 liters
Answer: B
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
Choose the correct answer:
A) 6
B) 3 × 2^a
C) 2 × 3^(2a)
D) 6^a
E) 6^(2a)

Solution: Since, q is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1   Only for 6^(2a), 6^(2a) doesn't satisfy, if a = 1 and q=18, it is not divisible by 6^2 (i.e 36)   Hence answer is 6^(2a)
Answer: E
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?	Choose the correct choice from the following.
A) 7/12  B) 1/4  C) 1/2  D) 7/24  E) 17/24

Solution: 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.   1/2
Answer: C
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
Answers:	A) 2 mph	B) 2.5 mph	C) 3 mph	D) 4 mph	E) None

Solution: 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.   2 mphnswer 2 mph
Answer: A
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?	Choose the correct choice from the following answers:
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

Solution: 100 --- 10 22 1/2 kmphS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 21/2 kmph   Answer:22 1/2 kmph
Answer: D
Find the value of 10 + 2 â€¢ (8 â€“ 3) Options.
A) 25
B) 13
C) 17
D) 20
E) 15

Solution: 10 + 2 â€¢ (8 â€“ 3)   = 10 + 2 (5)   = 10 + 2 *5   = 10 + 10= 
10 + 10 = 20
20   correct answer 20
Answer: D
A person crosses a 300 m long street in 4 minutes. What is his speed in km per hour?
Pick
A) 1.6 B) 4.5 C) 8.2 D) 6.5 E) 2.9

Solution: distance = 300 meter   time = 4 minutes = 4 x 60 seconds = 240 seconds   Speed = distance/time=300/240= 
300/240 = 5/4 = around 1.25
1.25 m/s=1.25Ã—18/5 km/hr=4.5 km/hr   Answer :4.5
Answer: B
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?  Select the correct option:
A) Baskar  B) They have equal popularity  C) Dinesh  D) Raja  E) Kamal

Solution: 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 Dinesh
Answer: C
The radius of a wheel is 25.4 cm. What is the distance covered by the wheel in making 500 resolutions? Pick one
A) 724 m	B) 798.3 m	C) 287 m	D) 278 m	E) 927 m

Solution: 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:798.3 m
Answer: B
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?  Choose the correct choice from the following answers.
A) 6Rs	B) 2Rs	C) 4Rs	D) 9Rs	E) 3Rs

Solution: 5M = xW = 8B   5M + xW + 8B ----- 90 Rs.   5M + 5M + 5M ----- 90 Rs.   15M ------ 90 Rs. => 1M = 6Rs.   6Rsnswer: 6Rs
Answer: A
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 ?  Choose one:
A) 3  B) 2.  C) 1/2.  D) 1/3.  E) There isn't enough data to answer the question

Solution: X-Y = (X+Y)/2   2 X - 2 Y = X + Y   X = 3 Y   Y/X = 1/3   1/3. is the answer.
Answer: D
The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?	Choose the correct choice from the following options
A) 10 and 50 B) 12 and 18 C) 24 and 64 D) 21 and 63 E) 22 and 44

Solution: 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 24 and 64.
Answer: C
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?  Select the correct option:  A) Rs 15  B) Rs 12.10  C) Rs 22.70  D) Rs 26.80  E) None of these

Solution: Explanation :   Let the cost of the tax items = x   Given that tax rate = 6%   Rs 22.70ost 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= 
28 - 5 - 0.30 = 22.7
22.70   Answer : Rs 22.70
Answer: C
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?  Choose one:
A) 16 : 5 B) 14 : 5 C) 16 : 7 D) 19 : 5 E) None of these

Solution: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4= 
19/4 = 19/4 = around 4.75
4.75 litres   As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 4.75 : 1.25 = 19 : 5.   ANSWER:19 : 5
Answer: D
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of three rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after ___ minutes?  Choose the most appropriate option.
A) 11 min	B) 12 min	C) 10 min	D) 15 min	E) 30 min

Solution: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.   Relative speed of A and B = 3 - 1= 
3 - 1 = 2
2 rounds per hour.   Time taken to complete one round at this speed= 1/2 hr = 30 min.   30 min
Answer: E
What is the least number of digits (including repetitions) needed to express 10^300 in decimal notation?	Pick one:
A) a) 4	B) b) 100	C) c) 301	D) d) 1000	E) e) 1001

Solution: 10^n is a decimal number with a 1 followed by n zeros.   So 10^300 will include 300 0's + 1 digit for 1 = 301   So the answer is c) 301.
Answer: C
A train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. Choose the correct option
A) 67 kmph  B) 50 kmph  C) 55 kmph  D) 60 kmph  E) 70 kmph

Solution: Explanation:   Let the speed of the train be x kmph.   Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.   Therefore 120/((x+5)×5/18)=6 <=> 30 (x + 5) = 2160 <=> x = 67   Speed of the train is 67 kmph.   67 kmphnswer: Option 67 kmph
Answer: A
A boat can move upstream at 25 kmph and downstream at 31 kmph, then the speed of the current is?	Answers.
A) 3  B) 6  C) 7  D) 54  E) 8

Solution: US = 25   DS = 31   M = (31 - 25)/2 = 3.3nswer:3
Answer: A
In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 72%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
Pick one.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: The tests scores are 4k, 5k, 6k, 7k, and 8k.   The sum of the test scores is 30k.   The average test score is 30k/5 = 66. Then k = 11.   The test scores are 44, 55, 66, 77, and 88.   The student passed 4 subjects.   The answer is 4.
Answer: D
A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
Choose one:	A) 1/5	B) 2/7	C) 2/9	D) 3/5	E) 4/11

Solution: The total number of ways to choose 2 apples is 7C2 = 21   The number of ways that include the spoiled apple is 6C1 = 6   P(the spoiled apple is included) = 6/21 = 2/7   The answer is 2/7.
Answer: B
Find the number of elements in the power set of {1,2}  Choose the correct answer
A) 4	B) 0	C) 2	D) 3	E) 5

Solution: Power set is the set of subsets of {1,2}   That is { {1,2}, {1}, {2}, f}   4NSWER:4
Answer: A
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 8 is	Select
A) 189 B) 197 C) 221 D) 227 E) 230

Solution: In that case, the Sophie prime numbers greater than 8 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9   Product would be 1 x 3 x 7x9 =189 189nswer should be 189.
Answer: A