MU-NLPC/Calc-aqua_rat huggingface dataset:
Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water?  Select the correct option: A) 3:2 B) 1:4 C) 3:1 D) 5:2 E) 4:3

Solution: G = 10W   C = 5W   Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy   1gm gold + x gm copper = x+1 gm of alloy   10W+5Wx = x+1 * 6W   10+5x = 6(x+1)   x = 4   Ratio of gold with copper = 1:4 = 1:4   Answer is 1:4
Answer: B
If x is a positive integer, which of the following could NOT be the square of x?  Pick:
A) 9526  B) 4532  C) 4066  D) 6515  E) 3255

Solution: A number ending in 2 cannot be a perfect square.   4532 ends in a number 2, making that the correct answer   (4532) 4532
Answer: B
A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 10 people to travel x miles if he decides to give them a 50% discount?  Answers:
A) 3xr/2 B) 3x/200r C) 3r/200x D) 3xr/200 E) xr/20

Solution: 10xr/2 is in cents - 10xr/200 dollars = xr/20   Answer : xr/20
Answer: E
6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. Hence the current average age has become 45. Find the age of seventh person? Pick one:	A) 65	B) 67	C) 68	D) 69	E) 50

Solution: Explanation :   Let the sum of current ages of 6 persons = x   Given Average age of 6 person after 2 years = 43   => x+6(2)/6=43   => x+12=258   = x=246   Let the seventh's person age will be y   Given Current average age of 7 persons = 45   [Sum of current 6 person's age (x) + Seventh person's age (y)] /7= 45   => 246+y=45(7)   => y= 315 -246   => y = 69   Hence Seventh person's age = 69   Hence (D) is the correct answer.   Answer : 69
Answer: D
In a class of 60 students, 20 did not opt for math. 15 did not opt for science and 5 did not opt for either. How many students of the class opted for both math and science?  Choose the correct choice from the following answers
A) 23  B) 25  C) 27  D) 30  E) 48

Solution: 60 students total   20 did not opt for math   15 did not opt for science   5 did not opt for either   Total of 40 students in math and 10 did not opt for sci but did for math    40-10= 
 40-10 = 30
30   30 students of the class opted for both math and science   Answer:   D. 30
Answer: D
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?	Choose the correct choice from the following answers
A) 1	B) 7	C) 8	D) 9	E) 6

Solution: C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days'   Answer: 9
Answer: D
A rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $10 apiece, what is the total cost for the number of carpet squares needed to cover the floor?  Select
A) $200 B) $240 C) $480 D) $960 E) $1,920

Solution: The width of the rectangular floor(8 m) is a multiple of one side of the square(2 m), and the length of the floor(10 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (8/2)*(10/2)= 
(8/2)*(10/2) = 20
20.   The total cost is 20*10= 
20*10 = 200
$200.   The answer is, therefore, $200.
Answer: A
If 6 women can color 360 m long cloth in 3 days, then 5 women can color 100 m long cloth in?  Choose the correct option:	A) 2 days	B) 3 days	C) 2.5 days	D) 4 days	E) 1 day

Solution: The length of cloth painted by one woman in one day = 360/ 6× 3 = 20 m   No. of days required to paint 100 m cloth by 5 women = 100/ 5 × 20 = 1 day   Answer : 1 day
Answer: E
When a certain number X is divided by 54, the remainder is 22. What is the remainder when X is divided by 18?
Choose the most appropriate option
A) 3
B) 1
C) 2
D) 4
E) 5

Solution: Let possible value of x is 76   least possible value of x/18 is 76/18 =>4 quotient with remainder 4   Thus answer is (4) 4
Answer: D
If y is 60% greater than x, than x is what % less than y?
Choose the correct choice from the following answers: A) 29.3% B) 33.4% C) 37.5% D) 41.6% E) 45.7%

Solution: y = 1.6x   x = y/1.6 = 10y/16 = 5y/8   x is 3/8 less which is 37.5% less than y.   The answer is 37.5%.
Answer: C
Ayesha’s father was 38 years of age when she was born while her mother was 31 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?  Choose the correct choice from the following.
A) 2 years	B) 4 years	C) 11 years	D) 8 years	E) None

Solution: EXPLANATION   Mother’s age when Ayesha’s brother was born = 31 years.   Father’s age when Ayesha’s brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 – 31) years = 11 years.   Answer 11 years
Answer: C
There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 15% of all the students at Morse have cars, how many students are in the three lower grades? Choose the correct choice from the following choices:
A) 600
B) 900
C) 1200
D) 1600
E) 2100

Solution: Let x be the number of students in the lower three grades.   0.1x + 150 = 0.15(x+300)   0.05x = 105   x = 2100   The answer is 2100.
Answer: E
The difference between the ages of two persons is 11 years. Ten years ago, the elder one was twice as old as the younger one. The present age of the elder person is	Pick one: A) 18 B) 19 C) 20 D) 17 E) 16

Solution: Let their ages of x years and (x + 11) years respectively.   Then, (x + 11) - 10 = 2(x - 10)   ⇔ x +1 = 2x - 20   ⇔ 3x = 21.   ∴ Present age of the elder person = (7 + 11)= 
(7 + 11) = 18
18years.   18nswer :18 years
Answer: A
There is 66x33m rectangular area. Ram is 11/8 times faster than Krishna. Both of them started walking at opposite ends and they met at some point then, Ram said "See you in the other end" Then they continued walking. After some time Ram thought he will have tea so he turned back walked back 15 meters then he changed his mind again and continued walking .How much Krishna has traveled by the time they meet? Select.
A) 93  B) 34  C) 95  D) 96  E) 85

Solution: let x be the distance between the point they first met   total time taken by the two willbe equal   so (x+30)*8/11 = (198-x)   x= 102m   distance travelled by krishna= 198-102= 
198-102 = 96
96m   ANSWER:96
Answer: D
A boy runs 200 metres in 30 seconds. What is his speed ? Options:
A) 20 km/hr  B) 24 km/hr  C) 30 km/hr  D) 32 km/hr  E) 34 km/hr

Solution: 200/30 * 18/5= 
200/30 * 18/5 = 24
24 km/hr   ANSWER:24 km/hr
Answer: B
If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ? Pick:
A) 1/(8+8k) B) 2/(1+k) C) 1/(8+k) D) 4/(8+k) E) 4/(1+k)

Solution: 1/Y + 1/Y + 1/Y + 1/Y   = 4/Y   = 4/(2 + 2K)   = 2/(1 + K)   ANSWER:2/(1+k)
Answer: B
An automobile manufacturer offers a station wagon with either a 8-cylinder engine or a 6-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 8-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon? Pick one
A) 4	B) 6	C) 8	D) 10	E) 12

Solution: 8-cylinder engine wagons = 2*2*2= 
2*2*2 = 8
8 (manual or automatic, with or without trailer);   6-cylinder engine wagons= 2*2= 
2*2 = 4
4 (manual or automatic).   Total= 8 + 4= 
8 + 4 = 12
12.   Answer: 12.
Answer: E
In a simultaneous throw of 2 dice, what is the probability of not getting a doublet?  Answers.
A) 2/3
B) 1/6
C) 4/7
D) 5/6
E) 4/9

Solution: n(S) = 6*6= 
6*6 = 36
36   E= event of not getting a doublet = 36- event of getting a doublet= 36-6= 
36-6 = 30
30   {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}   Probability= 30/36 = 5/6   Answer is 5/6
Answer: D
11, 13, 17, 19, 23, 29, 31, 37, 41, ?	Options:
A) 47
B) 43
C) 51
D) 53
E) 50

Solution: 43   43   The series consists of prime numbers.
Answer: B
One fourth of one third of two fifth of a number is 16. What will be40% of that number
Choices:
A) 140  B) 150  C) 180  D) 192  E) 250

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 16 then x = 16 * 30= 
16 * 30 = 480
480   40% of 480= 192   Answer: Option 192
Answer: D
A man deposited 20% of 25% of 30% of an amount in a bank. If he deposited 750 then what was amount he had initially	Select.
A) 55000  B) 50000  C) 40000  D) 30000  E) 20000

Solution: if(20/100)*   (25/100)*(30/100)*x=750   then x=50000.   ANSWER:50000
Answer: B
There are 11engineers and 7 civil engineers in a company. Theyare selecting member for row. In how many ways can they be seated in a row so that no two of the civil engineers will sit together?  Options:
A) 9!×11!/5!
B) 11!×12!
C) 11!×12!/5!
D) 12!/5!
E) 10!×12!/5!

Solution: 11 software engineers can be arranged in 11! ways. ...(A)   Now we need to arrange civil engineers such that no two civil engineers can be seated together. i.e., we can arrange 7 civil engineers in any of the 12 (=11+1) positions marked as * below.   * 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 *   (where 1, 2… 11 represent software engineers)   This can be done in 12P7 ways. ...(B)   From (A) and (B),   required number of ways   = 11! × 12P7   =11!×12!/5!   11!×12!/5!
Answer: C
A letter lock consists of three rings each marked with EIGHT different letters. The number of distinct unsuccessful attempts to open the lock is at the most?	Pick one.
A) 4002	B) 4090	C) 4095	D) 177	E) 123

Solution: Since each ring consists of eight different letters, the total number of attempts possible with the three rings is   = 8 * 8 * 8 = 4096. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts = 4096 - 1= 
4096 - 1 = 4_095
4095   Answer:4095
Answer: C
A, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is :	Pick:
A) 5 : 6 : 18
B) 5 : 6 : 12
C) 5 : 6 : 11
D) 5 : 6 : 10
E) 5 : 6 : 128

Solution: Let their initial investments be x, 3x and 5x respectively. Then,   20x : 24x : 40x = 5 : 6 : 10   Answer: 5 : 6 : 10) 5 : 6 : 10
Answer: D
The temperature of a certain cup of coffee 30 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120*2^(-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
Choices.
A) 65	B) 120	C) 80	D) 85	E) 90

Solution: First, we have to find a.   We know that after t=30 minutes the temperature F=120 degrees.   Hence:   120 = 120*(2^-30a)+60   60 = 120*(2^-30a)   60/120 = 2^-30a   1/2 = 2^-30a   2^-1 = 2^-30a   -1 = -30a   1/30 = a   Now we need to find F after t=30 minutes:   F = 120*(2^-1/30*30)+60   F = 120* (2^-1) +60   F = 120* (1/2^1) +60   F = 120*1/2 +60   F = 60+60= 
60+60 = 120
120   Answer 120!
Answer: B
A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?  Answers: A) Rs.45 B) Rs.78 C) Rs.44 D) Rs.40 E) Rs.46

Solution: π (152 - 132) = 176   176 * 1/4 = Rs.44   ANSWER:Rs.44
Answer: C
The no. of girls in a class are seven times the no. of boys, which value can neverbe the of total students?	Pick.
A) 4
B) 5
C) 8
D) 10
E) 12

Solution: Let the boys are X, then girls are 7X, total = X+7X = 8X   So it should be multiple of 8, 30 is not a multiple of 8.   8
Answer: C
The ratio of investments of A, B and C is 5:7:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.
Choose the correct choice from the following answers.
A) 1:1:2 B) 3:5:6 C) 3:2:4 D) 2:4:3 E) 2:5:3

Solution: The ratio of investments of A, B and C is 5:9:7.   The ratio of shares of A, B and C is 5:9:14.   Therefore, Ratio of their periods of investments is   (5/5) : (9/9) : (14/7) = 1:1:2   1:1:2NSWER:1:1:2
Answer: A
Replace the ? by the correct Mathematics symbol to make the expression true
10 ? 10 ? 4 ? 7 = 12	Answers
A) 10 ÷ 10 x 4 - 7 = 12  B) 10 + 10 ÷ 4 + 7 = 12  C) 10 x 10 + 4 - 7 = 12  D) 10 x 10 ÷ 4 + 7 = 12  E) 10 x 10 ÷ 4 - 7 = 12

Solution: Answer : 10 + 10 ÷ 4 + 7 = 12
Answer: B
If 144/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.	Select:
A) I only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

Solution: The largest possible value of x is 36 (the greatest common factor of 144 and 108), and if x=36 then ONLY III is true.   Answer: III only.
Answer: B
The average score of a cricketer in 6 matches is 27 and in other 4 matches is 32. Then find the average score in all the 10 matches?
Pick one:
A) 25
B) 27
C) 30
D) 29
E) 42

Solution: Average in 10 matches = (6*27 + 4*32)/6+4 = 162+128/ 10 = 290/10= 
290/10 = 29
29   Answer is 29
Answer: D
If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. Find the number of participants.
Pick.
A) 15	B) 16	C) 17	D) 18	E) 19

Solution: Let P be the number of participants.   PC2 = 171   (P)(P-1) = 342 = 19*18   P = 19   The answer is 19.
Answer: E
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15% while buying and by 20% while selling. What is his percentage profit?
Answers
A) 10.22% B) 20.22% C) 21.22% D) 43.75% E) Can't be calculated

Solution: The owner buys 100 kg but actually gets 115kg;   The owner sells 100 kg but actually gives 80kg;   Profit:   (115-80)/80*100= 
  (115-80)/80*100 = 175/4 = around 43.75
~43.75%   Answer: 43.75%.
Answer: D
Two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?	Pick one:
A) 11
B) 9
C) 13
D) 14
E) 12.8

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/18 = 6.7 m/sec.   Relative speed = 12 + 6.7= 
12 + 6.7 = 18.7
18.7 m/sec.   Required time= (120 + 120)/18.7 = 12.8 sec.   Answer: Option 12.8
Answer: E
Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 36 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?	Choose the correct choice from the following options:
A) 2:5	B) 5:14	C) 3:5	D) 4:15	E) 14:5

Solution: Answer = D) 4:15   ........................ Rum ..................... Coke ................. Total   First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)   Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)   Total .................. 10 ............................. 28 .................... 38   Ratio = 8:30 = 4:15   4:15
Answer: D
A furniture manufacturer has two machines, but only one can be used at a time. Machine W is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine W can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?  Pick one: A) 14 B) 13 C) 11 D) 9 E) 7

Solution: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.   To finish a work Machine W say you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=9
Answer: D
6 men, 8 women and 6 children complete a job for a sum of Rs.950. If their individual wages are in the ratio 4:3:2, the total money earned by the children is Pick one: A) Rs. 150 B) Rs. 170 C) Rs. 180 D) Rs. 190 E) None of these

Solution: Explanation:   Ratio of wages of 6 men, 8 women and 6 children = 6 x 4 : 8 x 3 : 6 x 2   = 24 : 24 : 12   = 2 : 2 : 1   Money earned by children = 950 x (1/5) = Rs. 190   Answer: Option Rs. 190
Answer: D
Second Saturday and every Sunday is a holiday. How many working days will be there in a month of 30 days beginning on a Saturday?
Choose the correct answer.
A) 24 B) 23 C) 18 D) 21 E) 22

Solution: Explanation :   Mentioned month begins on a Saturday and has 30 days   Sundays = 2nd, 9th, 16th, 23rd, 30th   => Total Sundays = 5   Every second Saturday is holiday.   1 second Saturday in every month   Total days in the month = 30   Total working days = 30 - (5 + 1)= 
30 - (5 + 1) = 24
24. 24nswer : Option 24
Answer: A
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? Choose the correct choice.
A) 135 B) 144 C) 145 D) 146 E) 149

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 6= 
 24 * 6 = 144
144.   Answer:144
Answer: B
16.02 Ã— 0.00001 = ?
Pick one
A) 0.1602 B) 0.001602 C) 1.6021 D) 0.01602 E) None of these

Solution: 16.02 Ã— 0.00001 = 0.0001602   The answer is None of these.
Answer: E
If X = the product of eight distinct prime numbers, how many factors does X have besides 1 and itself?  Select the correct option:
A) 166  B) 188  C) 210  D) 232  E) 254

Solution: Since X has 8 distinct prime factors, X has a total of 2^8 = 256 factors.   Besides 1 and itself, X has 254 factors.   The answer is 254.
Answer: E
In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?	Choose the correct answer: A) A)5760 B) B)14400 C) C)480 D) D)56 E) E)40320

Solution: Consider the following arrangement:   *B*B*B*B*B*   Now, if girls occupy the places of 6 stars no girls will be together.   # of ways 3 girls can occupy the places of these 6 stars is C36=20;   # of ways 3 girls can be arranged on these places is 3!=6   # of ways 5 boys can be arranged is 5!=120   So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20∗6∗120=14,400   ANS:14400
Answer: B
A combustion reaction forms carbon dioxide. A carbon dioxide molecule contains one carbon and two oxygen atoms. If, over a period of 10 minutes, a combustion reaction creates 10,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute?
Pick one.
A) 1,000 B) 500 C) 250 D) 50 E) 0

Solution: Solution:   10,000 carbon dioxide molecules are created over a period of 10 minutes. Therefore 10,000/10 = 1,000 carbon dioxide molecules are created on average per minute   Each carbon dioxide molecule contains one carbon atom and two oxygen atoms. So 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms. The difference is 2,000 – 1,000 = 1,000.   The correct answer is 1,000.
Answer: A
There is a 40% chance that Germany will not win at all during the whole season. There is a 50% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Germany will win and Federer will play during the season?  Select the correct option:
A) 50%	B) 60%	C) 70%	D) 72%	E) 80%

Solution: There is a 40% chance that Germany will not win at all during the whole season   We can infer that there is 60% chance Germany will win .   Similarly There is a 50% chance that Federer will not play at all in the whole season   We can also infer that there is 50% chance that Federer will play.   50%nswer 50%
Answer: A
Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction? Answers
A) 5hours	B) 10hours	C) 8hours	D) 10hours	E) 12hours

Solution: To be 2km apart they take 1 hour   To be 10km apart they take = 1/2 * 20= 
1/2 * 20 = 10
10 hours   Answer is 10hours
Answer: B
Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?	Choose the correct choice from the following.
A) 9  B) 8  C) 6  D) 45  E) 2

Solution: There are five letters in the given word.   Consider 5 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.   The number of words   = 3! = 6.   Answer:6
Answer: C
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square? Choose the correct choice from the following answers
A) 5:17  B) 5:14  C) 5:10  D) 5:11  E) 5:16

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128   = 5:16   Answer:5:16
Answer: E
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
Choose the correct choice from the following answers
A) 1/5	B) 1/2	C) 1/3	D) 1/9	E) 1/2

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then   = 18/36 = 1/2   P(E) = 1 - 1/2   = 1/2.   Answer: 1/2
Answer: B
The perimeters of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares. Choose one:  A) 22  B) 24  C) 77  D) 99  E) 11

Solution: Explanation:   side of first square = 40/4= 
40/4 = 10
10cm   side of second square= 32/4= 
32/4 = 8
8cm   area of third squre= 10² - 8² = 36 sq cm   side of third square = \inline {\color{24lack}\sqrt{36}} = 6 cm   required perimeter = 6*4= 
6*4 = 24
24cm   Answer: 24) 24
Answer: B
The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively	Choose the correct option
A) 20,20 B) 20,10 C) 25,15 D) 30,10 E) 40,10

Solution: Explanation:   Let their ages be x and (x + 20) years.   5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.   Their present ages are 30 years and 10 years   Answer: Option 30,10
Answer: D
The cricket team of 11members is 26yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? Choose the correct choice.
A) 19
B) 21
C) 23
D) 27
E) 30

Solution: Let the average age of the whole team be x years.   11x - (26 + 29) = 9 (x - 1)   => 11x - 9x = 46   => 2x = 46   => x = 23.   So, average age of the team is 23 years.   23
Answer: C
Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 35 kmph.For how many minutes does the bus stop per hour?  Choose the correct choice from the following answers.
A) 17 minutes B) 18 minutes C) 19 minutes D) 16 minutes E) None of these

Solution: Explanation :   In one hour   Due to stoppages, it covers 15 km less.   Time taken to cover 15 km = [15/50 * 60= 
15/50 * 60 = 18
18 min   Answer : 18 minutes
Answer: B
If you flip a coin three times, what is the probability that you will get three heads?  Select.
A) 1/4  B) 1/5  C) 1/6  D) 1/7  E) 1/8

Solution: The probability of getting heads on a single flip is 1/2,   The probability of getting heads on each flip is P_1st * P_2nd * P_3rd,   Thus, P = (1/2)^3 = 1/8.   Answer = 1/8
Answer: E