MU-NLPC/Calc-aqua_rat huggingface dataset:
A trader marked the price of his commodity so as to include a profit of 25%. He allowed discount of 16% on the marked price. His actual profit was : Choose the correct choice:	A) 4	B) 5	C) 10	D) 12	E) None

Solution: Sol.   Let C.P. be Rs. 100. Then, marked price = Rs. 125.   S.P. = 84% of Rs. 125 = Rs. [84 /100 * 125] = Rs. 105.   ∴ Profit% = (105 - 100)= 
(105 - 100) = 5
5%.   Answer 5
Answer: B
In a store, the total price for 20 shirts is $360 and the total price for 45 sweaters is $900. By how much does the average (arithmetic mean) price of a sweater exceed that of a shirt in this store?  Choose the correct choice from the following answers:
A) $1 B) $2 C) $3 D) $4 E) $5

Solution: The average price of a shirt is: $360 / 20= 
360 / 20 = 18
$18.   The average price of a sweater is: $900 / 45= 
900 / 45 = 20
$20.   The difference in price is: $20 - $18 = $2.   The answer is $2.  20 -  18= 
  20 -  18 = 2
$2.   The answer is $2.
Answer: B
In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes Q of the competition are possible? Choose the correct option
A) 18	B) 20	C) 54	D) 84	E) 120

Solution: the ways the three teams can be selected is..   i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..   ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60   total Q=84 outcomes   84
Answer: D
P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 20 days to complete the same work. then Q alone can do it in Choose the correct choice from the following answers
A) 20	B) 22	C) 25	D) 27	E) 40

Solution: Work done by P and Q in 1 day = 1/10   Work done by R in 1 day = 1/20   Work done by P, Q and R in 1 day = 1/10 + 1/20 = 3/20   But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 3/20   => Work done by P in 1 day = 3/40   => Work done by Q and R in 1 day = 3/40   Hence work done by Q in 1 day = 3/40 â€“ 1/20 = 1/40   So Q alone can do the work in 40 days   Answer is 40.
Answer: E
January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?	Choose the correct choice from the following answers:
A) sunday
B) friday
C) monday
D) wednesday
E) thursday

Solution: The year 2008 is a leap year. So, it has 2 odd days.   1st day of the year 2008 is Tuesday (Given)   So, 1st day of the year 2009 is 2 days beyond Tuesday.   Hence, it will be Thursday.   Answer: thursday) thursday
Answer: E
The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
Choose the correct option.
A) 277
B) 960
C) 277
D) 266
E) 121

Solution: Let C.P. = Rs. x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.   Answer: 960
Answer: B
Find the odd man out.
1, 5, 2, 3, 6, 11, 13  Choose the correct choice.
A) 6
B) 5
C) 1
D) 13
E) 11

Solution: Explanation:   Each of the numbers except 6 is a prime number.   6nswer: 6) 6
Answer: A
If 45% of a number is 36, then the number is  Choose the correct choice from the following choices.
A) number is 60 B) number is 70 C) number is 90 D) number is 80 E) None of these

Solution: Solution:   Let "a" be the number we seek. We get   45% × a = 36   2 × 45% × a = 2 × 36 = 72   90% × a = 72   10% × a = 72 : 9 = 8   100% × a = 8 × 10 = 80   a = 80   Answer number is 80
Answer: D
A special municipal payroll tax charges not tax on a payroll less than $200,000 and only 0.2% on a company’s payroll above $200,000. If Belfried Industries paid $400 in this special municipal payroll tax, then they must have had a payroll of
Choose the correct answer
A) $180,000	B) $400,000	C) $220,000	D) $402,000	E) $2,200,000

Solution: ANSWER : B , ( with different approach) :   The 400 paid is 0.2% of the additional amount above 200,000. Let it be X   Now 0.2% of X = 400   Therefore X= 200,000   Total = 200,000 + X= 400,000
Answer: B
The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ? Select the correct option.
A) Rs. 11,300
B) Rs. 11,500
C) Rs. 11,302
D) Rs. 11,301
E) Rs. 11,303

Solution: Explanation:   Manager's monthly salary   = Rs. (1900 x 25 - 1500 x 24) = Rs. 11,500   Answer:Rs. 11,500
Answer: B
How many four letter words are formed using the letters of the word PROBLEM? Choose the correct choice from the following answers:
A) 760
B) 800
C) 840
D) 880
E) 920

Solution: The number of letters in the given word is seven.   The number of four letter words that can be formed using these seven letters is 7P4   = 7 * 6 * 5 * 4= 
7 * 6 * 5 * 4 = 840
840.   Answer: 840
Answer: C
A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
Pick one.
A) 40%
B) 50%
C) 55%
D) 65%
E) 70%

Solution: Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50%   50%
Answer: B
A began business with 12500 and is joined afterwards by B with 50000. When did B join, if the profits at the end of the year are divided equally?
Choose the most appropriate option:
A) 3 months
B) 9 months
C) 10 months
D) 7 months
E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 12500 : (12 – x) × 50000   or 12 : 4(12 – x)   Since profit is equally divided so   12 = 4(12 – x) or x = 3. Thus B joined after 8 months.   3 monthsnswer 3 months
Answer: A
Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel eight times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?  Choose the correct answer:
A) 4
B) 6
C) 8
D) 9
E) 12

Solution: W: the time for Wyane to do the job   S: the time for his son to do the job   We have 1/W + 1/S = 1/8 and W = 8S   Then we have 1/(8*S) + 1/S = 1/8 <=> 9/(8*S) = 1/8 <=> S = 9   ANS: 9
Answer: D
a, b are positive integers. The remainder of a to be divided by 8 is 5 and the remainder of b to be divided by 6 is 2.
Which is possible to be the remainder of a*b to be divided by 48  Choose the correct choice from the following choices
A) a) 10 B) b) 6 C) c) 8 D) d) 12 E) e) 20

Solution: Two ways to do it...   a=8x+5..   b=6y+2..   1) convenient way..   Take x and y as 0, and you will get a*b as   5*2= 
  5*2 = 10
10   a) 10nswer : a) 10
Answer: A
A and B complete a work in 8 days. A alone can do it in 14 days. If both together can do the work in how many days?
Answers
A) 5 days
B) 8 days
C) 6 days
D) 3.15 days
E) 2.75 days

Solution: 1/8 + 1/14 = 11/56   56/11 = 5 days   5 daysnswer: 5 days
Answer: A
Here the sum of the series is 4+8+12+16+….. =612. find how many terms are there in the series?
Options: A) 15 B) 19 C) 17 D) 14 E) 13

Solution: Solution: This is an A.P. in which a=4, d=4 and Sn=612   Then, n/2[2a+(n-1)d]=612 => n/2[2*4+(n-1)*4]=612   => 4n/2(n+1)=612   => n(n+1)=306   => n^2+n-306=0   => n^2+18n-17n-306=0   => n(n+18)-17(n+18)=0   => (n+18)(n-17)=0   => n=17.   Number of terms=17.   Answer 17
Answer: C
If a man crosses a 600 m long street in 5 minutes. What is his speed?  Choices
A) 7 km/hr B) 7.1 km/hr C) 7.2 km/hr D) 8 km/hr E) 9.2 km/hr

Solution: distance = 600 meter   time = 5 minutes = 5 x 60 seconds = 300 seconds   Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr   7.2 km/hr
Answer: C
P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 40 meter/sec.
Select:
A) 21 meter/sec	B) 7 meter/sec	C) 14 meter/sec	D) 18 meter/sec	E) 35 meter/sec

Solution: P's speed =40 m/s   P's distance = 1000m (as it is a km race)   t = 1000/16 =25 sec   Q's distance = 1000-125= 
1000-125 = 875
875m   Q's time to complete this distance is also 62.5 sec.   Q's speed= dist/time = 875/25= 
875/25 = 35
35 m/s   Hence 35 meter/sec is the answer.
Answer: E
I have two 10 paise coins. If 4 If 4/5 of what I have is 8is 8/9 of what you have, how much do you have?  Select the correct option.
A) 13	B) 17	C) 11	D) 18	E) 11

Solution: 18   18 paise.
Answer: D
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-seventh of its original value. How many amperes of electrical current will flow through the wire?  Pick.
A) 4/7  B) 7  C) 14  D) 28  E) 35

Solution: Given that, I∝1/R, I*R is a constant value.   I1*R1 = I2*R2   I1*R1 = I2*R1/7   I2 = 7*I1 = 28 amperes   The answer is 28.
Answer: D
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 12, the how old is B? Pick:
A) 10 years B) 4 years C) 6 years D) 15 years E) 16 years

Solution: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 12   5x = 10   x = 2.   Hence, B's age = 2x = 4 years.   4 years)
Answer: B
In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together.  Choose the correct choice
A) W8  B) 789  C) 279  D) 277  E) 191

Solution: Answer:277
Answer: D
A car salesman earns a base salary of $800 per month plus a commission of $200 for each car he sells. If the car salesman earned $1600 in May, how many cars does he need to sell in June in order to double his May earnings? Pick:
A) 10  B) 11  C) 12  D) 13  E) 14

Solution: 800+200x=3200   x=12 cars.   The answer is 12.
Answer: C
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?  Select.
A) 833 1/0 B) 833 1/3 C) 833 1/21 D) 833 1/2 E) 833 1/3

Solution: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.   Answer: 833 1/3
Answer: B
In an election between two candidates, 10% of votes are were declares invalid. First candidate got 9000 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:	Pick.
A) 9000  B) 98000  C) 50000  D) 11000  E) 12000

Solution: 100 % - 10 % = 90 %   54%-36%=18%   18% ------> 9000 ( 18 × 500   54 -36= 
  54 -36 = 18
18%   18% ------> 9000 ( 18 × 500= 9000)   100% -------> 50000 votes (100 × 500 = 50000)   50000
Answer: C
Reeya obtained 40, 60, 70, 80 and 80 out of 100 in different subjects, What will be the average	Choose the most appropriate option:
A) 66  B) 75  C) 80  D) 85  E) 90

Solution: Explanation:   (40+60+70+80+80 / 5)=66   Option 66
Answer: A
Convert 0.38 in to a vulgar fraction ?  Choices:
A) 18/50 B) 16/50 C) 17/50 D) 19/50 E) None

Solution: Answer   0.38 = 38/100 = 19/50   Correct Option: 19/50
Answer: D
A worker is paid x rupees for painting every 25 metres of a wall and y rupees for painting every extra metre. During one week, he painted 25 metres on Monday, 50 metres on Tuesday, 25 metres on Wednesday, 45 metres on Thursday and 25 metres on Friday. What is his average daily earning rupees for the five day week?	Select the correct option
A) x + (8/5)y B) (5x + 9y)/5 C) x + 9y D) None of these E) Cannot be determined

Solution: Explanation :   On Monday, the payment = Rs x   On Tuesday, the payment = Rs (x + 25y)   On Wednesday, the payment = Rs x   On Thursday, the payment = Rs (x +20y)   On Friday, the payment = Rs x   Average daily earning during the five-day week = (5x + 45y)/5   = x + 9y   Answer : x + 9y
Answer: C
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
Pick
A) 24000  B) 23000  C) 22000  D) 25000  E) 26000

Solution: 25 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   25 = 1/100 * x => x = 25000   ANSWER:25000
Answer: D
If there are 200 questions in a 3 hr examination. Among these questions are 20 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? Choose the most appropriate option
A) 72 min B) 62 min C) 70 min D) 32.72727 min E) 76 min

Solution: x=time for type B prolems   2x=time for type A problem   total time=3hrs=180min   180x+20*2x=180   x=180/220   x=0.818182   time taken for type A problem=20*2*0.818182=32.72727min   ANSWER:32.72727 min
Answer: D
A runs twice as fast as B and gives B a start of 42m.How long should the racecourse be so that A and B might reach in the same time?  Choices.
A) 75 m.	B) 80 m.	C) 84 m.	D) 100 m.	E) None of the above

Solution: ratio of speeds of a and b is 2:1   b is 42m away from a but we know that a covers 1 meter(2-1) more in every second than b   the time taken for a to cover 42m is   42/1= 
  42/1 = 42
42m   so the total time taken by a and b to reach=2*42= 
2*42 = 84
84m   ANSWER:84 m.
Answer: C
The speed of a boat in still water in 22 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 24 minutes is:	Select:
A) 10.6 B) 10.2 C) 10.8 D) 10.4 E) 10.0

Solution: Speed downstream = (22 + 5)= 
(22 + 5) = 27
27 kmph   Time= 24 minutes =24/60 hour = 2/5 hour   Distance travelled = Time × speed =2/5×27 = 10.8 km   Answer is 10.8.
Answer: C
A car that has an original value of $52,500 depricates $10000 in the first year and there original cost per year. What is its value after 8 years? Pick.
A) $12100
B) $13100
C) $14100
D) $15100
E) $16100

Solution: 1st year depreciation amount = 10000   next 7 year's depreciation amount = 7 * 8% original cost price   = 7*8/100 * 52500= 
7*8/100 * 52500 = 29_400
29400   Total depreciation amount= 39400   Value after 8 years = $13100   ANSWER:$13100
Answer: B
Which of the following is an integer?
I. 13! / 6!
II. 13! / 8!
III. 13! / 7!5!
Choose the correct choice from the following.
A) I only B) II only C) III only D) I and II only E) I, II and III

Solution: 13!/6! = 13*12*11*10*9*8*7 which is an integer.   13!/8! = 13*12*11*10*9 which is an integer.   13!/7!5! = 13*12*11*10*9*8 / 5*4*3*2 = 13*12*11*3*2 which is an integer.   The answer is I, II and III.
Answer: E
If a computer program generates three-digit odd numbers using the numbers 9, 7, 0, 6, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
Choose the correct choice from the following options.
A) 1/3  B) 1/4  C) 1/5  D) 1/6  E) 1/7

Solution: 1/3
Answer: A
Last year the range of the annual sales of the 100 lamps at Company X was $30,000. If the annual sale of each of the 100 lamps this year is 10 percent greater than it was last year, what is the range of the annual sales of the 100 lamps this year?  Choose the correct answer: A) $27,000 B) $30,000 C) $33,000 D) $36,000 E) $63,000

Solution: let the lowest sale be x.   Therefore, highest sale is x +30000.   Now sale of each lamp is increased by 10%.   Therefore the sale will remain arranged in the same order as before.   or Lowest sale = 1.1x and Highest = 1.1 * (x+30000)   or Range = highest - lowest = 1.1 * (x+30000) - 1.1x   = 33000, Hence, $33,000
Answer: C
A sum of 1200 lent at S.I at 10% will become twice in how many years?	Choose the correct answer: A) 12 years B) 14 years C) 10 years D) 8 years E) 6 years

Solution: Explanation:   To become twice means S.I should be as much as initial sum i.e, 1200   (1200 x 10 x T)/100 = 1200   T = 10 years   Answer: Option 10 years
Answer: C
If the sum of two positive integers is 12 and the difference of their squares is 48, what is the product of the two integers? Pick one:
A) 32	B) 119	C) 128	D) 135	E) 143

Solution: Let the 2 positive numbers x and y   x+ y = 12 -- 1   x^2 - y^2 = 48   => (x+y)(x-y)=48 -- 2   Using equation 1 in 2 , we get   => x-y = 4 -- 3   Solving equation 1 and 3 , we get   x= 8   y= 4   Product = 8*4= 
8*4 = 32
32   32nswer 32
Answer: A
The output of a factory was increased by 15% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?	Choose the correct choice.
A) 20%	B) 27%	C) 30%	D) 32%	E) 79%

Solution: The original output increases by 15% and then 20%.   Total % change = a + b + ab/100   Total % change = 15 + 20 + 15*20/100= 
15 + 20 + 15*20/100 = 38
38%   Now, you want to change it to 0, so,   0= 38 + x + 38x/100   x = -38(100)/138 = 27% approximately   Answer is 27%
Answer: B
In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 53900. How many times did he participate in the competition?  Pick one:
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: 53900 = 2*2*5*5*7*7*11   John participated 7 times.   The answer is 7.
Answer: A
In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is Choose the most appropriate option.
A) 9 years  B) 19 years  C) 29 years  D) 39 years  E) None

Solution: Solution   Let B's present age	= x years.   Then, A's present age	‹=› (x + 9) years.   ∴(x + 9) + 10 = 2 (x - 10)   ‹=› x + 19 = 2x - 20   ‹=› x = 39.   Answer 39 years
Answer: D
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?=	Pick:	A) y = 1.2 × 10^a, where a is a positive integer.	B) y = 1.5 × 10^b, where b is a positive integer.	C) y = 1.8 × 10^c, where c is a positive integer.	D) y = 2.5 × 10^d, where d is a positive integer.	E) y = 2.7 × 10^e, where e is a positive integer.

Solution: Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option y = 1.2 × 10^a, where a is a positive integer. is correct answer?
Answer: A
A cycle is bought for Rs.900 and sold for Rs.1170, find the gain percent?	Answers:
A) 27%
B) 20%
C) 80%
D) 30%
E) 24%

Solution: 900 ---- 270   100 ---- ? => 30%   Answer: 30%
Answer: D
A person has three children with at least one boy. Find the probability of having at least two boys among the children.  Choose the correct choice: A) 3/4 B) 1/3 C) 2/3 D) 1/4 E) 1/5

Solution: Explanation :   The event is occuring under the following situations:   Second is a boy and third is a girl OR   Second is a girl and third is a boy OR   Second is a boy and third is a boy   This will be represented by: (1/2) x (1/2) + (1/2) x (1/2) + (1/2) x (1/2) = 3/4   3/4nswer : 3/4
Answer: A
39 persons can repair a road in 24 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?  Choose the most appropriate option:
A) 10	B) 13	C) 14	D) 15	E) 26

Solution: Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons	30	:	39	:: 12 : x   Working hours/day	6	:	5   30 x 6 x x = 39 x 5 x 24   x =	(39 x 5 x 24)/(30 x 6)   x = 26.   ANSW26R:26
Answer: E
P software has coding line 5% more than N, N software has coding line 4/20 more than M. M software has 80 lines of coding. find P lines.
Options
A) 101	B) 107	C) 108	D) 109	E) 110

Solution: M s/w has 80 line of code   N s/w has = 80+80*4/20= 
80+80*4/20 = 96
96 line of code   P s/w 5% more N' code 96+4.8= 
96+4.8 = 100.8
100.8   or   101 line of code   101NSWER:101
Answer: A
Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?	Choose the correct choice from the following answers.
A) 2 years	B) 6 years	C) 8 years	D) 3 years	E) 9 years

Solution: 9261 = 8000(21/20)N   (21/20)3   = (21/20)N   => N = 3   Answer:3 years
Answer: D
The ratio of the incomes of Uma and Bala is 4:3 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $5000 then the income of Uma is?	Choose the correct option.
A) $24000  B) $23000  C) $22000  D) $21000  E) $20000

Solution: Let the income of Uma and Bala be $4x and $3x   Let their expenditures be $3y and $2y   4x-3y = 5000-------1)   3x-2y = 5000-------2)   From 1) and 2)   x = 5000   Uma's income = 4x = 4*5000= 
4*5000 = 20_000
$20000   Answer is $20000
Answer: E
A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 15days, A finished the remaining work. In how many days A alone can finish the job?	Choose the correct choice from the following
A) 10	B) 25	C) 60	D) 30	E) 20

Solution: A+B 10days work = 10*1/40 +  10= 
+  10 = 10
10*1/40= 1/4   Remaining work = 1-1/4 = 3/4   3/4 work is done by A in 15days   whole work will be done by A in 15*4/3= 
15*4/3 = 20
20days   Answer is 20
Answer: E
The number of years of service of the eight employees in a production department are 15, 10, 9, 19, 6, 4, 14 and 16. What is the range in the number of years of service of the eight employees? Choose the correct answer.
A) 10  B) 11  C) 12  D) 13  E) 15

Solution: = 19-4= 
19-4 = 15
15   Answer 15
Answer: E
From the set of numbers {p, t, u, v, w, x, y, z}, how many different combinations can we have without the t or the u in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
Choose the correct choice from the following choices.
A) 16
B) 31
C) 32
D) 63
E) 64

Solution: Any letter (p, v, w, x, y, z) can be included or not.   Thus there are 2^6 combinations - 1 empty combination = 63 combinations   The answer is 63.
Answer: D
650 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?	Choose the correct choice from the following:  A) a) 162  B) b) 138  C) c) 60  D) d) 38  E) e) 13

Solution: Passed in english = 65%   Passed in maths = 55%   Passed in both = 40% of 55% = 2/5 * (55%) = 22%   Passed in (e) 13nglish + Maths - Both + Neither) 2/5 * (55 )= 
2/5 * (55 ) = 22
22%   Passed in (e) 13nglish + Maths - Both + Neither)= 100%   65 + 55 - 22 + Neither = 100   Neither = 100 - 98= 
100 - 98 = 2
2%= 0.02 * 650= 
0.02 * 650 = 13
13   Answer: e) 13
Answer: E
Which of the following is always true for any real number 'a' and 'b'?  Choose the correct choice from the following.
A) |ab| = |a||b| B) |a/b| = |a|/|b| C) |-ab| < |a||b| D) |ab| > |a/b| E) |ab| = -|ab|

Solution: This one is obvious if you know how absolute value works. One of the fundamental principles of absolute value is multiplicativeness, which holds that for absolute values, f(ab) = f(a) f(b). Thus the answer is |ab| = |a||b|.
Answer: A
The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?  Choose the most appropriate option.
A) 8981 B) 3799 C) 1200 D) 2693 E) 1732

Solution: P --- 10 ---- 600   P --- 5 ----- 300   3P --- 5 ----- 900   ------   => 1200   Answer: 1200
Answer: C