MU-NLPC/Calc-aqua_rat huggingface dataset:
If a trader sold two cars each at Rs. 325475 and gains 10% on the first and loses 10% on the second, then his profit or loss percent on the whole is?  Choose the correct choice from the following answers.
A) 1.44% B) 1.74% C) 1.84% D) 1.47% E) 1.00%

Solution: SP of each car is Rs. 325475, he gains 10% on first car and losses 10% on second car.   In this case, there will be loss and percentage of loss is given by   = [(profit%)(loss%)]/100   = (10)(10)/100 % = 1.00%   Answer:1.00%
Answer: E
Two tailors x and y are paid a total of $550 per week by their employer. If x is paid 120% of the sum paid to y. How much is y paid per week?
Select the correct option:
A) 150  B) 100  C) 240  D) 190  E) 550

Solution: Let the sum paid to y per week be $z   then, z+120% of z = 550   z+(120/100)z = 550   z = 250   Answer is 550
Answer: E
Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $8.10?	Pick one:
A) 426
B) 430
C) 443
D) 520
E) 486

Solution: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:   -the 100 pack costs 1.5$, meaning 0.015$ per envelope   -the 50 pack costs 1$, meaning 0.02$ per envelope   -the single envelope costs 0.03$ per envelope   Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.   Having 8.1$, we can buy as many as 5 packs of 100 (5 x 1.5$ = 7.5$). We then have 0.6 $ left. so we buy 20 individual envelopes. If we add up the numbers, we get   500+20= 
  500+20 = 520
520 envelopes. Answer 520
Answer: D
If 23^3*19^4*14^2 = x, what is the units digit of x ? Choose the most appropriate option: A) 2 B) 3 C) 6 D) 7 E) 9

Solution: 23^3*19^4*14^2 = x   Units digit of x will be   3^3 * 9^4 * 4^2   =7* 1 *6= 
7* 1 *6 = 42
42   Therefore , units digit of x= 2   2nswer 2
Answer: A
A car takes 6 hours to cover a distance of 270 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	Choose the correct choice from the following answers:
A) 10Kmph
B) 20Kmph
C) 25Kmph
D) 30Kmph
E) 27Kmph

Solution: Time = 6   30Kmphistence = 270   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 270/9= 
270/9 = 30
30 Kmph   30Kmph)
Answer: D
What sum of money will produce Rs.70 as simple interest in 5 years at 3 1/2 percent?
Choose the correct option
A) 400
B) 500
C) 367
D) 368
E) 339

Solution: 70 = (P*5*7/2)/100   P = 400   400nswer: 400
Answer: A
Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so.
If she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides?
Choose the correct option.
A) 1 B) 2 C) 3 min D) 4 E) 5

Solution: 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done. 3 min
Answer: C
Adding two non multiples of Q always results in a multiple of Q; which of the following must be the value of Q ?	Choose the correct choice from the following:  A) [A] two  B) [B] three  C) [C] five  D) [D] ten  E) [E] hundred

Solution: NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.   so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..   [A] two
Answer: A
A towel, when bleached, lost 30% of its length and 40% of its breadth. What is the percentage decrease in area?  Answers: A) 24% B) 30 % C) 44% D) 58% E) 64%

Solution: percentage change in area   =(−30−40+(30×40)/100)%=−58%   i.e., area is decreased by 58%   ANSWER:58%
Answer: D
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?	Choose one:	A) 5	B) 6	C) 8	D) 4	E) 2

Solution: US = 25   DS = 35   M = (35 - 25)/2= 
(35 - 25)/2 = 5
5 5nswer:5
Answer: A
in how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together  Choose the correct answer:
A) 520 B) 620 C) 720 D) 750 E) 800

Solution: The word 'OPTICAL' contains 7 different letters.   When the vowels OIA are always together, they can be supposed to form one letter.   Then, we have to arrange the letters PTCL (OIA).   Now, 5 letters can be arranged in 5! = 120 ways.   The vowels (OIA) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   ANSWER:720
Answer: C
The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 40 kg of rice previously?	Choose the correct choice from the following choices:
A) 5 kg	B) 15 kg	C) 25 kg	D) 50 kg	E) None

Solution: Solution: Let Rs. 100 be spend on rice initially for 40 kg.   As the price falls by 20%, new price for 40 kg rice,   = (100 -20% of 100) = 80   New price of rice = 80/40 = Rs. 2 per kg.   Rice can bought now at = 100/2= 
100/2 = 50
50 kg.   Answer: Option 50 kg
Answer: D
John has taken four (4) tests that have an average of 80. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
Answers.
A) 87  B) 101  C) 92  D) 94  E) 97

Solution: 87-80= 
87-80 = 7
7*4= 
7*4 = 28
28 points    2*87= 
 2*87 = 174
174   174+28= 
174+28 = 202
202 points to be scored in the 2 tests.   Avg of 2 tests= 202/2= 
202/2 = 101
101   Answer: 101   Traditional Method:   Total scored till now   80*4= 
  80*4 = 320
320   Total score to avg 87 in 6 tests= 87*6= 
87*6 = 522
522   Total to be scored on 2 tests= 522-320= 
522-320 = 202
202   Avg on 2 tests= 202/2= 
202/2 = 101
101   Answer 101
Answer: B
Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly? Pick one:
A) 19587	B) 1987	C) 1951	D) 1998	E) 1912

Solution: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.   Amount = [15625 * (1 + 4/100)3]   = (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.   Answer: 1951
Answer: C
A large research project was scheduled over the course of a 30-month period, and a budget of $99,000 was allotted for the course of the entire project. After ten months, the project had spent $30,000. Was the project at this point over budget or under budget, and by how much?  Choose the correct choice from the following options:
A) under, $4200
B) under, $1200
C) under, $700
D) on bugdget
E) over $5800

Solution: cost per month = 99,000/30 = 3,000.   Now, multiply by seven months: 10*($3000) = $30,000. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is equal to this, so it is on budget.   $30,000 â€“ #30,000 = $0   Answer = (on bugdget)
Answer: D
Directions : In questions no. 1 to 8, select the one which is different from other three alternatives.
Choose the correct choice.
A) Delegate
B) Person
C) Manager
D) Deputy
E) Representative

Solution: Person   Except (Person) all are designations.
Answer: B
What percentage of numbers from 1 to 20 have squares that end in the digit 9?
Choose the correct option:  A) 1  B) 14  C) 20  D) 21  E) 22

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 18 are 3,7,13,17.   Number of such numbers = 4.   Required percentage = (4/18 * 100) = 22%   ANSW22R:22
Answer: E
Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 10 candidates. She plans to have one working interview with 3 of the 10 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates? Choose the correct choice
A) 720
B) 120
C) 300
D) 30
E) 333

Solution: There are C310=120 different groups of three possible out of 10 candidates and since each of these groups is interviewed every day then total of 120 days are needed.   Answer: 120
Answer: B
A constructor estimates that 3 people can paint Mr khans house in 4 days. If he uses 4 people instead of 3,how long will they take to complete the job? Answers:  A) 2  B) 8  C) 1  D) 3  E) 4

Solution: Explanation:   Use formula For a work Members × days = constant   3 × 4 = 4 × a   a = 3   so answer is 3 days   Answer: 3
Answer: D
John has on his shelf three books of poetry, five novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?  Choose the correct option:	A) 1/2	B) 2/9	C) 3/10	D) 7/20	E) 8/45

Solution: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 5/10*2/9 + 2/10*5/9 = 2/9.   Answer: 2/9.
Answer: B
After his first semester in college, Thomas is applying for a scholarship that has a minimum Grade Point Average (GPA) requirement of 3.5. The point values of pertinent college grades are given in the table below. If Thomas took 3 courses, each with an equal weight for GPA calculations, and received two grades of A-, one grade of B+, and one grade of B, what is the lowest grade that Thomas could receive for his fifth class to qualify for the scholarship?
Point Values of Select Grades
Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 | 3.7 | 3.3 | 3 | 2.7 | 2.3 | 2 | 1.7
Choices:
A) A B) B+ C) B D) B- E) C+

Solution: Grade: A | A- | B+ | B | B- | C+ | C | C-   Value: 4 |3.7|3.3|3| 2.7 | 2.3 | 2 | 1.7   7.4 + 3.3 + 3 + x = 3.5 * 5= 
3.5 * 5 = 17.5
17.5 - 13.7= 
17.5 - 13.7 = 3.8
3.8   Grade A is required to qualify   Answer= C+   C+
Answer: E
A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B	Options.
A) 1000 yards
B) 1200 yards
C) 1400 yards
D) 1600 yards
E) 1800 yards

Solution: If X is the distance, a is speed of A and b is speed of 1200 yards, then ;   500/a= (x-500)/b and (x+300)/a = (2x-300)/b , solving it, we get x=1200 yards   ANSWER:1200 yards
Answer: B
A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it? Select.
A) 110	B) 114	C) 128	D) 130	E) 138

Solution: First Purchased = 250 Wes= 128   128
Answer: C
The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 360 m, its area is? Select the correct option.
A) 180	B) 882	C) 277	D) 261	E) 281

Solution: 5x + 12x + 13x = 360 => x = 12   a = 60, b = 144, c = 156   S = (60 + 144 + 156)/2= 
(60 + 144 + 156)/2 = 180
180   180nswer: 180
Answer: A
Find the area of a parallelogram with base 10 cm and height 20 cm.
Choose the correct choice from the following answers: A) 200 B) 384 C) 200 D) 244 E) 242

Solution: Area of a parallelogram = base * height = 10 * 20= 
10 * 20 = 200
200 cm2   Answer: Option 200
Answer: C
If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: Select:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: B   2   Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.   x = 2.
Answer: B
In a rectangular coordinate system, if a line passes through the points (-17,-18), (13,22) and (x,2) then what is the value of x?  Choose the correct answer.
A) -2	B) -1	C) 0	D) 1	E) 2

Solution: The slope of the line m is rise/run = 22-(-18) / 13-(-17) = 4/3   4/3 = 22-2 / 13-x   52-4x = 66-6   x = -2   The answer is -2.
Answer: A
A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
Pick one:
A) 20 days  B) 16 days  C) 24 days  D) 28 days  E) 32 days

Solution: Explanation:   B = 1/8 – 1/2 = 1/24 => 24 days   Answer: 24 days
Answer: C
Of 30 applicants for a job, 14 had at least 4 years of exper, 18 had degrees, and 3 had less than 4 years exper and did not have a degree, how many applicants had at least 4 years exper and a degree?	Options.
A) a)14	B) b)13	C) c)9	D) d)7	E) e)5

Solution: Answer is E. Here is how:   The quickest way is to setup a matrix and work through the given values in the question.   For all such problems, set up a matrix with number of columns and rows corresponding to the divisions mentioned in the question stem.   Degrees and e)5xperience   > 4 yrs e)5xp< 4 yrs e)5xpTotal   Degree5Required Value1318Given   No Degree9312   Total14Given1630 Given answer is e)5
Answer: E
Set A: {1, 3, 4, 6, 10, 12, 15}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?	Choose the correct choice from the following options.
A) 3/14	B) 2/7	C) 9/14	D) 5/7	E) 4/35

Solution: using probability you can solve: 4/7*3/6*2/5=4/35.   Ans 4/35
Answer: E
If n is an integer and 5^n > 40,000,000,000, what is the least possible value of n?  Select:  A) 16  B) 8  C) 9  D) 10  E) 11

Solution: When you seperate the 40000000000 into factors of 5 and 2 you get - > 10^10 x 2^2 = 5^10 x 2^12   2 to the ^ 8 = 4096 so its4096 x 5^10   that means 5^10 x 5^x must be greater   5^x > 4096   5^1=5   5^2=25   5^3= 125   5^6= 15625 - > so x must be at least 6   5^(10+6)= 5^16   16
Answer: A
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 8 p.c?	Pick:
A) 28000 B) 36800 C) 37000 D) 38000 E) 40000

Solution: Option 36800   Explanation:   CP + CP/8 = 45000   CP = 40000   SP = 40000*(92/100)= 
40000*(92/100) = 36_800
36800   Option 36800
Answer: B
Jason flips a coin three times. What is the probability Q that the coin will land on the same side in all three tosses? Pick one:
A) 1/16
B) 1/8
C) 1/4
D) 1/3
E) 1/2

Solution: Total outcome is 2^3=8   Favorable cases HHH or TTT   Therefore, probability Q is 2/8 or 1/4=1/4
Answer: C
A man can row with a speed of 20 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is?	Choose the correct choice from the following choices.
A) 27
B) 41
C) 20
D) 50
E) 60

Solution: M = 20   S = 30   50S = 30+ 20= 
30+ 20 = 50
50   Answer:50
Answer: D
The largest 4 digit number exactly divisible by 88 is:	Choose the correct answer: A) 9944 B) 9768 C) 9988 D) 8888 E) None of these

Solution: Explanation:   Largest 4-digit number = 9999   88) 9999 (113   88   ----   119   88   ----   319   264   ---   55   ---   Required number = (9999 - 55)= 
(9999 - 55) = 9_944
9944.   9944NSWER IS 9944
Answer: A
The batting average of a particular batsman is 61 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Choose one.
A) 179	B) 202	C) 210	D) 223	E) 229

Solution: Explanation:   Total runs scored by the batsman = 61*46= 
61*46 = 2_806
2806 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2806 – 2552 = 254 runs.   Let the highest score be x, hence the lowest score = x – 150   x + (x - 150) = 254   2x = 404   x = 202 runs   ANSWER 202
Answer: B
A contest will consist of n questions, each of which is to be answered wither "True" or "False". Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?	Choose the correct choice from the following: A) 5 B) 10 C) 50 D) 100 E) 1000

Solution: (1/2)^n < 1/1000   (1/2)^n < (1/2)^3*(1/5)^3   10ecause 1/5 ~ (1/2)^2   n >  3 + 3*2= 
 3 + 3*2 = 9
9   ANSWER: 10
Answer: B
Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 res. The ratio in which these two mixtures be mixed to get a new mixture containing milk and a water in the ratio 9:4? Choose the correct option: A) 2:8 B) 2:1 C) 2:2 D) 2:3` E) 2:7

Solution: Step (i) : Let C.P. of milk be Re.1 Given ratio of mixture in A = 8:5  Milk in 1 lit mixture in A = 8/13 lit  C.P of 1 lit mixture in A = Rs. 8/13 Ratio of Mixture in B = 5:2  milk in 1 litre mixture in B – 5/7 lit  C.P of 1 lit mixture in B = Rs. 5/7 Ratio of new mixture = 9:4  milk in 1 lit mixture = 9/13 C.P of 1 lit mixture = Rs/ 9/13 (Mean price) Step (ii) : By the rule of allegation, i. C.P of 1 liter of mixture in A =8/13 ii. C.P of 1 liter of mixture in B = 5/7 iii. Mean price (p) = 9/13 iv. d – m = 9/13 – 5-7 = 2/91 v. m – c = 9/13 – 8/13 = 1/13  Required ratio = 2/91 : 1/13 = 2:7   Answer:2:7
Answer: E
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. How many notebooks were distributed in all?  Choose the correct choice from the following choices
A) 432 B) 640 C) 256 D) 512 E) None of these

Solution: In case I: Let the no. of children = x.   Hence, total no. of notebooks distributed   1⁄8x.x or x2⁄8.......(i)   In case II: no.of children = x⁄2   Now, the total no. of notebooks   = 16 × x⁄2 .......(ii)   Comparing (i) & (ii), we get   x2⁄8 = 8x   or, x = 64   Hence, total no. of notebooks   = 64×64/8=512   Answer 512
Answer: D
If n is a 27-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 27
Options:
A) I only	B) I and II only	C) I and III only	D) II and III only	E) I, II and III

Solution: Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3   Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.   Rules for divisibility by 27: The sum of the digits should a multiple of 27   Consider no 11111111...27 times = The sum 27*1= 
27*1 = 27
27----> divisbible by 3,9 and 27   consider number to be 222....27 times, then sum of the no. 27*2=54 divisible by 3,9 and 27   So why so because when you sum the numbers either you can add the digits 27 times or multiply the digit *27..   Note that since 27 is divisible by 27,9 and 3 and thus the sum of the nos will be divisible by all the nos.   Answer is I, II and III
Answer: E
The height of a triangle is decreased by 25% and its base increased by 50%. Its area will Select the correct option.
A) decrease by 12.5% B) increase by 12.5% C) decrease by 25% D) Increase by 25% E) None of these

Solution: Explanation :   Let the initial height be 100 and the base be 200 units.   ∴ Area = 1/2 x 100 x 200 = 1000sq units   Now, height = 75 units and base = 300 units   ∴ New area = 1/2 x 75 x 300 = 11250   ∴ Area is increased by (11250 - 10000)/10000 x 10   = 12.5%   Answer : Option increase by 12.5%
Answer: B
If p^2 – 12p + 36 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?	Options: A) 1/10 B) 1/5 C) 2/5 D) 3/5 E) 3/10

Solution: (p-4)(p-8) = q   p = 5 ,6 or 7 for this to be true, so   3/10   Ans :3/10
Answer: E
A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 4 days. In how many days can they complete the remaining work?
Choices:
A) 6 days  B) 2/3 days  C) 8 days  D) 3 days  E) 9 days

Solution: Work done by A in 4 days = 4/5   Remaining work = 1/5   Work done by both A and B in one day = 1/5 + 1/10 = 3/10   Remaining work = 1/5 * 10/3 = 2/3 days.   Answer: 2/3 days
Answer: B
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?	Choose the correct option
A) 40	B) 41	C) 48	D) 67	E) 45

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   Answer: Option 48
Answer: C
If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
Choose the correct answer:
A) 120000  B) 27778  C) 27779  D) 27767  E) 29087

Solution: X * (105/100) * (105/100) * (105/100) = 138915   X = 138915/1.157625= 
138915/1.157625 = 120_000
120000   120000nswer: 120000
Answer: A
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 6, what is the probability that one of the two cards drawn is numbered 3 ?	Options.
A) 1/3	B) 1/2	C) 1/5	D) 3/5	E) 4/5

Solution: (5,1) (1,5) (4,2) (2,4) (3,3) – only 5 possible scenarios for sum to be 6. One from this 5 has already happened.   From this five cases, only in one we have 3. So, the probability is 1 chances out of 5 that the one that occurred had 3: P=1/5.   Answer: 1/5.
Answer: C
A train 300 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Choose the most appropriate option:  A) 5 sec  B) 9 sec  C) 12 sec  D) 15 sec  E) 18 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 300 m at 50/3 m / sec   = 300 *3/ 50= 
300 *3/ 50 = 18
18sec   Answer : 18 sec
Answer: E
Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 40%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved? Choose the correct answer
A) 56% B) 67.6% C) 62.2% D) 68% E) 61%

Solution: If initial cost is Rs 100, then   Final cost will be 100*0.6*0.6*0.9 = Rs. 32.4   savings = 100-32.4= 
100-32.4 = 67.6
67.6   so 67.6%   ANSWER:67.6%
Answer: B
There are two names given JOHNSON and JONES. If one letter is picked from both simultaneously at random, then find the probability that the letter is same?
Choose the correct choice from the following options:	A) 24/35	B) 17/35	C) 8/25	D) 6/35	E) 1/25

Solution: This question can also be solved by using 'brute force' - you just have to 'map out' the possibilities.   The nameJohnsonhas 7 letters and the nameJoneshas 5 letters, so there are (7)(5) = 35 possible pairings of letters that can occur.   Of those 35, the pairings that include the SAME letter both times are:   J and J   1st O and O   1st N and N   S and S   2nd O and O   2nd N and N   Total: 6   So the probability that the two randomly selected letters will match is 6/35.   6/35
Answer: D
the age of man is three time the sum of the age of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. the father’s present age is : Choose the correct choice from the following: A) 40 year B) 45 year C) 50 year D) 55 year E) 65 year

Solution: Solution   Let the sum of present ages of the two sons be x years.   Then, father's present age = 3x years.   ∴ (3x + 5) = 2 (x + 10) ⇔ 3x + 5 = 2x + 20 ⇔ x = 15.   Hence, father's present age = 45 years. Answer 45 year
Answer: B
In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2? Choose the correct option:
A) 76 liters
B) 16 liters
C) 60 liters
D) 16 liters
E) 86 liters

Solution: 2:1 --- 60   1:2   2:4   ---------------   3   3 ----------- 60   3 ----------- ? => 60 liters   Answer: 60 liters
Answer: C
The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? Options: A) Rs.1718 B) Rs.1729 C) Rs.1750 D) Rs.1724 E) Rs.1723

Solution: C.I. = [4000 * (1 + 10/100)2 - 4000]   = (4000 * 11/10 * 11/10 - 4000) = Rs. 840.   Sum = (420 * 100)/(3 * 8) = Rs.1750   Answer:Rs.1750
Answer: C