MU-NLPC/Calc-aqua_rat huggingface dataset:
There is a single elimination checkers tournament, meaning when one player loses, they are out of the tournament. There are 50 players in the tournament, how many games are played?	Pick one:
A) 49
B) 25
C) 20
D) 10
E) 5

Solution: A   The number of games always adds up to one less than the number of players in a single elimination tournament. You may calculate it any way. Therefore, 49 games were played.
Answer: A
7 people sit at the round table. In how many ways can we sit them so that Bob and Bill don't sit opposing each other?  Choose the most appropriate option:  A) A)400  B) B)420  C) C)440  D) D)460  E) E)480

Solution: 7 People: Bob,Bill,Red,Blue,White,Pink,Purple   Round Table: T   7 Chairs: 1,2,3,4,5,6,7   Let chairs 1 and 4 be opposite each other;   Bob is sitting on 1 and Bill is sitting on 4;   The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways   Now, Bill and Bob swap their positions;   Bob is sitting on 4 and Bill is sitting on 1;   The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways   Thus total number of ways in which Bob and Bill are sitting opposite each other = 2*5! = 120*2= 
120*2 = 240
240   We have to find in how many ways they are NOT sitting opposite; subtract 240 from the total number of possible arrangements;   In circular permutation, Total number of arrangements of n people= (n-1)!   Here number of people = 7   Arrangements = (7-1)= 
(7-1) = 6
6!= 720   Number of ways Bob and Bill are NOT sitting opposite = 720-240= 
720-240 = 480
480.   Answer: 480
Answer: E
Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?
A. 11%
Select the correct option
A) 11 1/9%
B) 11 1/8%
C) 17.65%
D) 11 5/9%
E) 11 1/5%

Solution: 850 --- 150   100 --- ? => 17.65%   Answer:17.65%
Answer: C
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?	Select the correct option
A) 8%  B) 7%  C) 10%  D) 12%  E) 4%

Solution: Option 4%   4%xplanation:   65*(90/100)*((100-x)/100) = 56.16   x = 4%
Answer: E
In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 8th Rd and 7th Ave in the shortest possible time, how many different routes could he take?
Options:
A) 150
B) 180
C) 210
D) 240
E) 270

Solution: Bills needs to walk 6 blocks north and 4 blocks east.   One possible solution is NNNNNNEEEE.   There are 10C6 = 210 possible solutions.   The answer is 210.
Answer: C
A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?
Options
A) 18	B) 20	C) 24	D) 26	E) 40

Solution: Let the original side of the square be x.   (x-8)*(x-6) = 120 = 10*12   x = 18   The answer is 18.
Answer: A
62467 × 9998 = ? Choose the correct option
A) 624545037  B) 627745452  C) 624545077  D) 624545066  E) 625454211

Solution: 624545066   624545066   62467 × 9998 = 62467 × (10000 - 2)   = 62467 × 10000 - 62467 × 2   = 624670000 - 124934= 
624670000 - 124934 = 624_545_066
624545066
Answer: D
A car travels 25 km an hour faster than a bus for a journey of 500 km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are Select.
A) 25 km/h and 40 km/h, respectively
B) 25 km/h and 60 km/h, respectively
C) 25 km/h and 50 km/h, respectively
D) 25 km/h and 70 km/h, respectively
E) None of these

Solution: Let the speed of the bus be x km / h.   Then speed of the car = (x + 25) km / h   ∴ 500/x=500/x+25+10   ⇒ x2 + 25x – 1250 = 0 ⇒ x = 25   Thus, speed of the bus = 25 km/h   Speed of the car = 50 km/h   Answer 25 km/h and 50 km/h, respectively
Answer: C
This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3r/y is a prime integer greater than 2, which of the following must be true?
I. r = y
II. y = 1
III. r and y are prime integers.
Select.
A) None  B) I only  C) II only  D) III only  E) I and III

Solution: 3r/y and if r=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post ONone.
Answer: A
In May Mrs Lee's earnings were 90 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? Pick one:
A) 92	B) 35	C) 64	D) 46	E) 355

Solution: Lets say the Family Income is 100   In May, lee earned 90Family income is 10   In june, Lee earned 20% more than May, so it is (90+20*90/100 = 108)   Family Income is same 10   In June Lee's Income percent is 108*100/118 ~ 92   92ns is 92
Answer: A
Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 50% per annum is Rs.200 of money?  Select.
A) 1256 B) 2000 C) 3600 D) 8400 E) 4566

Solution: P = 200(100/50)5 => P = 2000   Answer: 2000
Answer: B
Three carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if two of the carpenters work together at their respective rates ?	Choose the correct choice from the following options:
A) 11/15
B) 3/5
C) 11/30
D) 47/90
E) 5/9

Solution: Farmer A, B, C, and D   A's rate: 1/3 job/hour   B's rate: 1/4 job/hour   C's rate: 1/5 job/hour   D's rate: 1/7 job/hour   By intuition we know that the three fastest farmers are A B and C.   As such   (1/3 + 1/4 + 1/5)*(2/3) = ?   47/90 or (47/90)
Answer: D
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?  Choose the correct choice from the following
A) Rs. 45  B) Rs. 50  C) Rs. 55  D) Rs. 60  E) Rs. 40

Solution: A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.   C's rent = Rs. (175 x9/35) = Rs. 45.   THE CORRECT Rs. 45NSWER IS Rs. 45.
Answer: A
Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/2 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? Options:
A) 2/5  B) 1/3  C) 4/13  D) 8/29  E) 6/33

Solution: Now ultimately the speed of every machine is given with respect to Mach O.   So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4   Mach O makes x units in 12 hrs   So, Mach N = 1/2 of O = 1/2*12= 
1/2*12 = 6
6 hrs to make x units   and Mach M= 3/4 of N = 3/4*6 = 6 hrs to make x units   No they are running simultaneously. Lets see how much each mach makes in 1 hr   Mach O = x/12 units   Mach N = x/6 units   Mach M = x/6 units   In 1 hr, together they make - x/12+x/6+x/6 = 5x/12   So what ratio of this has Mach N made?   (x/6) / (5x/12) = 2/5   2/5ns:2/5=2/5
Answer: A
A polling company reports that there is a 80% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
Pick.
A) 10 B) 16 C) 6 D) 4 E) 5

Solution: 80% - Candidate Elected   100%-60% = 40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   80% x 40% x 50%   0.8 x 0.4 x 0.5 100 -60= 
100 -60 = 40
40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   80% x 40% x 50%   0.8 x 0.4 x 0.5= 0.16 = 16%   Answer (16)
Answer: B
Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?	Choose the correct choice:
A) 6 years B) 7 years C) 9 years D) 4 years E) 1 years

Solution: 4 years   Answer: 4 years
Answer: D
Last year, for every 100 million vehicles that travelled on a certain highway, 92 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Choose the correct choice from the following answers:
A) 288	B) 320	C) 2,760	D) 3,200	E) 28,800

Solution: To solve we will set up a proportion. We know that “100 million vehicles is to 92 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. 2,760reating a proportion we have:   100/92 = 3,000/x   2,760ross multiplying gives us:   100x = 3,000 * 92   x = 30 * 92 = 2,760   2,760orrect answer is 2,760.
Answer: C
Using all the letters of the word "THURSDAY", how many different words can be formed? Choose the correct option:
A) 8	B) 8!	C) 7!	D) 7	E) 5

Solution: Total number of letters = 8   Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.   Answer:8!
Answer: B
If n = 2×3×5×7×11×13×17x19, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV . n is divisible 35.  Choose the correct choice from the following answers:
A) I only  B) b- II only  C) III only  D) I and III only  E) none and IV only

Solution: n = 2×3×5×7×11×13×17x19=9699690   I. n2 is not divisible by 600   II. n + 19 is not divisible by 19   III. is even n+4 / 2 = odd   IV . n is divisible 35.   none and IV only
Answer: E
Which of the following are/is prime?
I. 143
II. 145
III. 149  Choose the correct choice from the following choices
A) II only  B) III only  C) III  D) IIII  E) I, II,III

Solution: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice   which leaves us with 2 ) and 3) as possible answers   From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution   II only
Answer: A
In a school of 900 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?	Choose the correct choice
A) 144
B) 153
C) 162
D) 171
E) 180

Solution: 44 + 28 + 10= 
44 + 28 + 10 = 82
82%   100 – 82= 18%    900 * 18/100= 
 900 * 18/100 = 162
162   The answer is 162.
Answer: C
Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Ingrid bake?	Pick one.
A) 0.125%	B) 1.25%	C) 31.33%	D) 125%	E) 0.152%

Solution: 9.18x+5.17x+2.05x = 16.4x 9.18 +5.17 +2.05= 
9.18 +5.17 +2.05 = 16.4
16.4x= 150 cookies   x= 150/16.4 = 9.14 (approx)   So, Ingrid baked 9.14*5.17 cookies or 47cookies (approx)   % share = 47/150 = 31.33 approx   Hence, answer is 31.33%.
Answer: C
hoose the number pair/group which is different from others.
1. 40 : 50
2. 30 : 36
3. 8 : 10
4. 28 : 35
5. 16 : 20	Choose the correct choice from the following answers:
A) 30 : 36 B) 30 : 39 C) 30 : 332 D) 30 : 37 E) 30 : 34

Solution: Explanation:   40 : 50 ==> 4 : 5   30 : 36 ==> 5 : 6   8 : 10 ==> 4 : 5   28 : 35 ==> 4 : 5   16 : 20 ==> 4 : 5   In each of the pair except 30 : 36, the ratio of the two numbers is 4 : 5.   30 : 36NSWER: 30 : 36
Answer: A
A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 14 unsaleable mangoes in the crate then how msny mango are there in the crate?  Choose the correct choice from the following:	A) 100 mangoes	B) 110 mangoes	C) 120 mangoes	D) 130 mangoes	E) 140 mangoes

Solution: 140 mangoes   ANSW140 mangoesR:140 mangoes
Answer: E
A can do a piece of work in 5 days of 9 hours each and B alone can do it in 5 days of 3 hours each.how long will they take it to do working together
2 1/4 hours a day?
Choose the correct choice
A) 2 days B) 3 days C) 4 days D) 5 days E) 6 days

Solution: A's work per hour=1/45   B's work per hour=1/15   A & B's work per hour together=(1/45)+(1/15)=4/45   so a & B together complete the work in 45/4 hours...   if they work 2 1/4=9/4 hours a day,   it will take  (45/4)/(9/4)= 
 (45/4)/(9/4) = 5
5 days...   ANSWER:5 days
Answer: D
The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year? Choose the correct choice from the following answers.
A) 4370, 4730 liters and 3800, 4300 liters B) 4300, 3800 liters and 4730, 3800 liters C) 4730, 3800 liters and 4300, 3800 liters D) 3800, 4300 liters and 4370, 4730 liters E) 4300, 4370 liters and 3800, 4730 liters

Solution: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15% or 10%.   So 8100+15100⋅x+10100⋅(8100−x)=9100   Therefore 8100+320x+110(8100−x)=9100   120x=190   x=3800   Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.   So answer is 3800, 4300 liters and 4370, 4730 liters.
Answer: D
one bottle is half-full of oil and another bottle with twice the capacity is one quarter full of oil. if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both, what fractions of the contents in the third bottle is oil?	Choose the correct choice from the following options
A) 1/4	B) 1/3	C) 3/8	D) 2/3	E) 1/2

Solution: Let assume that 1st bottle capacity = 1Litre;   Therefore, it contain 1/2 litre Oil and 1/2 litre water .   (i.e) Water = 1/2 litre   Oil = 1/2 litre   2nd bottle is twice the capacity   i.e. 2 litre capacity   It means, 1/2litre filled with oil and 1(1/2)litre filled with water.   i.e. Oil = 1/2 liter   Water = 1(1/2)litre   In total the third bottle will contain,   1 litre oil and 2 litre water.   i.e., Oil = 1 litre   Water = 2 liter   Therefore, oil proportion is 1/3   ANSWER:1/3
Answer: B
The perimeter of a semi circle is 144 cm then the radius is?  Answers:
A) 22	B) 28	C) 99	D) 77	E) 21

Solution: 36/7 r = 144 => r = 28   Answer: 28
Answer: B
A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E 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?  Select the correct option:
A) 14
B) 13
C) 11
D) 9
E) 7

Solution: machine E finish the job in 2*12= 
2*12 = 24
24 shifts   machine B finish the job in   2*15= 
  2*15 = 30
30 shifts   Lets assume total work require 120 shifts   Therefore,   rate of E= 5 shifts/day   rate of B = 4 shifts/day   rate of (E+B) = 9 shifts/day   According to current schedule work complete in a day = 5+4+(9/2)= 
5+4+(9/2) = 27/2 = around 13.5
13.5 shifts/day   Therefore, Time required to finish 120 shifts= (120/13.5) = 8.88.. days ~ 9 days=9
Answer: D
9+2+2^2+2^3+2^4+2^5=？	Pick:
A) (2^3-1)(2^3+1)
B) 2^6+1
C) 2^5-1
D) 2^6+7
E) 2^5-2

Solution: From 9+2+2^2+2^3+2^4+2^5=71,   2^6+7=71   the correct answer is 2^6+7.
Answer: D
A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 800 more than that by the previous schema, his sales were worth?
Choose one
A) s. 4,000  B) s. 12,000  C) s. 30,000  D) s. 40,000  E) s. 50,000

Solution: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 800   X =4000   s. 4,000NSWER:s. 4,000
Answer: A
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12400 after a year?  Choose the correct choice from the following choices
A) 3630
B) 3637
C) 3720
D) 3631
E) 3635

Solution: 6300:4200:10500   3:2:5   3/10 * 12400= 
3/10 * 12400 = 3_720
3720   Answer: 3720
Answer: C
A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock?	Choose the correct choice from the following answers:
A) None of these B) 9.7% C) 7.5% D) 8% E) 8.5%

Solution: Explanation :   By investing Rs.1552, income = Rs.128   By investing Rs.97, income = 128×97/1552=8   ie, dividend = 8%   Answer : Option 8%
Answer: D
I. a2 + 8a + 16 = 0,
II. b2 - 4b + 3 = 0 to solve both the equations to find the values of a and b?  Choose the correct choice from the following answers:  A) If a < b  B) If a ≤ b  C) If the relationship between a and b cannot be established  D) If a > b  E) If a ≥ b

Solution: Explanation:   I. (a + 4)2 = 0 => a = -4   II.(b - 3)(b - 1) = 0   => b = 1, 3 => a < b   Option If a < b
Answer: A
A certain fruit stand sold apples for $0.80 each and bananas for $0.70 each. If a customer purchased both apples and bananas from the stand for a total of $7.30, what total number of apples and bananas did the customer purchase? Choose the correct choice from the following options.
A) 9 B) 10 C) 11 D) 12 E) 13

Solution: Let's start with 1 apple for $0.80.   Let's subtract $0.80 from $7.30 until we get a multiple of $0.70.   $7.30, $6.50, $5.70, $4.90 = 7*$0.70   The customer purchased 7 bananas and 3 apples.   The answer is 10.
Answer: B
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?	Choose the correct choice from the following answers
A) 16.5%	B) 20%	C) 35%	D) 55%	E) 65%

Solution: In my view easiest method would be, eliminating the percentage sign   Let 3.5 be 35   5.5 be 55   and 3 be 30   then first eq: S+F=E   130S+155F=135E   5s=20F   therefore, s=4F and then E=5F   F/E=F/5F=20%   Therefore, Answer is 20%
Answer: B
If integer k is equal to the sum of all even multiples of 35 between 280 and 630, what is the greatest prime factor of k?
Choices:
A) 5
B) 7
C) 11
D) 13
E) 11*455

Solution: if we break down what the stem is asking what is the sum of all mult of 30 between 300 and 600.   using arithmetic progression to find n : 630 =280+ (n - 1) 35   350+ 35 = 35n   385 = 35n => n = 11   the sum would be: 11* mean   mean = [630 + 280] / 2 = 455   11*455 =   11*455
Answer: E
Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 6 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? Choose the correct answer:
A) 1
B) 4
C) 9
D) 13
E) 24

Solution: Solving through algebra route:   3B + 4F = x amount   If we multiply this equation with 6 we get:   18B + 24F =6X   Therefore, we got 18 ounces of butter and 6X amount of quantity when we use 24 ounces of floor.   Ans:24
Answer: E
In the coordinate plane, the points F (-2,1), G (1,6), and H (6,1) lie on a circle with center P. What are the coordinates of point P ?	Pick one:
A) (0,0)
B) (1,1)
C) (2,2)
D) (1,-2)
E) (2.5, -2.5)

Solution: I thought I need to find the 4th point that would lie on the circle   Hence my answer was D (1,-2)   But the the center of the circle will lie on (2,2)   (2,2)
Answer: C
An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?	Choices.
A) 4/9
B) 4/5
C) 4/2
D) 4/4
E) 4/1

Solution: 2/3 ---- 12   ? ----- 8 ==> 4/9   4/9nswer:4/9
Answer: A
A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.
Options
A) 27 days	B) 54 days	C) 56 days	D) 68 days	E) 78 days

Solution: Explanation:   As per question, A do twice the work as done by B.   So A:54 days = 2:1   Also (A+54 days) one day work = 1/18   To get days in which 54 days will finish the work, lets calculate work done by 54 days in 1 day =   =(1/18∗1/3)=1/54   [Please note we multiplied by 1/3 as per 54 days share and total of ratio is 1/3]   So 54 days will finish the work in 54 days   Option 54 days
Answer: B
30% loss on cost price in what percent loss on selling price?	Choose the correct option.
A) 28.44 %  B) 38 %  C) 40.35 %  D) 42.85 %  E) None

Solution: Sol.   Loss = 30% on CP i.e., 0.3CP ⇒ SP = 0.7CP Loss % on   SP = loss/SP * 100 = 0.3CP/0.7CP * 100 = 42.85%.   Answer 42.85 %
Answer: D
Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 42 yr. How old is E?  Choose the correct choice from the following:
A) 10 yr
B) 40 yr
C) 45yr
D) 64 yr
E) NOne

Solution: Solution:   Total present age of A, B, C and D,   = (45*4)+(4*5)= 
(45*4)+(4*5) = 200
200 yr;   Total age present age of A, B, C, D and E,= 42*5= 
42*5 = 210
210 yr.   So, age of E= 10 yr.   10 yrnswer: Option 10 yr
Answer: A
How much interest can a person get on Rs. 8400 at 17.5% p.a. simple interest for a period of two years and six months?	Select the correct option
A) 3587.58  B) 3587.59  C) 3675  D) 3587.52  E) 3587.56

Solution: I = (8400 * 2.5 * 17.5)/100 = (8400 * 5 * 35)/(100 * 2 * 2) = Rs. 3675.Answer: 3675
Answer: C
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?	Select the correct option.
A) 28 4/7 years  B) 31 5/7 years  C) 32 1/7 years  D) None of these  E) 31

Solution: Required average   =((67 x 2 + 35 x 2 + 6 x 3)/(2 + 2 + 3))   =(134 + 70 + 18)/7   =222/7   = 31 5/7	years.   Answer : 31 5/7 years
Answer: B
Rosy is 2 years elder than Mary. After 6 years the total of their ages will be 7 times of their current age. Then age of Rosy is :	Choose one:	A) 10 Years	B) 16 Years	C) 17 Years	D) 20 Years	E) Data inadequate

Solution: Data inadequate   Given data are inadequate.
Answer: E
A train leaves Delhi at 7 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Choose the correct choice from the following
A) 229	B) 840	C) 600	D) 888	E) 121

Solution: D = 30 * 7= 
30 * 7 = 210
210   RS= 40 – 30 = 10   T = 210/10= 
210/10 = 21
21   D= 40 * 21= 
40 * 21 = 840
840 km   Answer: 840
Answer: B
In how many possible ways can 5 people draw water from 5 taps if no tap can be used more than once?  Choose the correct choice from the following answers.
A) 120	B) 700	C) 300	D) 150	E) 600

Solution: 1 - can draw from any of 5 taps   2 - draw remain 4   3rd - draw remain 3   4th -draw remain 2   5th - draw remain 1   so total possible = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   120NSWER 120
Answer: A
If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a heart?	Choices:	A) 15/26	B) 7/13	C) 2/3	D) 3/4	E) 11/13

Solution: There are 26 black cards and 13 hearts.   P(black card or heart) = 39/52 = 3/4   The answer is 3/4.
Answer: D