MU-NLPC/Calc-aqua_rat huggingface dataset:
Two employees X and Y are paid a total of Rs. 580 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Choices.
A) s.263
B) s.283
C) s.293
D) s.300
E) s.383

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 580   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 580   ⇒ y[12/10 + 1] = 580   ⇒ 22y/10 = 580   ⇒ 22y = 5800   ⇒ y = 5800/22 = Rs.263   s.263)
Answer: A
63 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?	Choose the correct choice from the following answers: A) A)87 B) B)77 C) C)66 D) D)55 E) E)97

Solution: (63 * 8)/30   = (x * 6)/50   => x =140   140 – 63   = 77   Answer:77
Answer: B
If the complement of a certain angle is six times the measure of that certain angle, then what is the measure of that certain angle?
Pick one: A) 45° B) 30° C) 12.9° D) 18° E) 15°

Solution: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.   The original angle is x, so the complement is 6x, and together, these add up to 90 degrees.   x + 6x = 90   7x = 90   x = 12.9°   Answer = (12.9°)
Answer: C
The least number which must be subtracted from 709 to make it exactly divisible by 9 is:	Choose the correct choice from the following choices
A) A)2 B) B)3 C) C)7 D) D)5 E) E)6

Solution: On dividing 709 by 9, we get remainder= 7   Therefore, required number to be subtracted= 7   Answer: 7
Answer: C
The length of a rectangle is one fourth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 784 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 5 units?  Pick:
A) 35 sq.units	B) 45 sq.units	C) 55 sq.units	D) 50 sq.units	E) 40 sq.units

Solution: Given that the area of the square = 784 sq.units   => Side of square = âˆš784 =28 units   The radius of the circle = side of the square = 28 units   Length of the rectangle = 1/4 * 28= 
1/4 * 28 = 7
7 units   Given that breadth= 5 units   35 sq.unitsrea of the rectangle = lb = 7 * 5= 
7 * 5 = 35
35 sq.units   35 sq.unitsnswer:35 sq.units
Answer: A
In a 100-mile trip, the first 30 miles were completed at 60 mph. If the average speed for the whole trip was 40 mph, what was the average speed in the last 70 miles?	Answers:
A) 30 mph
B) 32 mph
C) 35 mph
D) 37 mph
E) 38 mph

Solution: The time to complete the first 30 miles was (30 miles / 60 mph) = (1/2) hours.   The time to complete the whole trip was (100 miles / 40 mph) = (5/2) hours.   The time to complete the last 70 miles was (5/2) - (1/2) = (2) hours.   The average speed in the last 70 miles was (70 miles / 2 hours) = 35 mph.   The answer is 35 mph.
Answer: C
The average of the marks of 30 students in a class is 45. If the marks of each student are doubled, find the new average?	Select:
A) 85
B) 77
C) 33
D) 90
E) 75

Solution: Sum of the marks for the 30 students   = 30 * 45= 
30 * 45 = 1_350
1350. The marks of each student are doubled, the sum also will be doubled.   The new sum= 1350 * 2= 
1350 * 2 = 2_700
2700. So, the new average= 2700/30= 
2700/30 = 90
90.   Answer:90
Answer: D
How long does a train 110 meters long running at the rate of 36km/hr take to cross a bridge 132 meters in length?
Pick:	A) 24.2 sec	B) 30.6 sec	C) 32.6 sec	D) 28.1 sec	E) 20.4 sec

Solution: Distance = length of train + length of bridge = 110+132= 
110+132 = 242
242   speed= 36km/hr = 36*5/18= 
36*5/18 = 10
10m/s   Required time= 242/10= 
242/10 = 121/5 = around 24.2
24.2 seconds   24.2 secnswer is 24.2 sec
Answer: A
A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?  Select:
A) 24 B) 28 C) 26 D) 21 E) 23

Solution: 2/7 - 1/x = 1/4   x = 28   Answer: 28
Answer: B
Train Q leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?  Choices: A) 8:15 am B) 8:45 am C) 9:00 am D) 9:30 am E) Cannot be determined from the information given

Solution: train Q will cover 60 kms in 45 min at 7:45, the time when train B starts...   distance left to cover is 210-60=150..   combined speed=80+70=150..   so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45   8:45 am
Answer: B
Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block? Select the correct option:
A) 113	B) 114	C) 115	D) 116	E) 117

Solution: The total volume (in terms of number of cubes) of the solid = 3*9*5= 
3*9*5 = 135
135   The total volume (in terms of number of cubes) of the hollow= (3-2)*(9-2)*(5-2)= 
(3-2)*(9-2)*(5-2) = 21
21   so number of cubes required= 135-21= 
135-21 = 114
114   ANSWER:114
Answer: B
For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.25000, my total savings for the two-year is Choose the correct choice from the following
A) s. 6000 B) s. 9000 C) s. 9900 D) s. 9990 E) s. 10000

Solution: Sol. Income in first year = * x 42000 = Rs. 24000   Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (25000 + 35000)   = 66000 - 60000 = Rs. 6000   s. 6000
Answer: A
What will be the cost of building a fence around a circular plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? Choices
A) A)Rs.3944  B) B)Rs.3495.28  C) C)Rs.3988  D) D)Rs.3949  E) E)Rs.3923

Solution: Let the side of the circular plot be a ft.   pi*(r)^2 = 289 => r = 9.59   Length of the fence = Perimeter of the plot = 2*pi*r = 60.26 ft.   Cost of building the fence = 60.26 * 58 = Rs.3495.28   Answer: Rs.3495.28
Answer: B
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.40000?
Choose the correct choice from the following answers:
A) 6620  B) 3277  C) 2688  D) 13240  E) 2789

Solution: A = 40000(11/10)3   = 53240   = 40000   ----------   13240   Answer:13240
Answer: D
A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?	Pick one.
A) 1 hour 70 minutes B) 1 hour 28 minutes C) 1 hour 20 minutes D) 2 hour 20 minutes E) 1 hour 30 minutes

Solution: Let the distance and original speed be d km and k kmph respectively.   d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3   => (5d - 4d)/4k = 1/3 => d = 4/3 k   Time taken to cover the distance at original speed   = d/k = 4/3 hours = 1 hour 20 minutes.   Answer: 1 hour 20 minutes
Answer: C
If m=9^(x−1), then in terms of m, 3^(4x−4) must be which of the following? Choose the correct choice
A) m/3
B) 9m
C) 9m^2
D) m^2
E) m^2/9

Solution: m = 9 ^ (X-1)   m = 3 ^ (2x-2)   m^2 = 3 ^ (4x-4)   Answer m^2
Answer: D
Find a sum for first 12 prime no's from number series?  Select the correct option.
A) 190
B) 178
C) 197
D) 189
E) 100

Solution: Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37)= 
(2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29+31+37) = 197
197   Note: 1 is not a prime number   Option 197
Answer: C
In how many ways can 4 boys be allotted 3 different rooms such that none of the rooms are empty and all the 4 boys are accommodated?	Choose the correct choice from the following.
A) 15
B) 24
C) 18
D) 20
E) 22

Solution: 3 boys can be selected from 4 boys in 4C3 ways = 4   3 boys can be arranged in 3 rooms in 3! ways   and since 1 boy has to share a room with one of the 3 boys, therefore total ways = 1! = 1   Hence total number of ways in which allocation can be done = 4C3 * 3! * 1! = 4*1*3! = 24   answer is 24
Answer: B
The average mark of the students of a class in a particular exam is 60. If 5 students whose average mark in that exam is 44 are excluded, the average mark of the remaining will be 80. Find the number of students who wrote the exam?	Select
A) 12  B) 10  C) 7  D) 9  E) 8

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 60 x.   Total marks of (x - 5) students = 90(x - 5)   60x - (5 * 44) = 80(x - 5)   180 = 20x => x = 9   Answer: 9
Answer: D
WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 3/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not? Select the correct option: A) 1/20 B) 3/40 C) 13/40 D) 3/20 E) 13/22

Solution: P(1 and not 2)=3/8*(1-3/5)=14/40=3/20.   Answer: 3/20.
Answer: D
If a survey shows that 34 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill? Pick.
A) 56% B) 64% C) 72% D) 83% E) 86%

Solution: Those who support = 34.   % of those who don't support it is (200-34)/ 200 = 83%   Answer 83%
Answer: D
The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?
Choose the most appropriate option:  A) 30  B) 20  C) 10  D) 5  E) 15

Solution: Let present age of the elder person =x and   present age of the younger person =x−16   (x−6)=3(x−16−6)⇒x−6=3x−66⇒2x=60⇒x=602=30   30nswer is 30.
Answer: A
A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 20 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?  Pick:
A) 40  B) 80  C) 70  D) 60  E) 50

Solution: 200 men do the rest of the work in   100-20= 
  100-20 = 80
80days   100 men can do the rest of the work in 80*200/100= 
80*200/100 = 160
160days   Required number of days= 160-80= 
160-80 = 80
80 days   Answer is 80
Answer: B
$6,000 is deposited in a savings account that pays 10% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year? Choose the most appropriate option.
A) $6615.15  B) $6615.00  C) $6714.10  D) $6655.55  E) $6698.20

Solution: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2   So,   new time=2periods and new rate=10/2= 
10/2 = 5
5%   Now,   CA=6000(1+5/100)^2=$6615.00   Hence answer is $6615.00
Answer: B
A train is 310 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?  Choose the correct choice from the following answers:
A) 36 seconds B) 18 seconds C) 40 seconds D) 19 seconds E) 45 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 310+140 = 500 meter   Time = Distance/speed   = 450 * (2/25)= 
450 * (2/25) = 36
36 seconds   36 secondsnswer: 36 seconds
Answer: A
If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,713 minutes earlier? (Assume standard time in one location.)	Choose the correct answer.
A) 6:22 B) 6:24 C) 6:27 D) 6:30 E) 6:32

Solution: 6:27minus 2,880,713in any way must end with 4, the only answer choice which ends with 4 is B.   Answer: 6:24.
Answer: B
1/2, 1/4, 1/8, 1/16, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities? Choose the correct choice from the following.
A) 0.1 < x < 1
B) 0.01 < x < 0.1
C) 0.001 < x < 0.01
D) 0.0001 < x < 0.001
E) 0.00001 < x < 0.0001

Solution: In the Sequence notice that the sequence is just the 1/(2^n) ...   so for 1st term=1/2^1=1/2   2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...   Thus the 10th term will be 1/(2^10)=1/1024   Roughly, 1/1024 can be   1/1000= 
  1/1000 = 1/1_000 = around 0.001
0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.   thus the ans will lie btw. 0.001 and 0.01.(0.001 < x < 0.01)
Answer: C
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? Choose the correct choice from the following choices:	A) 1/7	B) 2/7	C) 3/4	D) 4/5	E) 8/9

Solution: n(S)=10+25= 
10+25 = 35
35   n(E)= 10   P(E)=10/35=2/7   ANSWER 2/7
Answer: B
Paul bought 100 books from $1250. If he sold 30 % of books to the $10 unit price and the other books in the $15 unit price, then what total profit did he realize?  Options:
A) $100
B) $105
C) $110
D) $120
E) $150

Solution: Profit = revenu - cost   Revenu =   (100 books * 30%) * $10 = $300   [100 books * (100% - 30%) * $15 = (100 books * 70%) * $15 = 1050   cost: given in the question: $1250   Profit = $1350 - $1250 = 100$   Correct option: $100) 100$1350 -  1250= 
1350 -  1250 = 100
100$   Correct option: $100) 100$
Answer: A
How many three letter words are formed using the letters of the word COMPUTER?	Choose the most appropriate option.
A) 22
B) 334
C) 356
D) 336
E) 91

Solution: Explanation:   The number of letters in the given word is eight.   The number of three letter words that can be formed using these eight letters is Ã¢Â´PÃ¢â€šÆ’ = 8*7*6= 
8*7*6 = 336
336.   Answer: 336
Answer: D
The length of a rectangle is 2 times its width. If the width of the rectangle is 4 inches, what is the rectangle's area, in square inches? Select:
A) 30 square inches	B) 75 square inches	C) 68 square inches	D) 89 square inches	E) 32 square inches

Solution: If the width is 4 in and the length is 2 times the width, then the length is    2 * 4= 
 2 * 4 = 8
8 in   The area is given by     4 * 8= 
  4 * 8 = 32
32 square inches   correct answer 32 square inches
Answer: E
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?  Choose the correct choice from the following options:  A) 33 1/8 %  B) 33 9/3 %  C) 33 1/3 %  D) 32 1/3 %  E) 33 1/2 %

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his 33 1/3 %P = 3   He selling at 3 a rupee, his SP = 4   Profit = SP - 33 1/3 %P = 4 - 3= 
4 - 3 = 1
1   Profit Percent= 1/3 * 100 = 33 1/3 %   Answer:33 1/3 %
Answer: C
If equation |x/2| + |y/2| = 4 encloses a certain region on the coordinate plane, what is the area of this region?  Choose the correct choice from the following choices.
A) 20 B) 50 C) 108 D) 200 E) 400

Solution: The equation can be reduced to intercept form as |x/8| + |y/8| = 1, so these are lines in four quadrants with x and y intercept as 8, so it is a rhombus with diagonals of 16 each and hence area = 1/2*d1*d2 = 1/2*16*16 1/2* 1* 2= 
1/2* 1* 2 = 1
1/2*16*16= 108. Answer 108.
Answer: C
For Consecutive integers x, y and z, where x > y > z, which of the following CANNOT be the value of (x2−y2)∗(y2−z2)(x^2−y^2)∗(y^2−z^2) ?
Choose the correct choice from the following answers
A) 63
B) 99
C) 195
D) 276
E) 323

Solution: 2 ways:   1) x-odd y-even z-odd (odd^2−even^2)(even^2−odd^2)=even   2) x-even y-odd z-even (even^2−odd^2)(odd^2−even^2)=even   The only even answer we have is 276) 276
Answer: D
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 440 sq. feet, how many feet of fencing will be required?  Choices
A) 34 B) 40 C) 64 D) 88 E) 92

Solution: Given that length and area, so we can find the breadth.   Length x Breadth = Area   20 x Breadth = 440   Breadth = 22 feet   Area to be fenced = 2B + L = 2 (22) + 20 = 64 feet answer : 64
Answer: C
Which of the following is a prime number  Choose the most appropriate option
A) 23  B) 24  C) 25  D) 26  E) 27

Solution: Clearly, 23 is a prime number.   Option 23
Answer: A
A train 120 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
Select the correct option.
A) 54 kmph  B) 60 kmph  C) 66 kmph  D) 72 kmph  E) 82 kmph

Solution: speed of train relative to man: 120/6 * 18/5 km/hr   = 72 km/hr   let speed of train= x   therefore x+6 = 72   x= 72-6= 
72-6 = 66
66 km/hr   ANSWER:66 kmph
Answer: C
A fill pipe can fill 1/4 of cistern in 16 minutes in how many minutes, it can fill 3/4 of the cistern?	Choose the correct choice from the following answers:
A) 48min	B) 36min	C) 25min	D) 30min	E) 50min

Solution: 1/4 of the cistern can fill in 16 min   3/4 of the cistern can fill in = 16*4*3/4= 
16*4*3/4 = 48
48min   48minnswer is 48min
Answer: A
How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?	Answers
A) 360 B) 197 C) 278 D) 279 E) 274

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is   ⁶P₄ = 6 * 5 * 4 * 3= 
6 * 5 * 4 * 3 = 360
360.   360nswer: 360
Answer: A
When y is divided by 276, the remainder is 42. What is the remainder when the same y is divided by 23?
Choose one.
A) 13 B) 15 C) 17 D) 19 E) 21

Solution: y = 276*a + 42 = (23*12)*a + 23 + 19   The answer is 19.
Answer: D
Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is:
A. 32 years
Pick one:
A) 22  B) 27  C) 38  D) 29  E) 12

Solution: Let Rajan's present age be x years.   Then, his age at the time of marriage = (x - 8) years.   x = 6/5 (x - 8)   5x = 6x - 48 => x = 48   Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.   Rajan's sister's present age = (30 + 8)= 
(30 + 8) = 38
38 years.Answer: 38
Answer: C
In a certain town, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 390 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?  Choose the correct answer:
A) 84
B) 96
C) 104
D) 112
E) 120

Solution: The ratio of Yankees:Mets:Red Sox = 6:4:5   The Mets fans are 4/15 of the population.   (4/15)*390= 
(4/15)*390 = 104
104   The answer is 104.
Answer: C
If the simple interest on a certain sum of money for 2 years is one–fifth of the sum, then the rate of interest per annum is
Choose the correct option:
A) 14%
B) 7%
C) 10%
D) 15%
E) 3%

Solution: Explanation:   Let the Principal(P) be x   Then, Simple Interest(SI) = x/5   Time(T) = 2 years   Rate of interest per annum(R) = (100×SI)/PT   = (100 × (x/5)/(x × 2) = 20/2= 
20/2 = 10
10%   Answer: Option 10%
Answer: C
If three painters can complete three rooms in two hours, how many hours 5 painters would it take to do 20 rooms?  Choose the correct choice from the following options.
A) 6
B) 9
C) 7
D) 8
E) 5

Solution: Explanation:   Three painters can complete three rooms in two hours. So 20 rooms can be painted in 8 hrs by 5 painters   Answer: 5) 5 painters
Answer: E
If the equation x^2−4x=k has at least one solution, which of the following must be true? Choose the correct choice from the following answers
A) k ≥−4 B) k < −9 C) k = 9 D) k ≤ 9 E) k ≥ −9

Solution: x^2−4x=k   => x^2−4x - k = 0   For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.   b^2-4ac ≥0   => 16 - 4*1*(-k) ≥0   => 16 + 4k ≥0   => k ≥ -4   k ≥−4nswer k ≥−4
Answer: A
David is 12 years older than his daughter Rosy. In 4 years David will be twice as old as Rosy. What is Rosy current age.
Answers: A) 9 B) 10 C) 11 D) 8 E) 12

Solution: Now: Rosy = x, 8avid =x+12   In 4 years Rosy = x+4, 8avid = x+12+4 or 2(x+4)   x+16= 2x+8   x= 8   Rosy is 8 years old   Answer : 8
Answer: D
Twelve pipes of equal capacity can fill a tank in four days. If the tank has to be filled in 3 days, the number of extra pipes needed is:	Answers:
A) 4  B) 7  C) 16  D) 28  E) 30

Solution: Explanation :   3 : 4 :: 12 : x   or 3x =4 * 12   or x = 4*12/3= 
4*12/3 = 16
16   Extra pumps needed= (16 - 12)= 
(16 - 12) = 4
4.   4nswer : 4
Answer: A
Three types of tea (namely a, b and c) costs Rs. 95/kg, Rs. 100/kg and Rs. 70/kg respectively. How many Kg. of each should be blended to produce 100 kg of mixture worth Rs. 90/kg, given that the quantities of band c are equal ?	Select:  A) 70,15,15  B) 50,25,25  C) 60,20,20  D) 40,30,30  E) 40,30,80

Solution: Total cost should be Rs 9000/-.   Average cost of B and C = (100+70)/2= 
(100+70)/2 = 85
Rs 85   For making average cost of A,B and c equal to Rs 95, quantity of A should be equal to sum of quantity of B and C.   50*95+25*(100+70)= 25*(190+170) = 25*360= 
25*360 = 9_000
Rs 9000/-   ANSWER:50,25,25
Answer: B
The probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 3/5. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts? Pick one:
A) 4/11
B) 5/12
C) 6/17
D) 7/20
E) 11/30

Solution: Let, A ≡ event of getting hardware contract   B ≡ event of getting software contract   AB ≡ event of getting both hardware and software contract.   P(A) = 3/4, P(~B) =5/9   => P(B) = 1- (3/5) = 2/5.   A and B are not mutually exclusive events but independent events. So,   P(at least one of A and B ) = P(A) + P(B) - P(AB).   => 4/5 = (3/4) + (2/5) - P(AB).   => P(AB) = 7/20.   Hence, the required probability is 7/20.   The answer is 7/20.
Answer: D
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6600?  Choose the correct option
A) s. 4991
B) s. 5591
C) s. 6001
D) s. 6991
E) s. 7991

Solution: total fr 5 mnths=(6435+6927+6855+7230+6562)= 
(6435+6927+6855+7230+6562) = 34_009
Rs34009.   Reqd.sale=Rs.[(6600*6)-34009]   = Rs.(39600-34009)   = Rs.5591.   ANSWER:s. 5591
Answer: B
Teams A, B, C and D were in a baseball tournament. Each team played each other team once. Team A beat team D. Teams A, B and C won the exact same number of games. How many games did team D lose?
Choose the correct choice from the following:	A) 2	B) 3	C) 4	D) 6	E) 7

Solution: There are 4 teams and each team played each other team once. That tells us 2 facts:    Each team played 3 games    4 teams played a total of 6 games.   Since there are only 6 games, only 6 total wins are possible. Since A, B and C won the exact same number of games, they either all won 1 game or all won 2 games. Let’s examine both scenarios:   Scenario #1: A, B and C each won 1 game. In this scenario, D must have won all 3 games it played. That contradicts with the fact that A beat D. So, scenario 1 is not possible. So, it has to be scenario #2.   Scenario #2: A, B and C each 2 games. In this scenario, D won 0 games. That means D lost all 3 games it played.   correct answer 3
Answer: B
V is the volume of a cylinder; the radius r is 3.4. The height is 350% more than the radius. Which of the following is true? Choose the most appropriate option:
A) 100 < V < 300	B) 300 < V < 500	C) 500 < V < 700	D) 700 < V < 900	E) 900 < V < 1100

Solution: As we see the answers are in form of range we can use approximation   Volume of cylinder is πr^2h   Given π= 22/7 and r = 3.4 so r^2 ~ 12 and h = 4.5 * 3.4 ~ 15   So 22/7 * 12 * 15 = 566   so answer should be   C. 500 < V < 700   Answer : 500 < V < 700
Answer: C
The average of 55 results is 28 and the average of other 28 results is 55 . what is the average of all the results?
Pick.
A) 37
B) 25
C) 48
D) 50
E) None

Solution: Answer   Sum of 83 result = sum of 55 result + sum of 28 result.   = 30 x 20 + 20 x 30   = 3080   Correct Option: 37
Answer: A