mathewhe/aqua_rat huggingface dataset:
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 288
(B) 180
(C) 1288
(D) 1771
(E) 231
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: (B) 180
Question: A pyramid has a square base of 6 cm, and the four lateral faces are four congruent equilateral triangles. What is the total surface area of the pyramid in square cm?
(A) 36 + 18*sqrt(3)
(B) 36 + 36*sqrt(3)
(C) 72
(D) 72 + 36*sqrt(3)
(E) 72 + 72*sqrt(3)
Rationale: First of all, of course, the base has an area of 36. For the lateral surfaces, it would be helpful to remember the formula for the area of an equilateral triangle.
The area of one equilateral triangle is A = (s^2*sqrt{3})/4. We know the side of the equilateral triangle must be the same as the square: s = 6. Thus, one of these equilateral triangles has an area of A = (6^2*sqrt{3})/4 = 9*sqrt{3}. There are four identical triangles, so their combined area is A = 36*sqrt{3}. Now, add the square base, for a total surface area of A = 36 + 36*sqrt{3}. Answer = B
Answer: (B) 36 + 36*sqrt(3)
Question: Jim wishes to buy 3 gifts that cost 15 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
(A) $57
(B) $47
(C) $7
(D) $17
(E) $27
Rationale: $15 + $9 + $12 = $36 needed
1/4 x $36 = $9 on hand
$36 - $9 = $27 to earn
correct answer E
Answer: (E) $27
Question: The commuter rail between Scottsdale and Sherbourne is 200 km of track, and one train makes a round trip in 5 hours. If Harsha boards the train at the Forest Grove station, which is located one fifth of the track's length out from Scottsdale, how long will it take her to get to Sherbourne?
(A) .5 hours
(B) 1 hour
(C) 1.5 hours
(D) 2 hours
(E) 2.5 hours
Rationale: Distance between Scottsdale and Sherbourne = 200 km
Time for a one-way trip between Scottsdale and Sherbourne: 5/2 = 2.5 hours
Distance between Forest Grove and Scottsdale: 200/5 = 40 km
Distance between Forest Grove and Sherbourne: 40 x 4 = 160 km
Time between Scottsdale and Forest Grove: 2.5/5 = .5 hours
Time between Forest Grove and Sherborne: .5 x 4 = 2 hours.
Answer: (D) 2 hours
Question: If |x + 3| = 5, what is the sum of all the possible values of x?
(A) -16
(B) -12
(C) -8
(D) -6
(E) 12
Rationale: There will be two cases
x+3 = 5 or x+3 = -5
=> x = 2 or x= -8
sum of both the values will be -8 + 2 = -6
Answer: D
Answer: (D) -6
Question: Find the odd man out. 4, 9, 16, 25, 49, 20
(A) 12
(B) 9
(C) 1
(D) 20
(E) 19
Rationale: 20 is an square. All other given numbers are square
Answer : Option D
Answer: (D) 20
Question: When x is divided by y, the quotient is s with remainder r. What is x in terms of r, y, and s?
(A) y + r + s
(B) ys + r
(C) x/y+r
(D) y/s+r
(E) rs + y
Rationale: (x/y) = s + r
solve for x
x=(s*y)+r
Ans B.
Answer: (B) ys + r
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 19.9
(C) 21.5
(D) 22
(E) 23.7
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: (A) 19.7
Question: 10women can complete a work in 7days&10children take 14days to complete the work. How many days will 5women and 10children take to complete the work?
(A) 5 days
(B) 7 days
(C) 8 days
(D) 9 days
(E) 11 days
Rationale: 1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work =
(5/70+10/140)=1/7
So 5 women and 10 children will finish the work in 7 days.
B)
Answer: (B) 7 days
Question: The ratio between x and y is 8/5; x and y are decreased by 5, what is the ratio between the new values of x and y?
(A) 8/5
(B) 5/8
(C) 4
(D) 5
(E) It Cannot Be Determined
Rationale: Ratio = 8k/5k = 8/5, 16/10, etc.
x and y are decreased by 5 --> (8k - 5)/(5k - 5)
New ratio can be 3/0, 11/5, etc.
Answer: E
Answer: (E) It Cannot Be Determined
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $20,000?
(A) $38,796.
(B) $40,000.
(C) $19,488.
(D) $39,679.
(E) $36,796.
Rationale: 20,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option C fulfills the condition and hence is the answer
Answer: (C) $19,488.
Question: A pet store has 4 birds, 6 cats and 5 dogs available. In how many ways can 2 birds, 2 cats and 3 dogs be selected from the store?
(A) 987 ways
(B) 960 ways
(C) 900 ways
(D) 157 ways
(E) 134 ways
Rationale: The number of ways of selecting three birds, two cats and three dogs is:
= ⁴C₂ * ⁶C₂ * ⁵C₃
= (4 * 3)/(2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 6 * 15 * 10
= 900 ways.
Answer: C
Answer: (C) 900 ways
Question: What is 15 percent of 64?
(A) 7.2
(B) 8.4
(C) 9.6
(D) 10.4
(E) 11.8
Rationale: (15/100) * 64 = 9.6
The answer is C.
Answer: (C) 9.6
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 600 m
(B) 200 m
(C) 300 m
(D) 400 m
(E) 100 m
Rationale: A
600 m
Distance covered by Amar = 18/4.8 (1.6km) = 3/8(1600) = 600 m
Answer: (A) 600 m
Question: Choose any 4 desserts from a menu of 10?
(A) 120
(B) 140
(C) 180
(D) 210
(E) 240
Rationale: 10c4 = 210
Answer is D
Answer: (D) 210
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) 92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 680
Breadth = 34 feet
Area to be fenced = 2B + L = 2 (34) + 20 = 88 feet answer : D
Answer: (D) 88
Question: Anne bought doughnuts for a class breakfast party. She bought 6 chocolate doughnuts, 8 coconut doughnuts, and 8 jam-filled doughnuts. How many doughnuts did Anne buy in all?
(A) 22
(B) 36
(C) 39
(D) 21
(E) 11
Rationale: Add the numbers of doughnuts.
6 + 8 + 8 =22.
Answer is A.
Answer: (A) 22
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: (B) 12
Question: Rs.1560 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) s.528
(B) s.542
(C) s.528
(D) s.720
(E) s.549
Rationale: A+B+C = 1560
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1560 = Rs.720
Answer: D
Answer: (D) s.720
Question: John makes $65 a week from his job. He earns a raise andnow makes $72 a week. What is the % increase?
(A) 16%
(B) 10.76%
(C) 10.69%
(D) 10.98%
(E) 10%
Rationale: Increase = (7/65)*100 = (7/65)*100 = 10.76%.
B
Answer: (B) 10.76%
Question: Jimmy has a pot of soup, and he ate 1/5 of the soup for lunch. If Jimmy ate 1/6 of the remaining soup for dinner, what fraction of the soup was left after dinner?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: Let x be the amount of soup at the beginning.
After lunch, the remaining soup was (4/5)x.
After dinner, the remaining soup was (5/6)(4/5)x = (2/3)x.
The answer is B.
Answer: (B) 2/3
Question: By investing Rs. 1800 in 9% stock, Syam earns Rs. 120. find out the stock is then quoted at which rate?
(A) 130
(B) 135
(C) 140
(D) 150
(E) 145
Rationale: Assume that face value = Rs.100.
Dividend per share = Rs.9 (as it is a 9% stock)
By investing Rs. 1800, he earns Rs.120
Investment needed to earn Rs.9 = 1800×9/120 = Rs.135
ie, stock is then quoted (then market value) = Rs.135
Answer is B.
Answer: (B) 135
Question: Ashok secured average of 80 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 38
(B) 27
(C) 99
(D) 110
(E) 80
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 80
Therefore total marks in 6 subjects = 80 * 6 = 480
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 480 – 370 = 110
ANSWER: D
Answer: (D) 110
Question: A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
(A) 350
(B) 250
(C) 450
(D) 550
(E) 650
Rationale: The number of chocolate bars is equal to
18 ? 25 = 450
correct answer C
Answer: (C) 450
Question: The average age of 50 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher.
(A) 30
(B) 65
(C) 60
(D) 55
(E) 56
Rationale: Explanation:
If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15.
Age of teacher = Average age of all + Total increase in age
= 15 + (1 x 50 ) = 65 years
Answer:B
Answer: (B) 65
Question: It costs a publishing company 50,000 dollars to make books. The 50,000 is a fixed cost or a cost that cannot change. To help the publishing company sell the books, a marketing company charges 4 dollars for each book sold. If the company charges 9 dollars per book, how many books should they sell to break even?
(A) 100
(B) 1000
(C) 10000
(D) 100000
(E) None
Rationale: Let C be the cost of producing and selling x books
Let R be the revenue made for selling x books
R = selling price of 1 book × number of books sold
R = 9x
C = fixed cost + variable cost
variable cost = fee charged for 1 book × number of books sold
variable cost = 4x
C = 50000 + 4x
R = C
9x = 50000 + 4x
9x - 4x = 50000 + 4x - 4x
5x = 50000
x = 10000 since 5 × 10000 = 50000
The break even point is to sell 10000 books.
Answer C
Answer: (C) 10000
Question: How many positive integers less than 14 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
(A) 14
(B) 13
(C) 12
(D) 11
(E) 8
Rationale: The number = 2a + 3b < 20
When a = 1, b = 1, 2, 3, 4, 5 -> 2a = 2; 3b = 3, 6, 9-> the number = 5, 8, 11 --> 3 numbers
when a =2, b = 1,2,3-> ....--> 3 numbers
when a =3, b = 1,2,3,4 --> ....--> 2 numbers
Total number is already 8. Look at the answer there is no number greater than 8 --> we dont need to try any more
Answer must be E
Answer: (E) 8
Question: 01-Jan-2007 was Monday. What day of the week lies on 01-Jan-2008?
(A) Wednesday
(B) Sunday
(C) Friday
(D) Tuesday
(E) None of these
Rationale: Explanation :
Given that January 1, 2007 was Monday.
Odd days in 2007 = 1 (we have taken the complete year 2007 because we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)
Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday. Answer : Option D
Answer: (D) Tuesday
Question: If x is 20 percent more than y and y is 50 percent less than z, then x is what percent of z?
(A) 500%
(B) 250%
(C) 500/3%
(D) 125%
(E) 60%
Rationale: Let's take values of x,y,z which can satisfy given equations.
Let Z= 200, so Y becomes 100 ( since Y is 50% less than Z),
X becomes 120 ( since 20% more than Y)
now req is (X/Z) * 100 = (120/200) *100 = 60 %
ANSWER:E
Answer: (E) 60%
Question: Find the odd man out
864, 420, 200, 96, 40, 16, 6
(A) 420
(B) 200
(C) 96
(D) 40
(E) 6
Rationale: 6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on.
ANSWER:C
Answer: (C) 96
Question: In how many ways can the letters of the word "SUN" be arranged?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The total ways of arranging the letters = 3! = 6
The answer is B.
Answer: (B) 6
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
5, 25, 325, 4325, ?
(A) 56189
(B) 54367
(C) 54325
(D) 53182
(E) 62819
Rationale: C
54325
Explanation:
Consider 1 = 5
2 = 25
3 = 325
4 = 4325
Then 5 = 54325
See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54325
Answer: (C) 54325
Question: The bankerâ€™s discount of a certain sum of money is Rs. 78 and the true discount on the same sum for the same time is Rs. 66. The sum due is
(A) 429
(B) 280
(C) 360
(D) 450
(E) None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[78 * 66 / 78 - 66] = Rs. [78 * 66 / 12] = Rs. 429
Answer A
Answer: (A) 429
Question: Jim and John are workers in a department that has a total of 7 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
(A) 2/21
(B) 4/21
(C) 5/21
(D) 6/21
(E) 1/21
Rationale: Probability = 2c2/7c2
= 1/21
Answer E
Answer: (E) 1/21
Question: In how many different ways can a group of 4 men and 4 women be formed out of 7 men and 8 women?
(A) 2450
(B) 105
(C) 1170
(D) Cannot be determined
(E) None of these
Rationale: Reqd no. of ways = 7C4 × 8C4
= 7×6×5×4/1×2×3×4 × 8×7×6×5/1×2×3×4
= 35 × 70 = 2450
Answer A
Answer: (A) 2450
Question: Anand and Deepak started a business investing Rs. 34,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
(A) 2777
(B) 2888
(C) 8400
(D) 7000
(E) 2781
Rationale: Ratio of their shares = 34000 : 35000 = 34:35
Deepak's share = 13800 * 35/69 = Rs. 7000.
Answer: D
Answer: (D) 7000
Question: number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9
(A) 1290
(B) 1296
(C) 1380
(D) 1480
(E) 1580
Rationale: we have to make 4 digit number
in which the format is d> c > b > a
__ __ __ __
1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4)
2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3)
3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2)
4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1)
hence every place can be filled by 6 digits,
6* 6* 6* 6 = 1296
ANSWER:B
Answer: (B) 1296
Question: The length of the longest tape in cm which can be used to measure exactly, the length 100cm; 2m25cm; and 7m80cm is:
(A) 30
(B) 5
(C) 10
(D) 36
(E) 25
Rationale: The three lengths in cm are 100, 225 &780.
HCF of 100, 225 &780 is 5.
Hence, the answer is 5 cm.
ANSWER:B
Answer: (B) 5
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1000 resolutions?
(A) 794 m
(B) 704 m
(C) 1408 m
(D) 1860 m
(E) 1760 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1000 resolutions.
= 1000 * 2 * 22/7 * 22.4
= 140800 cm
= 1408 m
Answer: C
Answer: (C) 1408 m
Question: Grace has 16 jellybeans in her pocket. She has 8 red ones, 6 green ones, and 2 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
(A) 4
(B) 8
(C) 12
(D) 13
(E) 15
Rationale: The worst scenario is when she takes 8 red and 6 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.
Answer: E.
Answer: (E) 15
Question: A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is :
(A) 12 cm
(B) 14 cm
(C) 16 cm
(D) 17 cm
(E) None
Rationale: Sol.
Volume of meterial in the sphere = [4/3 ∏ * {(4)³ - (2)²}] cm³
= [4/3 ∏ * 56] cm³
Let the height of the cone be h cm.
Then, 1/3 ∏ * 4 * 4 * h = [4/3 ∏ * 56]
⇔ h = [4 * 56 / 4 * 4] = 14 cm.
Answer B
Answer: (B) 14 cm
Question: find value for x from below equation? x + 1 = -4
(A) -5
(B) -4
(C) 4
(D) 3
(E) 2
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = -4 - 1
2. Simplify both sides:
x = -5
A
Answer: (A) -5
Question: Prints a page 50 pg per min .If the printed for 2 hours except 15 min.Where there
was an paper jam,how many page did it print
(A) 10,880
(B) 12,880
(C) 5,250
(D) 8,880
(E) 18,880
Rationale: 50 pages ------->1 min
2 hrs except 15 mints means=2*60=120-15=105 mints
i.e.,105*50=5,250 pages printed.
ANSWER:C
Answer: (C) 5,250
Question: A certain auto manufacturer sold 7% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 63,000
(B) 1,960,000
(C) 2,030,000
(D) 2,040,000
(E) 2,300,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-7/100(X)
If sales in 2006,X= 2.1 million find X-7/100(X)
(2.1 x 10^6)-7/100(2.1 x 10^6)
2100000-147000=1,953,000-----> 1,960,000(approx)
ANSWER:B
Answer: (B) 1,960,000
Question: Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346
(A) If x>y
(B) If x>y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=+5,-5 and Y= +5,-5
Comparing, we get X=Y, XY.
Therefore, no relationship can be established between X and Y.
E
Answer: (E) x=y or relationship cannot be established
Question: If f(x)=7x+6 and g(y)=3y^2+ 5y-8 then g(f(x))
(A) 96x^2+78x+74
(B) 857x^2+99x+89
(C) 852x^2+96x+87
(D) 147x^2+119x+58
(E) 852x^2+69x+98
Rationale: g(f(x))=3(7x+6)^2+5(7x+6)-8
=3(49x^2+36+84x)+35x+30-8
=147x^2+119x+58
the answer is D
Answer: (D) 147x^2+119x+58
Question: When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y?
(A) 96
(B) 75
(C) 50
(D) 25
(E) 12
Rationale: Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 6.12 and remainder is 6
So .12 X y = 6
hence y= 50
Ans C
Answer: (C) 50
Question: An artist wishes to paint a circular region on a square poster that is 2.4 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?
(A) 1/pi
(B) sqrt(2.88/pi)
(C) 1
(D) 2/sqrt(pi)
(E) pi/2
Rationale: Area of the poster is 2.4x2.4 = 5.76
1/2 the area = 2.88
pi*r^2 = 2.88
r^2 = 2.88/pi
r = sqrt(2.88/pi) answer (B)
Answer: (B) sqrt(2.88/pi)
Question: From a point P, on the surface of radius 3 cm, two cockroaches A and B started moving along two different circular paths, each having the maximum possible radius, on the surface of the sphere, that lie in the two different planes which are inclined at an angle of 45 degree to each other. If A and B takes 18 sec and 6 sec respectively, to complete one revolution along their respective circular paths, then after how much time will they meet again, after they start from P?
(A) 9 sec
(B) 18 sec
(C) 24 sec
(D) 20 sec
(E) 23 sec
Rationale: Explanation :
Both the circular paths have the maximum possible radius hence, both have a radius of 3 cm each. Irrespective of the angle between the planes of their circular paths, the two cockroaches will meet again, at the point Q only, which is diametrically opposite end of P.
A will takes 9 seconds to reach point Q, completing half a revolution.
On the other hand, B would have completed 32 of his revolution and it will also reach pointQ simultaneously.
Answer : A
Answer: (A) 9 sec
Question: If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $16,000 is invested at the same interest rate, what is the interest from the investment?
(A) $700
(B) $750
(C) $850
(D) $800
(E) $900
Rationale: -> 250/5,000=5% and 16,000*5%=800.
Thus, D is the answer.
Answer: (D) $800
Question: Plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
(A) 54
(B) 72
(C) 96
(D) 144
(E) 432
Rationale: Plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. 2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Answer: (A) 54
Question: What is the place value of 2 in the numeral 2734?
(A) 4500
(B) 5000
(C) 2000
(D) 8000
(E) 8400
Rationale: Option 'C'
2 * 1000 = 2000
Answer: (C) 2000
Question: Mary can do a piece of work in 12 days. Rosy is 50% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?
(A) 7
(B) 8
(C) 9
(D) 11
(E) 10
Rationale: Ratio of times taken by Mary and Rosy = 150:100 = 3:2
Suppose Rosy takes x days to do the work.
3:2 :: 12:x => x= 8 days.
Hence, Rosy takes 8 days to complete the work.
Answer: B
Answer: (B) 8
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 40 paise per sq. metre
(A) s340
(B) s780
(C) s880
(D) s480
(E) s980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*40
= 34000p
in Rs =34000/100=Rs340
ANSWER:A
Answer: (A) s340
Question: A retailer sells 10 shirts. The first 3 he sells for $82,$100 and $90. If the retailer wishes to sell the 10 shirts for an overall average price of over $100, what must be the minimum average price of the remaining 7 shirts?
(A) $100.00
(B) $104.00
(C) $110.00
(D) $115.00
(E) $119.00
Rationale: First 3 shirts are sold for $82,$100 and $90=$272.
To get average price of $100,total sale should be 10*$100=$1000
So remaining 7 shirts to be sold for $1000-$272=$728
Answer should be 728/7=$104.00 that is B
Answer: (B) $104.00
Question: Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
(A) 670 pages
(B) 442 pages
(C) 451 pages
(D) 553 pages
(E) 344 pages
Rationale: Pages read in the first book in one week which is 7 days with 25 pages everyday.
25* 7 = 175 pages
Pages read in the second book in 12 days with 23 pages everyday.
23* 12 = 276 pages
Total number of pages read
175 + 276 = 451 pages
correct answer C
Answer: (C) 451 pages
Question: A contract is to be completed in 46 days sad 117 men were said to work 8 hours a day. After 33 days, (4/7) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
(A) 91
(B) 87
(C) 85
(D) 81
(E) None of them
Rationale: Remaining work = (1-(4/7) =(3/7)
Remaining period = (46 - 33) days = 13days
Let the total men working at it be x.
Less work, Less men	(Direct Proportion)
Less days, More men	(Indirect Proportion)
More Hours per Day, Less men	(Indirect Proportion)
Work (4/7): (3/7)
Days 13:33 } : : 117: x
Hrs/day 9 : 8
Therefore (4/7) x 13 x 9 x x =(3/7) x 33 x 8 x 117 or x=(3 x 33 x 8 x 117)/(4 x 13 x 9)=198
Additional men to be employed = (198 - 117) = 81.
Answer is D.
Answer: (D) 81
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 20 years
(B) 21 years
(C) 18 years
(D) 29 years
(E) 30 years
Rationale: 9 * 2 = 18 years
Answer:C
Answer: (C) 18 years
Question: John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the third throw?
(A) 1/4
(B) 2/16
(C) 3/16
(D) 7/16
(E) 9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
T-T-T ----> P = (1/2)^3 = 1/8
H-H-H ----> P = (1/2)^3 = 1/8
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/8 + 1/8 = 2/8 = 1/4
Answer(A).
Answer: (A) 1/4