mathewhe/aqua_rat huggingface dataset:
Question: In a caravan, in addition to 60 hens, there are 35 goats and 6 camels with some keepers. If the total number of feet be 193 more than the number of heads in the caravan, the number of keepers is
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Explanation: Let number of keepers be x. Then, Total number of feet = 2 x 60 + 4 x 35 + 4 x 6 + 2x = 2x + 284. Total number of heads = 60 + 35 + 6 + x= 101 + x. Therefore (2x + 284) = (101 + x) + 193 or x = 10. Answer: B
Answer: (B) 10
Question: If a, b, c, d, and x are nonzero numbers, which of the following conditions must be true for (ax)^61(bx)^21(cx)^14(dx)^6>0?
(A) x > 0
(B) a × b > 0
(C) c × d > 0
(D) a × d > 0
(E) a × b < 0
Rationale: The question becomes a^(61) *b ^(21) *c^(14) *d^6*x^(102) >0
c^14 , d^6 , x^102 are positive no matter what the sign of c ,d and x respectively
=>a^61 *b ^21 must me positive
=> a*b should be positive
Ans B
Answer: (B) a × b > 0
Question: A cricket player whose bowling average was 23.50 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.50. What will be the number of wickets taken by him till the last match?
(A) 64
(B) 72
(C) 131
(D) 456
(E) 108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 23.5w + 52
Total wickets after last match = w + 5
(23.5w + 52) / (w + 5) = 23.5 - 0.5 = 23
w = 126
so total wickets aftr last match = w+5 = 131
ANSWER:C
Answer: (C) 131
Question: The list price of an article is Rs.70. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 10.85%
(B) 14.85%
(C) 15.85%
(D) 16.85%
(E) 17.85%
Rationale: 70*(90/100)*((100-x)/100) = 56.16
x = 10.85%
ANSWER:A
Answer: (A) 10.85%
Question: A certain galaxy is known to comprise approximately 4 x 10^10 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 8,000
(D) 12,000
(E) 80,000
Rationale: Total no. of stars on galaxy = 4 * 10^10
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 4 * 10^10 / 50 * 10^6
=40 * 10^2 /5
= 800
therefore answer is A
Answer: (A) 800
Question: A train 125 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 36
(B) 50
(C) 28
(D) 26
(E) 65
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 20) km/hr. x - 20 = 45 ==> x = 65 km/hr
Answer: E
Answer: (E) 65
Question: Albert started a business investing Rs. 45,000. After 3 months, peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the share of each.
(A) 3300
(B) 4400
(C) 5500
(D) 6600
(E) None
Rationale: Sol.
Clearly, Albert invested his capital for 12 months, Peter for 9 months and Ronald for 3 months.
So, ratio of their capitals = (45000 * 12) : (60000 * 9) : (90000 * 3)
= 540000 : 540000 : 270000 = 2:2:1.
∴ Alfred’s share = Rs. [16500 * 2/5] = Rs. 6600;
Peter’s share = Rs. [16500 * 2/5] = Rs. 6600;
Ronald’s share = Rs. [16500 * 1/5] = Rs. 3300.
Answer A
Answer: (A) 3300
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
(A) 2 : 3
(B) 3 : 2
(C) 3 : 4
(D) 4 : 3
(E) 4:6
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 --> 1/x + 4/y = 1/15 ------ (i)
Also, 200/x + 400/y = 25/3 --> 1/x + 2/y = 1/24 ----(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
Answer : C.
Answer: (C) 3 : 4
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
(A) 10
(B) 99
(C) 17
(D) 11
(E) 12
Rationale: Explanation:
2420 --- 242
100 --- ? => 10%
Answer: A
Answer: (A) 10
Question: The average of first seven multiples of 3 is:
(A) 9
(B) 16
(C) 12
(D) 8
(E) 10
Rationale: Explanation :
(3(1+2+3+4+5+6+7)/7
= 3x28/7
= 12
Answer : C
Answer: (C) 12
Question: Thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50mm greater than the other. If the original uncut slab is 600mm, what is the length of the other piece of the potato after it is cut.
(A) 550
(B) 275
(C) 50
(D) 300
(E) 250
Rationale: piece one as p1, and piece two as p2.
p2+50=p1 as eq.a
p1+p2=600 as eq.b
substitute eq. a into eq.b, resulting in (p2+50) + p2=600mm.
Group like terms, p2+p2=600-50
(2*p2/2)=550/2 solves to p2= 275.
Ansewr is B.
Answer: (B) 275
Question: Length of a rectangular plot is 20mtr more than its breadth. If the cost of fencing gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 40 m
(B) 60 m
(C) 70 m
(D) 90 m
(E) 100 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: If y exceeds x by 40%, then x is less than y by?
(A) 4/5%
(B) 4/7%
(C) 4/9%
(D) 4/11%
(E) 4/13%
Rationale: X=100	y=140
140------40
100-------? => 28 4/7%
Answer:B
Answer: (B) 4/7%
Question: Two trains 210 m and 260 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 16.92 sec
(B) 14.8 sec
(C) 10.68 sec
(D) 10.8 sec
(E) 20.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 210 + 260 = 470 m.
Required time = 470 * 9/250 = 16.92
= 16.92 sec.
Answer: A
Answer: (A) 16.92 sec
Question: Mary invested a certain sum of money in a bank that paid simple interest. The amount grew to $260 at the end of 2 years. She waited for another 4 years and got a final amount of $380. What was the principal amount that she invested at the beginning?
(A) $200
(B) $220
(C) $230
(D) $240
(E) $250
Rationale: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $260
At the end of 6 years, Amount = $380
This means she earned an interest of $120 in 4 years. Or $30 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $60 in 2 years.
Hence Principal Amount = $260 - $60 = $200 Option A
Answer: (A) $200
Question: It takes Warner 30 minutes to walk to the car park and 90 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
(A) 8:50 a.m
(B) 5:50 a.m
(C) 7:00 a.m
(D) 6:50 a.m
(E) 9:50 a.m
Rationale: The time it takes Warner to get to work: time to walk to car park + time to drive
30 + 90 = 120 minutes = 2 hours
Warner needs to get out of the house 2 hours before 9:00 am at
9:00 - 2:00 = 7:00 a.m
correct answer C
Answer: (C) 7:00 a.m
Question: Marcella has 23 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
(A) 21
(B) 20
(C) 19
(D) 18
(E) 15
Rationale: Marcella has 23 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 23 pairs of shoes minus the 5 'destroyed' pairs yields 20 pairs that still fulfill the requirements.
Answer: D
Answer: (D) 18
Question: The ratio between the length and the breadth of a rectangular park is 3 : 4. If a man cycling along the boundary of the park at the speed of 15 km/hr completes one round in 10 min, then the area of the park (in sq. m) is?
(A) 244907.04 m
(B) 244000 m
(C) 244900 m
(D) 400000 m
(E) 154300 m
Rationale: Perimeter = Distance covered in 10 min. = (15000 x 8)/60 m = 2000 m.
Let length = 3x metres and breadth = 4x metres.
Then, 2(3x + 4x) = 2000 or x = 142.86.
Length = 428.58 m and Breadth = 571.44 m.
Area = (428.58 x 571.44 ) m2 = 244907.76 m
A
Answer: (A) 244907.04 m
Question: 97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?
I.At most 49 students’ score are equal to or more than 85
II. At least 49 students’ score are less than 85.
III. .At least 49 students’ score are equal to or more than 85.
(A) I
(B) II
(C) III
(D) III
(E) IIII
Rationale: If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.
The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.
Answer C.
Answer: (C) III
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 100
(B) 150
(C) 280
(D) 290
(E) 240
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer:C
Answer: (C) 280
Question: One hour after Matthew started waking from q to y, a distance of 45km, Johnny started walking along the same road from y to q. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 19.5
Rationale: Just an alternative method...
After the first hour the distance q is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.
Hence A.
Answer: (A) 24
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much T does she have in her account after two years?
(A) $10079.44
(B) T=$10815.83
(C) $12652.61
(D) $14232.14
(E) $20598.11
Rationale: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
Answer: (B) T=$10815.83
Question: Ten high school boys gather at the gym for a game of basketball. Two teams of 5 people each will be created. How many ways are there to create these 2 teams?
(A) 90
(B) 105
(C) 126
(D) 252
(E) 525
Rationale: Question involves simply selecting 5 players out of 10 players.
10C5 = 10!/5!5! = 10.9.8.7.6/5! = 252
Answer: D
Answer: (D) 252
Question: An college has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
(A) 10
(B) 12
(C) 15
(D) 24
(E) 30
Rationale: An college has 6 employees; for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: (A) 10
Question: The population of a city increases by 6% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
(A) 9%
(B) 9.27%
(C) 27%
(D) 15.76%
(E) None of these
Rationale: Actual increase in population=5%
Let, earlier population=100 then the population after 3 years
=100(1+5/100)^3=115.7625
∴Required percentage=15.7625%
ANSWER:D
Answer: (D) 15.76%
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 110. What was the number he chose?
(A) 123
(B) 267
(C) 277
(D) 124
(E) 120
Rationale: Let xx be the number he chose, then
2â‹…xâˆ’138=110
x=124
Answer:D
Answer: (D) 124
Question: Sandy buys an old scooter for $800 and spends $200 on its repairs. If Sandy sells the scooter for $1200, what is the gain percent?
(A) 15%
(B) 18%
(C) 20%
(D) 22%
(E) 25%
Rationale: selling price / total cost = 1200/1000 = 1.2
The gain percent is 20%.
The answer is C.
Answer: (C) 20%
Question: What is the smallest number H which when increased by 5 is completely divisible by 8, 11 and 24?
(A) 264
(B) 259
(C) 269
(D) 270
(E) 282
Rationale: This question includes a number of great Number Property shortcuts that you can take advantage of:
1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.
2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.
3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.
The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.
Final Answer:
B
Answer: (B) 259
Question: 10^(60) Ã· 10^(58) = ?
(A) 10(6)
(B) 100000
(C) 100
(D) 10000
(E) None of these
Rationale: 10^(60) Ã· 10^(58) = 10^ (60-58) = 10^2
= 10*10 = 100
Answer : C
Answer: (C) 100
Question: 1395 x 1395
(A) 1946025
(B) 1981709
(C) 18362619
(D) 2031719
(E) None of these
Rationale: 1395 x 1395 = (1398)2
= (1400 - 2)2
= (1400)2 + (5)2 - (5 x 1400 x 5)
= 1946025.
Answer: Option A
Answer: (A) 1946025
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 15
(B) 13
(C) 18
(D) 19
(E) 12
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C
Answer: (C) 18
Question: 63 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 21
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 63 x 12 x 5 = 30 x 6 x X
X = 21
Hence, the number of days = 21.
ANSWER:A
Answer: (A) 21
Question: In a board game, a stack of 44 cards, 7 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
(A) 1/11
(B) 1/9
(C) 1/6
(D) 2/7
(E) 1/4
Rationale: After 2 cards have been selected, there are 42 cards remaining.
P(third card has a picture of fruit) = 7/42 = 1/6
The answer is C.
Answer: (C) 1/6
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y + z is odd
II. (x+z)/y is not an integer
III. xy/2 is not an integer
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: consecutive odds are:
2x+1, 2x+3, 2x+5
I. 2x+1+2x+3+2x+5=6x+9=3(2x+3), 2x+3 is not divisible by 2 hence odd, odd * odd = odd Hence I is odd - TRUE
II. 2x+1+2x+5=4x+6/2x+3=2(2x+3)/2x+3=2, so integer - TRUE
III. (2x+1)*(2x+3)=4x^2+6x+2x+3=4x^2+8x+3=(4x(x+2)+3)/2 is not integer, so TRUE
ANSWER: E
Answer: (E) I, II, and III
Question: If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?
(A) 1/4
(B) 2/4
(C) 3/4
(D) 1/5
(E) 2/5
Rationale: If x be the side of the original square, then its area is equal to
x2*square
If x is doubled to 2x, then the new area is equal to
(2x)2* = 4 x2*
The ratio of the areas of the original square to the area of the new square
x2* / (4 x2*) = 1 / 4 or 1:4
correct answer is A)1/4
Answer: (A) 1/4
Question: The average salary of all the workers in a workshop is Rs. 9000. The average salary of 6 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
(A) A)23
(B) B)21
(C) C)52
(D) D)56
(E) E)12
Rationale: Let the total number of workers be x. Then,
9000x
= (12000 * 6) + 6000(x - 6)
=> 3000x = 36000
= x =12.
Answer:E
Answer: (E) E)12
Question: Susan drove an average speed of 30 miles per hour for the first 40 miles of a trip then at a average speed of 15 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip
(A) 35
(B) 20
(C) 45
(D) 50
(E) 55
Rationale: Avg. speed = total distance / total time
Total distance = 80 miles
Total time = 40 / 30 + 40/15 = 4
Avg. speed = 20.
Answer - B
Answer: (B) 20
Question: In 10 years, P will be as old as Q is now. Forty years ago, Q was twice as old as P was then. How old is P now?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Q = P+10
Q-40 = 2(P-40)
P-30 = 2P-80
P = 50
The answer is E.
Answer: (E) 50
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is:
(A) 24.4
(B) 18.4
(C) 12.4
(D) 14.4
(E) 15.4
Rationale: (3x-9):(4x-9) = 9:17
x = 4.8 => 3x = 14.4
ANSWER:D
Answer: (D) 14.4
Question: The bankers gain of a certain sum due 2 years hence at 10% per annum is Rs 24 .The percent worth is
(A) 600
(B) 398
(C) 279
(D) 211
(E) 331
Rationale: T.D = (B.G * 100) / (Rate * Time)
(24*100) / (10 * 2)
= 120.
P.W = (100 *T.D) / (Rate * Time)
= (100 * 120) /(10 * 2)
= 600
Answer:A
Answer: (A) 600
Question: If 2994 Ã· 14.5 = 175, then 29.94 Ã· 1.45 = ?
(A) 17.1
(B) 17.3
(C) 17.5
(D) 17.7
(E) 17.2
Rationale: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 175 in the place of 2994/14.5 ]
= 175/10
= 17.5
Answer is C.
Answer: (C) 17.5
Question: A cupcake recipe calls for 2 cups of sugar, and makes 2 dozen cupcakes. A caterer will supply cupcakes for 150 guests at a birthday party in which there should be at least 2 cupcakes per guest. What is the minimum amount of sugar needed?
(A) 24 cups
(B) 75 cups
(C) 2 cups
(D) 15 cups
(E) 250 cups
Rationale: The proportion equation can be used. Let C = sugar needed.
Note: 12 = 1 dozen
Proportion: A/B = C/D
2 cups of sugar (A) makes 24 cupcakes (B).
(2)(150 guests) = 300 (D) is the least number cupcakes needed.
Proportion: 2/24 = C/300
C = (2)(300)/24 = 600/24 = 24. At least 24 cups are needed.
Answer is A
Answer: (A) 24 cups
Question: The least number which must be subtracted from 820 to make it exactly divisible by 9 is:
(A) A)2
(B) B)3
(C) C)1
(D) D)5
(E) E)6
Rationale: On dividing 820 by 9, we get remainder= 1
Therefore, required number to be subtracted= 1
Answer: C
Answer: (C) C)1
Question: A man buys s cycle for $100 and sells it at a loss of 50%. What is the selling price of the cycle?
(A) $50
(B) $60
(C) $70
(D) $80
(E) $90
Rationale: S.P. = 50% of the $100 = 50/100 * 100 = $50
Answer is A
Answer: (A) $50
Question: What is the value of the 201st
term of asequence if the first term of the sequence is2 and each successive term is 4 more thanthe term immediately preceding it?
(A) 801
(B) 802
(C) 803
(D) 804
(E) 805
Rationale: Here the first term "a"=2
and the common difference "d"=4
and the sequence is an A.P.
Finding the 201st term, use the following formula
Tn=a+(n-1)d
=2+(201-1)*4
=802
ANSWER:B
Answer: (B) 802
Question: In X game of billiards, X can give Y 20 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 100?
(A) 30
(B) 20
(C) 25
(D) 40
(E) 50
Rationale: C
25
X scores 60 while Y score 40 and Z scores 30.
The number of points that Z scores when Y scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In X game of 100 points, Y gives (100 - 75) = 25 points to C.
Answer: (C) 25
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 3/4 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 3/5
(B) 4/5
(C) 11/15
(D) 16/25
(E) 19/25
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (3x/4)(3y/4) = 9xy/16
The total number of boxes is xy + 9xy/16 = 25xy/16
The fraction loaded by the day crew is xy / (25xy/16) = 16/25
The answer is D.
Answer: (D) 16/25
Question: If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15%, the gain is:
(A) 16(2/3)%
(B) 13(1/3)%
(C) 15 (1/6)%
(D) 15%
(E) None of these
Rationale: Let C.P.=Rs. 100. First S.P.=Rs. 120
Now, S.P. =Rs. 120, commission=10%
Therefore, Marked Price=[(100/90)X120]=Rs. 400/3.
No, marked price=400/3, commission=15%
Therefore, S.P.=85% of 400/3=[(85/100)X(400/3)]=340/3.
Therefore, Gain%=[(340/3)-100]=40/3=13(1/3)%.
ANSWER:B
Answer: (B) 13(1/3)%
Question: A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.
(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Rationale: Explanation :
Let the maximum marks be x.
The pass percentage is 42%−12%=30%.
By hypothesis, 30% of x–20% of x=10 (marks).
i.e., 10% of x=10.
Therefore, x = 100 marks.
Answer : B
Answer: (B) 100
Question: In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 60 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?
(A) 25.5%
(B) 21.5%
(C) 17.5%
(D) 13.5%
(E) 9.5%
Rationale: Fathers without full-time jobs are 1/4*2/5 = 2/20 of all the parents surveyed.
Mothers without full-time jobs are 1/8*3/5 = 3/40 of all the parents surveyed.
The percent of parents without full-time jobs is 2/20 + 3/40 = 7/40 = 17.5%
The answer is C.
Answer: (C) 17.5%
Question: Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?
(A) 3 hours
(B) 5 hours
(C) 7 hours
(D) 10 hours
(E) 15 hours
Rationale: Explanation:
(A+B)'s 2 hour's work when opened =
1/6+1/4=5/12
(A+B)′s 4 hour's work=5/12∗2
=5/6Remaining work = 1−5/6=1/6
Now, its A turn in 5 th hour 1/6 work will be done by A in 1 hourTotal time = 4+1=5hours
Option B
Answer: (B) 5 hours
Question: The number of years of service of the eight employees in a production department are 15, 10, 9, 17, 6, 3, 14 and 16. What is the range in the number of years of service of the eight employees?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: = 17-3
= 14
Answer E
Answer: (E) 14
Question: 1397 x 1397 = ?
(A) 1951609
(B) 1951601
(C) 1951602
(D) 1951603
(E) 1951604
Rationale: 1397 x 1397	= (1397)2
= (1400 - 3)2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Answer:A
Answer: (A) 1951609
Question: If it would take one machine 8 minutes to fill a large production order and another machine 12 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
(A) 4 4/5
(B) 5
(C) 5 5/11
(D) 5 1/2
(E) 11
Rationale: Since , Machine 1-M1 take 8 mins to fill the order
The work done by M1 in a min = 1/8
Machine 2- M2 take 12 mins to fill the same order
and work done by M2 in a min = 1/12
Total work done by M1 and M2 in a min = 1/8 + 1/12 = 5/24
Time needed for M1 and M2 to complete the order = 24/5 = 4 4/5
Answer A
Answer: (A) 4 4/5
Question: If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $15,000 is invested at the same interest rate, what is the interest from the investment?
(A) $700
(B) $850
(C) $800
(D) $750
(E) $900
Rationale: -> 250/5,000=5% and 15,000*5%=750.
Thus, D is the answer.
Answer: (D) $750
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
(A) 52.7 m2
(B) 57.8 m2
(C) 52.8 m2
(D) 72.8 m2
(E) 52.8 m2
Rationale: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer: C
Answer: (C) 52.8 m2