mathewhe/aqua_rat huggingface dataset:
Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
(A) 3/21
(B) 2/91
(C) 4/91
(D) 8/81
(E) 9/72
Rationale: Let S be the sample space.
Then, n(S)	= number of ways of drawing 3 balls out of 15
= 15C3
= (15*14*13)/(3*2*1)
= 455
Let E = event of getting all the 3 red balls
n(E) = 5C3 = 5C2 =(5*4)/(2*1)
= 10
P(E) =n(E)/n(S)
= 10/455
= 2/91
Answer should be B
Answer: (B) 2/91
Question: What is the remainder when the number R=14^2 * 15^8 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus R=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: (A) 0
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 63 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 70
(B) 450
(C) 150
(D) 35
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 63, so 0.14*{total} = 63 --> {total} = 450.
Answer: B.
Answer: (B) 450
Question: A researcher computed the mean, the median, and the standard deviation Y for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
Rationale: If we add or subtract a constant to each term in a set the standard deviation Y will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
Answer: (D) The mean and the median
Question: In the coordinate plane, one of the vertices of a square is the point (-4, -4). If the diagonals of that square intersect at point (3, 2), what is the area of that square?
(A) 180
(B) 196
(C) 160
(D) 164
(E) 172
Rationale: One point (-4-4), Intersection (3,2) so the distance from the first point -4-3=-7 is the midpoint of the square --> whole side 14, 14*14=196
B
Answer: (B) 196
Question: In what time will a train 240 metres long cross an electric pole, if its speed be 126 km/hr?
(A) 6.75 sec
(B) 6.85 sec
(C) 6.55 sec
(D) 6.44 sec
(E) 7.85 sec
Rationale: Solution
Speed	= (126 x 5 /18) m/sec
= 35 m / sec
Time taken	= (240 /35) sec
= 6.85 sec.
Answer B
Answer: (B) 6.85 sec
Question: The instructions state that Cheryl needs 5/9 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/24 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
(A) 1/12
(B) 1/9
(C) 2/3
(D) 5/9
(E) 2 1/9
Rationale: Total bought = 5/9+1/3
left part 8/24--->1/3
so used part 5/9+1/3-1/3=5/9
ANSWER:D
Answer: (D) 5/9
Question: If a is a positive even integer, and n and m are consecutive integers, then (n - m)^a/(m - n)^a =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: a= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^a)/((m-n)^a)= ((n-m)/(m-n))^a = (-1)^a
Since we are raising the difference of n and m to power a , which is even , the answer will be 1 .
Answer D
Answer: (D) 1
Question: Convert the following unit:
7 hectares in mÂ²
(A) 50000 mÂ²
(B) 60000 mÂ²
(C) 65000 mÂ²
(D) 70000 mÂ²
(E) 75000 mÂ²
Rationale: 7 hectares in mÂ²
1 hectare = 10000 mÂ²
Therefore, 7 hectares = 7 Ã— 10000 mÂ²
= 70000 mÂ²
ANSWER : OPTION D
Answer: (D) 70000 mÂ²
Question: A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.685 in all. For how many days was he absent?
(A) 8
(B) 10
(C) 2
(D) 17
(E) 19
Rationale: 30 * 25 = 750
685
-----------
65
25 + 7.50 = 32.5
62/32.5 = 2
C
Answer: (C) 2
Question: An amount of Rs. 10000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested at 11% was?
(A) 2377
(B) 3750
(C) 2997
(D) 2677
(E) 1987
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (10000 - x). Then,
(x * 9 * 1)/100 + [(10000 - x) * 11 * 1]/100 = (10000 * 39/4 * 1/100)
(9x + 110000 - 11x)/100 = 3900/4 =975
(9x + 110000 - 11x) = 97500
x = 6250
Sum invested at 9% = Rs. 6250
Sum invested at 11% = Rs. (10000 - 6250) = Rs. 3750.
Answer: B
Answer: (B) 3750
Question: The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. x T (-z)=0
II. z T z/z-1=1
III. 2/z T 2/z=1
(A) a.) I
(B) b.) I and II only
(C) c) I and III only
(D) d) II only
(E) e) I, II and III only
Rationale: Statement I is not TRUE
Statement II is TRUE
Statement III is not TRUE
Answer : D
Answer: (D) d) II only
Question: A gardener increased the length of a rectangle-shaped garden by 25 percent and decreased its width by 20 percent. The area of the new garden
(A) has increased by 20 percent
(B) has increased by 12 percent
(C) has increased by 8 percent
(D) is exactly the same as the old area
(E) cannot be expressed in percentage terms without actual numbers
Rationale: Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.8W*1.25L = (0.8)(1.25)L*W = L*W
The answer is D.
Answer: (D) is exactly the same as the old area
Question: A train 360 m long is running at a speed of 90 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 29 sec
(C) 26 sec
(D) 20 sec
(E) 34 sec
Rationale: Speed = 90 * 5/18 = 25 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/25
= 20 sec
Answer: D
Answer: (D) 20 sec
Question: On return from a business trip Mr. Chidambaram was to be picked up from the railway station by
his coachman. Someone he managed a train connection earlier and thus arrived two hours too early.
Immediately on arrived he rang up home for the coach and was told that it had just left in order to be
exactly in time for the train by which he was scheduled to come. To save the time he started walking
homeward at 3kmph. On the way he met the coachman who brought him home an hour before
schedule. How far is the Mr. Chidambaram’s house from the railway station?
(A) 22
(B) 18
(C) 99
(D) 27
(E) 11
Rationale: Very good questions. Appeared in Puzzles book of Ravi Nirula.
Let the train's correct time is 9.00 am. Now chidambaram reached the station at 7 am and he was informed that the coachman (car) left at 7 am. So car takes 2 hours to reach the station. This car expected to reach home at 11 am.
But the car after picking up chidambaram, reached home 1 hour early. i.e., 10 am. So car has travelled 3 hours and 1.5 hours towards the station. So it picked him up at 8.30 am. Car saved distance equivalent to 30 minutes. but this distance is covered by Chidambaram by walk. He took 1.5 hours to cover this distance.
So Car speed is 3 times that of his walking speed. Car speed = 3 × 3 = 9 km.
We know that car takes 2 hours to reach station. So the distance = 9 × 2 = 18 km.
Answer:B
Answer: (B) 18
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 2
(B) 3
(C) 16
(D) 18
(E) 23
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
Answer: Option A
Answer: (A) 2
Question: A certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
(A)  30%
(B)  33 1/2%
(C)  40%
(D)  60%
(E)  114.28%
Rationale: Original visual range = 70 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-70)/70 * 100%
= 8/7 * 100%
= 114.28 %
Answer E
Answer: (E)  114.28%
Question: ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 170 students answered yes only for subject M, how many of the students did not answer yes for either subject?
(A) 100
(B) 230
(C) 300
(D) 400
(E) 500
Rationale: Since 170 students answered yes only for subject M, then the remaining 330 students who answered yes for subject M, also answered yes for subject R. So, 330 students answered yes for both subjects.
If 320 students answered yes for both subjects, then 400-330=70 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
70 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+70+300)=230 students did not answer yes for either subject.
Answer: B.
Answer: (B) 230
Question: If M is a negative integer and Q is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, M, 0, 1, 3, Q, 7}?
I. -1.5
II. -2
III. 0
(A)  I only
(B)  II only
(C)  III only
(D)  I and III only
(E)  None
Rationale: If M is a negative integer and Q is a positive integer,The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either=E
Answer: (E)  None
Question: How many of the positive divisors Q of 120 are also multiples of 4 not including 120?
(A) 3.
(B) 4.
(C) 5.
(D) 7.
(E) 8.
Rationale: 4,8,12,20,24,40,60. (7) is the answer
Other way : factors of 120 = 2^3 * 3*5
Separate 2^2 ( which means 4)
Now, calculate the number of other factors.
Q=2*3*5 = total positive factors are 2*2*2 = 8
This 8 factors include 120
So subtract 1 from 8
Ans is 7=D
Answer: (D) 7.
Question: If x/y = 5 and (4a - x)/(b - y) = 5, then the value of a/b is?
(A)  –3
(B)  -2
(C)  1
(D)  5/4
(E)  3
Rationale: x = 5y
4a - 5y = 5(b - y)
4a - 5y = 5b - 5y
4a = 5b
a/b = 5/4
Answer: D
Answer: (D)  5/4
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 3 hours. Harvesting machine K harvested how many acres of wheat per hour?
(A)  7
(B)  8
(C)  12
(D)  13
(E)  17
Rationale: Rate of H = 3 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/3 = 20 acres/hr
Rate of K = 20-3= 17
Answer: E
Answer: (E)  17
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on November 1 than were in stock on January 1?
(A)  8
(B)  12
(C)  40
(D)  32
(E)  36
Rationale: Jan 1 = C
Feb 1 = C - 4
March 1 = C - 8
April 1 = C - 12
May 1 = C - 16
June 1 = C - 20
July 1 = C - 24
Aug 1 = C - 28
Sept 1 = C - 32
Oct 1 = C - 36
Nov 1 = C - 40
Difference between stock on November 1 than were in stock on January 1 will be -
C - ( C - 40 )= 40
Hence answer will be (C)
Answer: (C)  40
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Find the sum?
(A) 30
(B) 15
(C) 40
(D) 45
(E) 20
Rationale: a2+b2+c2=138 and(ab+bc+ca)=131
a+b+c^2=400
root(400)=20
ANSWER E
Answer: (E) 20
Question: Rs.1170 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) 227
(B) 540
(C) 882
(D) 266
(E) 222
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: (D) 266
Question: Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
(A) $506.00
(B) $726.24
(C) $900.00
(D) $920.24
(E) $926.24
Rationale: If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;
Total: 200+306+(~420)=~$926.
Answer: E.
Answer: (E) $926.24
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120
(B) 110
(C) 130
(D) 140
(E) 150
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: Option A
Answer: (A) 120
Question: When 10 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
(A) 10
(B) 24
(C) 46
(D) 48
(E) 45
Rationale: Explanation:
Let the number be x. Then,
x - 10 = 7x/12 => x - 7x/12 = 10
5x/12 = 10 => x = 24
Answer: Option B
Answer: (B) 24
Question: 6^4 is equal to which of the following?
(A) 1,296
(B) 752
(C) 660
(D) 662
(E) 1,608
Rationale: A is the correct answer. We do not really need to calculate it. The last digit for 6^4 will be 6. Hence A is the correct answer
Answer: (A) 1,296
Question: In a group of cows and hens, the number of legs are 18 more than twice the number of heads. The number of cows is
(A) 5
(B) 7
(C) 9
(D) 12
(E) 14
Rationale: Explanation:
Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 18
4x + 2y = 2x + 2y + 18
2x = 18
x = 9.
Answer: C
Answer: (C) 9
Question: If a is an even integer and b is an odd integer which of the following must be an odd integer :
(A) a/b
(B) ab
(C) 2a+b
(D) 2(a+b)
(E) 3a/b
Rationale: We can always look for low hanging fruits first to solve such questions under 30secs.
Expression in C, is basically 2*Even+Odd or simply Even+Odd which is always going to be odd.
Hence C
Answer: (C) 2a+b
Question: Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 1. Find the larger integer.
(A) 8
(B) 16
(C) 32
(D) 48
(E) 54
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.
If adding 12 to the smaller integer makes the ratio 1 to 1, then x+12=y.
Substituting y=4x into the second equation yields x+12=4x.
So, x=4 (smaller integer) and, y=4x=16 (larger integer) so B is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 8
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 2
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (2), we get 14.
So, the new ratio is 14 to 8 which is the same as 7 to 4.
No good. We want a resulting ratio of 1 to 1
ELIMINATE A
B) the larger number is 16
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 4
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (4), we get 16
So, the new ratio is 16 to 16 which is 1 to 1.
Therefore (B) is correct.
C) the larger number is 32
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 8
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (8), we get 20
So, the new ratio is 20 to 32 which is 5 to 8.
No good. We want a resulting ratio of 1 to 1
ELIMINATE C
D) the larger number is 48
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 12
If 12 is added to the smaller number, the ratio becomes 1 to 1
If we add 12 to the smaller number (12), we get 24
So, the new ratio is 24 to 48. This is the same as the ratio of 1 to 2
No good. We want a resulting ratio of 1 to 1
ELIMINATE D
E) the larger number is 54
Given: the two integers are in the ratio of 1 to 4
So, the smaller number must be 13.5 (which is not an integer)
Since both numbers are integers, the larger number cannot be 54.
ELIMINATE E
Therefore B is the only correct choice.
Answer: (B) 16
Question: The 38 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=38
solving for x you get 10
Answer E
Answer: (E) 10
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 30, find the ages of Toby and Debby?
(A) 10 and 14
(B) 3 and 7
(C) 6 and 10
(D) 5 and 10
(E) 12 and 16
Rationale: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 30
x = 7
The ages of Toby and Debby are 3 and 7.
Answer : B
Answer: (B) 3 and 7
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120.To obtain equal dividends from both,he must invest the money in the ratio :
(A) 3 : 4
(B) 3 : 5
(C) 4 : 5
(D) 16 : 15
(E) None
Rationale: Solution
For an income of Rs. 1 in 9% stock at 96, investment = Rs. (96/9)= Rs. 32/3 .
For an income of Rs. 1 in 12% stock at 120, investment = Rs.(120/12) = Rs. 10.
∴ Ratio of investments = 32/3 :10 =32:30 = 16:15
Answer D
Answer: (D) 16 : 15
Question: When asked how old she was, Pooja replied, 'In 2 years I will be twice as old as I was five years ago.'
How old is she ?
(A) 11 years
(B) 12 years
(C) 8 years
(D) 10 years
(E) 15 years
Rationale: B
12 years
Answer: (B) 12 years
Question: Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {9, 11}
(B) {2, 10}
(C) {10, 18}
(D) {7, 13}
(E) {16, 16}
Rationale: answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is more. therefore accepted
answer is A mean is 10 and S.D decreases minimum.
A
Answer: (A) {9, 11}
Question: Out of 6 balls a pair is to be selected for a game. At most, how many different pairs are possible?
(A) 100
(B) 90
(C) 50
(D) 15
(E) 25
Rationale: N=6C2=6!/(4!2!)=6*5/2=15
Correct Option: D
Answer: (D) 15
Question: A train starts with the speed of 50km/hr with its speed increasing every two hours by 20kmph. In how many hours will it cover 330 kms
(A) 4 hrs
(B) 5 hrs
(C) 6 hrs
(D) 4 ½ hrs
(E) 5 hrs
Rationale: Explanation:
Distance covered in first 2 hours = 50×2 =100km
Distance covered in next 2 hours = 70×2 =140km
Remaining distance = 330 -100-140 =90km
Speed of the fifth hour =90km/hr
Time taken to cover 90km = 90/90 = 1 hr
Total time taken = 2+2+ 1 = 5 hrs
Answer: Option B
Answer: (B) 5 hrs
Question: A cyclist covers a distance of 500m in 4 min 30sec. What is the speed in km/hr of the cyclist?
(A) 2
(B) 2.5
(C) 3.2
(D) 4.6
(E) 2.8
Rationale: distance = 500 m
time = 4min 10 sec = 250 sec
speed = (500/250) m/s = 2m/s
speed in km/hr = 2*18/5 = 3.2 km/hr
correct option is C
Answer: (C) 3.2
Question: A certain tire company can produce tires at a cost of $22,500 per batch plus $9 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?
(A) $9.00
(B) $9.50
(C) $11.00
(D) $13.50
(E) $20.00
Rationale: CP(15000 tires) = $22500 +($9×15000) =$157500
SP (15000 tires) = $20×15000 = $300000
Profit = SP-CP
= $300000-$157500= $142500
PROFIT/TIRE = $142500/15000 = $9.50
Answer B
Answer: (B) $9.50
Question: During a Thanksgiving weekend, a car rental company rented six-tenths of their vehicles, including three-fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
(A) 20%
(B) 30%
(C) 40%
(D) 60%
(E) 25%
Rationale: 4/10 of all the vehicles were not rented.
(2/5)(3/5) = 6/25 of all the vehicles were 4WDs that were not rented.
(6/25) / (4/10) = 3/5 is the fraction of non-rented vehicles that were 4WDs
1 - 3/5 = 40% of non-rented vehicles were not 4WDs.
The answer is C.
Answer: (C) 40%
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation s of the mean, what percent of the distribution is less than m+s?
(A)  16%
(B)  32%
(C)  48%
(D)  84%
(E)  92%
Rationale: 16%
________________________________________________ m+s
34%
________________________________________________ m
34%
________________________________________________ m-s
16%
since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-s and 16% lie above m+s
now below m+s = 16+34+34 = 84%
hence D
Answer: (D)  84%
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 5 hours?
(A) 675
(B) 750
(C) 1,125
(D) 5,900
(E) 7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(5 hours)= 1125 cans. The answer is C.
Answer: (C) 1,125
Question: A sum was put a simple interest at a certain rate for 1 years. Had it been put at 6% higher rate, it would have fetched Rs. 30 more. The sum is:
(A) s.500
(B) s.600
(C) s.700
(D) s.800
(E) s.900
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+6) Ã— 1/100âˆ’xÃ—RÃ—1/100=30
â‡’x Ã— 6Ã—1/100=30
â‡’x Ã— 1 /100=5
â‡’x=500
Answer : Option A
Answer: (A) s.500
Question: If 12 men do a work in 80 days, in how many days will 16 men do it?
(A) 20
(B) 29
(C) 22
(D) 60
(E) 12
Rationale: 12 * 80 = 16 * x
x = 60 days
Answer: D
Answer: (D) 60
Question: The greatest common factor of positive integers m and n is 10. What is the greatest common factor of (2m^2, 2n^2)?
(A) 2
(B) 10
(C) 100
(D) 200
(E) 400
Rationale: m = 10j and n = 10k, where the greatest common factor of j and k is 1.
2m^2 = 2*10*10*j^2 and 2n^2 = 2*10*10*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*10*10 = 200
The answer is D.
Answer: (D) 200
Question: At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married?
(A) 5⁄7
(B) 7⁄10
(C) 2/7
(D) 7⁄30
(E) 5⁄70
Rationale: --------------------M------W--------Total
Marrried----------20-----20---------40
Not married-----10-----50---------60
Total-------------30-----70--------100
need married woman/total woman, so 20/70=2/7
C
Answer: (C) 2/7
Question: Two cars cover the same distance at the speed of 60 and 62 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 1873
(B) 1848
(C) 1860
(D) 1838
(E) 1939
Rationale: Explanation:
60(x + 1) = 62x
X = 30
60 * 31 = 1860 km
Answer: Option C
Answer: (C) 1860