mathewhe/aqua_rat huggingface dataset:
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 5: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
(A) 4: 45 p.m.
(B) 5: 00 p.m.
(C) 5: 20 p.m.
(D) 5: 35 p.m.
(E) 7: 20 p.m.
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 5:20 +2=7:20
Hence answer is E.Hope i am correct
Answer: (E) 7: 20 p.m.
Question: The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 11. What is the last numbers?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A + B + C = 18
B + C + D = 15
A + D = 11
A – D = 3
A + D = 11
2D = 8
D = 4
ANSWER:A
Answer: (A) 4
Question: In a box of 12 pens, a total of 4 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 1/6
(B) 2/33
(C) 14/33
(D) 9/16
(E) 3/44
Rationale: Method- 1
There are 9 fine pieces of pen and 4 defective in a lot of 12 pens
i.e. Probability of first pen NOT being defective = (8/12)
i.e. Probability of Second pen NOT being defective = (7/11) [11 pen remaining with 8 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (8/12)*(7/11) = 14/33
Answer: option C
Answer: (C) 14/33
Question: Insert the missing number
1, 8, 27, 64, 125, 216, (....)
(A) 554
(B) 343
(C) 354
(D) 392
(E) 245
Rationale: Series is 1^3,2^3,3^3,4^3,5^3,6^3,7^3
7^3=343
ANSWER:B
Answer: (B) 343
Question: If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the
stream is
(A) 5 km/hr
(B) 4 km/hr
(C) 2 km/hr
(D) 1 km/hr
(E) None of these
Rationale: Explanation:
Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph
Answer: D
Answer: (D) 1 km/hr
Question: Which of following is a leap year ?
(A) 2000
(B) 2800
(C) 1800
(D) 2600
(E) 3000
Rationale: The century year which is completely divisible by 400, is a leap year. Thus, the year 2800 is a leap year.
Answer : B
Answer: (B) 2800
Question: if Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 11x/y
(B) 11y/x
(C) x/11y
(D) 12x/y
(E) xy/11
Rationale: Answer is D
The rate of running hards: 12 minutes per y hards.
Thus the time for running x hards = x hards * 12 minutes/y hards = 12x/y
Answer: (D) 12x/y
Question: If QR = 3(Q+ 1) + R and Q and R are integers,Q could be any of the following values EXCEPT:
(A) 2
(B) 3
(C) 12
(D) 4
(E) 7
Rationale: QR = 3(Q + 1) + R
QR - R = 3(Q + 1)
R = 3(Q + 1)/(Q-1)
R won't be an integer only if Q = 12 (from the options).
Answer: C
Answer: (C) 12
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
(A) 35 years
(B) 17 years
(C) 77 years
(D) 88 years
(E) 16 years
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years.
Answer:A
Answer: (A) 35 years
Question: If 10 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 15
III. 20
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Let x be the length of the third side.
15-10 < x < 15+10
5 < x < 25
The answer is D.
Answer: (D) II and III only
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
(A) 343
(B) 147
(C) 189
(D) 063
(E) 027
Rationale: •P(Buy) = 3/10, P(No Buy) = 7/10
•2 Yes, 1 No = 3/10*3/10*7/10 = 63/1000
•3 Possibilities = YYN + YNY + NYY = 3(63/1000) = 189/1000 = .189%
Answer is C.
Answer: (C) 189
Question: Jane bought some pairs of pants on sale for 15% off the original price and received an additional 20% discount for buying three pairs. If one of the pairs of pants cost $10 after both discounts, what was the original price of that pair?
(A) $32.26
(B) $20.25
(C) $20
(D) $14.71
(E) $10.35
Rationale: Let f be the original price. Then the first discounted price, g, is given byg = f - 15%fand the second discounted price, h, is given byh = g - 20%gWith h = $10, solve for f$10 = (f - 15%f) - 20%(f - 15%f)f = $14.71Correct answer is D
Answer: (D) $14.71
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) Rs.2000
(B) Rs.2028
(C) Rs.2020
(D) Rs.2720
(E) Rs.2026
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer:A
Answer: (A) Rs.2000
Question: In an engineering class that contained 75 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
(A) 4
(B) 6
(C) 10
(D) 12
(E) 24
Rationale: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—75=45
2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(75âˆ’45)=4/5âˆ—30=24
total students who answered at least one Q correct =45+24=69
so students who answered BOTH incorrectly = 75âˆ’69=6
ANSWER:B
Answer: (B) 6
Question: What is the total number of prime numbers less than 70?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Solution
Prime numbers less than 70 are	=12.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,and 67
Their number is 19.
Answer C
Answer: (C) 19
Question: What amount does Kiran get if he invests Rs.5600 at 9% p.a. compound interest for two years, compounding done annually?
(A) 6653
(B) 6500
(C) 6400
(D) 5678
(E) 6886
Rationale: A= P{1 + R/100}n
=> 5600{1 + 9/100}2
= Rs.6653
Answer: A
Answer: (A) 6653
Question: A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5 kmph
(B) 7.5 kmph
(C) 8 kmph
(D) 9 kmph
(E) 4 kmph
Rationale: US = 20
DS = 35
M = (35 - 20)/2 = 7.5
Answer:B
Answer: (B) 7.5 kmph
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
(A) 20
(B) 22
(C) 24
(D) 48
(E) 36
Rationale: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times. Answer: Option B
Answer: (B) 22
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs.6158
(B) Rs.6120
(C) Rs.6119
(D) Rs.6150
(E) Rs.6151
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs.6150.
Answer:D
Answer: (D) Rs.6150
Question: In a 1000 m race, A beats B by 100 meters or 25 seconds. Find the speed of B?
(A) 8
(B) 9
(C) 7
(D) 5
(E) 4
Rationale: Since A beats B by 100 m or 25 seconds, i
t implies that B covers 100 m in 25 seconds.
Hence speed of B = 100/25 = 4 m/s.
Answer: E
Answer: (E) 4
Question: Two persons start from two places 160 km apart at the same time with velocities 50 km/hr and 30 km/hr. move in opposite direction. Where they meet ?
(A) 90 km from A
(B) 50 km from B
(C) 100 km from A
(D) 70 km from B
(E) None of these
Rationale: Explanation :
Solution: d = 160, v1 = 50, v2 = 30
relative speed vr = v1 + v2 = 50 + 30 = 80.
the distance covered by them will be indirectly proportional to their distance
of the persons of meeting from A = 160*50/(50+30) km
= 160*5/8 = 100 km.
Answer : C
Answer: (C) 100 km from A
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 3 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
(A) $1100
(B) $1240
(C) $1360
(D) $1480
(E) $1550
Rationale: The total surface area is 2(2*3 + 3*5 + 2*5) = 62 square feet
The total cost is 62*$20 = $1240
The answer is B.
Answer: (B) $1240
Question: If A^2 + B^2 = 10 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2?
(A) 10
(B) 20
(C) 30
(D) 60
(E) 70
Rationale: (a-b)^2 = a^2 + b^2 - 2ab = 10-20= -10
(a+b)^2 = a^2 + b^2 + 2ab = 10+20=30
so (a+b)^2 + (a-b)^2 = 30 - 10 =20
B
Answer: (B) 20
Question: The largest 4 digit number exactly divisible by 88 is:
(A) 4252
(B) 6287
(C) 7631
(D) 9944
(E) 6736
Rationale: D
Divide largest four digit number 9999 by 88. You get 113.625.
Obviously 113 would be exactly divisible so we want to know what that number is.
We get this by multiplying 113 with 88 = 9944
Answer: (D) 9944
Question: The average of runs of a cricket player of 10 innings was 30. How many runs must he make in his next innings so as to increase his average of runs by 4?
(A) 87
(B) 74
(C) 10
(D) 76
(E) 17
Rationale: Average after 11 innings = 34
Required number of runs
= (34 * 11) - (30 * 10) = 374- 300
= 74.
Answer: B
Answer: (B) 74
Question: Tough and Tricky questions: Combinations.
Six contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 12
(D) 18
(E) 24
Rationale: Number of ways First-place medal can be awarded to four contestants = 6
Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3
Therefore number of possibilities = 6 *3 =18
Answer:D
Answer: (D) 18
Question: A can build a wall in the same time in which B and C together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it?
(A) 275 days
(B) 178 days
(C) 185 days
(D) 175 days
(E) 675 days
Rationale: Explanation:
No explanation is available for this question!
ANSWER: D
Answer: (D) 175 days
Question: When positive integer n is divided by 3, the remainder is 2. When n is divided by 5, the remainder is 5. How many values less than 100 can n take?
(A)  0
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: a quick approac to this Q is..
the equation we can form is.. 3x+2=7y+5..
3x-3=7y... 3(x-1)=7y...
so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100..
ans 0.. A
Answer: (A)  0
Question: the largest four-digit number which is a perfect cube, is
(A) 8000
(B) 9261
(C) 9999
(D) None of these
(E) Cannot be determined
Rationale: Solution
Clearly, 9261 is a perfect cube satisfying the given property.
Answer B
Answer: (B) 9261
Question: The end of a blade on an airplane propeller is 20 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
(A) 200π
(B) 240π
(C) 600π
(D) 480π
(E) 1,200π
Rationale: Distance traveled in 1 revolution = 2πr= 2π20/5280
Revolutions in one second= 1320
Revolutions in 60 seconds (one minute)= 1320*60
Total distance traveled= total revolutions *distance traveled in one revolution
1320*60 *2π20/5280= 600π
C is the answer
Answer: (C) 600π
Question: A train which has 390 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ?
(A) 26 sec
(B) 39 sec
(C) 36 sec
(D) 29 sec.
(E) 19 sec.
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 390/((45-9) (5/18)
= 390/ 36*(5/18)
= 390/10
= 39 sec
ANSWER:B
Answer: (B) 39 sec
Question: In an engineering class that contained 25 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
(A) 2
(B) 6
(C) 10
(D) 12
(E) 24
Rationale: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—25=15
2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(25âˆ’15)=4/5âˆ—10=8
total students who answered at least one Q correct =15+8=23
so students who answered BOTH incorrectly = 25âˆ’23=2
ANSWER:A
Answer: (A) 2
Question: If x*y = xy – 2(x + y) for all integers x and y, then 1* (–3) =
(A) –16
(B) –11
(C) –4
(D) 4
(E) 1
Rationale: 1*(-3) = 1*(-3) - 2 (1 + (-3) ) = -3 +4 = 1
Option (E)
Answer: (E) 1
Question: Presently the ratio between the ages of Dan and James is 6:5. after 4 years Dan will be 28. What is the present age of James?
(A) 20
(B) 19
(C) 21
(D) 18
(E) 22
Rationale: Let the present ages Dan and James be 6x years and 5x years respectively
6x+4 = 28
6x = 24
x = 4
Kim's age = 5x = 20 years
Answer is A
Answer: (A) 20
Question: Of the 3,600 employees of Company X, 1/4 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
(A)  25%
(B)  22.2%
(C)  20%
(D)  12.5%
(E)  11.1%
Rationale: Welcome, just post the question and the choices
Let's see, the way I did it was
1/4 are clerical out of 3600 so 900 are clerical
900 reduced by 1/3 is 900*1/3
so it reduced 300 people , so there is 600 clerical people left
but since 600 people left, it also reduced from the total of 3600 so there are 3000 people total
since 600 clerical left / 300 people total
you get (A) 20%
Answer : C
Answer: (C)  20%
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.8.4. The true discount is
(A) Rs.70
(B) Rs.36
(C) Rs.54
(D) Rs.50
(E) none
Rationale: Solution
T.D	= [B.G x 100 / R x T]
= Rs.(8.4 x 100 / 12 x 1)
= Rs.70.
Answer A
Answer: (A) Rs.70
Question: Working individually, Allison can sew dresses for 9 hours and Al can sew dresses in 12 hours. If Allison and Al work together but independently at the task for 3 hours, at which point Al leaves, how many remaining hours will it take Allison to complete the task alone?
(A) 45/12
(B) 23/12
(C) 40/33
(D) 34/12
(E) 43/5
Rationale: In first 3 hrs Al will finish 3/12 = 1/4 of work and Allison will finish 3/9=1/3 work so total 1/4 + 1/3 = 7/12 work is finished and 1-7/12 = 5/12 work remaining. Now Allison will take (5/12)*9 = 45/12 hrs to finish it.
So answer is A.
Answer: (A) 45/12
Question: What is the probability for a family with four children to have two boys and two girls (assuming the probability of having a boy or a girl is equal)?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 3/8
(E) 5/16
Rationale: One possible case is: girl - girl - boy - boy
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C2 = 6 such cases so we should multiply by 6.
P(two boys and two girls) = 6/16 = 3/8
The answer is D.
Answer: (D) 3/8
Question: Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 20,the first number is :
(A) 22
(B) 23
(C) 77
(D) 99
(E) 27
Rationale: Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 48, b + c + d = 45
Now, d = 20
thus, b + c + 20 = 45 ⇒ b + c = 25
Putting the value of b + c in a + b + c = 48
a + 25 = 48 ⇒ a = 23
Answer: B
Answer: (B) 23
Question: 6x – 5y + 3z = 26
4x + 8y – 11z = 7
5x – 6y + 2z = 12
Given the equations above, x + y + z = ?
(A)  11
(B)  12
(C)  13
(D)  14
(E)  15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 26-12
or, x+y+z = 14
Option D is the ans
Answer: (D)  14
Question: Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 9000
interest only for the period. The principal amount borrowed by her was
(A) Rs. 25000
(B) Rs. 10000
(C) Rs. 15000
(D) Rs. 20000
(E) None of these
Rationale: Explanation :
Principal = Rs. (100×9000 / 12×3)
=> Rs. 25,000.
Answer : A
Answer: (A) Rs. 25000
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%
Rationale: Registered voters = 100
D = 60
R = 40
75% of D ( 60) = 45
20% of R ( 40 ) = 8
Total voter% of registered voters = 53 / 100
53%
Answer: B
Answer: (B) 53%
Question: On a scale of a map 0.6 cm represents 6.6km. If the distance between two points on the map is 80.5 cm , what is the the actual distance between these points?
(A) 885.5 km
(B) 860 km
(C) 892.5 km
(D) 825 km
(E) None of these
Rationale: Explanation :
Let the required actual distance be x km
More scale distance, More actual distance(direct proportion)
Hence we can write as
scale distance.6:80.5}::6.6:x
⇒.6x = 80.5 × 6.6
⇒ .1x = 80.5 × 1.1
⇒ x = 80.5 × 11 = 885.5. Answer : Option A
Answer: (A) 885.5 km
Question: Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 6/8 of its own speed and got to its destination in 11 hours?
(A) 2.5 hrs
(B) 2.9 hrs
(C) 4.5 hrs
(D) 3.5 hrs
(E) 1.5 hrs
Rationale: New speed = 6/8 of usual speed
New time = 6/8 of usual time
6/8 of usual time = 10 hrs
Usual time = 10*6/8 = 7.5 hrs
Time saved = 10-7.5 = 2.5 hrs
Answer is A
Answer: (A) 2.5 hrs
Question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 3 ?
(A) 4
(B) 0
(C) 3
(D) 2
(E) 1
Rationale: A number ending with 3 can never be a perfect square.
Answer: B
Answer: (B) 0
Question: Today is Tuesday. After 75 days, it will be:
(A) Saturday
(B) Sunday
(C) Friday
(D) Thursday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 77 days, it will be Tuesday.
After 75 days, it will be Sunday.
Answer :B
Answer: (B) Sunday
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 7 min
(B) 13 min
(C) 23 min
(D) 9 min
(E) 8 min
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
ANSWER:D
Answer: (D) 9 min
Question: What is the rate percent when the simple interest on Rs.2000 amount to Rs.500 in 2 Years?
(A) 5%
(B) 6%
(C) 12.5%
(D) 95%
(E) 1%
Rationale: Interest for 2yrs = 500
Interest for 1yr = 250
Interest rate = 250/2000 x 100 = 12.5%
Answer : C
Answer: (C) 12.5%
Question: Workers at a campaign office have 2000 fliers to send out. If they send out 1/10 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?
(A) 300
(B) 1350
(C) 1100
(D) 1200
(E) 1900
Rationale: (1/10)*2000 = 200
Remaining = 2000-200 = 1800
(1/4) of remaining = (1/4)*1800 = 450
Remaining now = 1800-450 = 1350
Answer: Option B
Answer: (B) 1350
Question: The number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 70: 1, 4, 9, 16, 25, 36, 49, 64.
Now, 70 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 70 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
We can find that 60 equals to 9+25+36=3^2+5^2+6^2=70 --> 3+5+6=14.
Answer: D.
Answer: (D) 14
Question: In what ratio must sugar at Rs.7.10 be mixed with sugar at Rs.9.20 so that the mixture may be worth Rs.8 per kg?
(A) 6:3
(B) 7:3
(C) 1:7
(D) 4:3
(E) 2:1
Rationale: CP of 1 kg sugar of 1st kind =7.1
CP of 1 kg sugar of 2nd kind=9.2
Mean Price=8
CP of 1 kg sugar of 1st kind - Mean Price=8-7.1=0.9
CP of 1 kg sugar of 2nd kind - Mean Price=9.2-8=1.2
Required ratio = 1.2 : 0.9 = 12 : 9 = 4 : 3
Answer:D
Answer: (D) 4:3
Question: 5,9,20,32,52,__
(A) 79
(B) 85
(C) 81
(D) 82
(E) 83
Rationale: (9+5) +6 = 20
(16+9) +7 = 32
(28+16)+8 = 52
(48+28)+9 = 85
ANSWER:B
Answer: (B) 85
Question: A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 1/12 work in 1 day...
They did 2/3 w in 8 days.
Total days=(8+10) = 18
ANSWER:D
Answer: (D) 18
Question: There are 7 players in a bowling team with an average weight of 85 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
.
(A) 75 Kg
(B) 80 Kg
(C) 85 Kg.
(D) 90 Kg
(E) 92 Kg
Rationale: New average weight= 110+60/2= 85 kgs
Since avg weight of 85 is added to avg weight of 85, the average will remain the same, i.e 85
C is the answer
Answer: (C) 85 Kg.
Question: A HEXAGON IS FORMED ABCDEF WHICH PERIMETER 36cm. A POLYGON IS FORMED BY JOINING THE POINTS AE &BD . FIND THE AREA OF THE POLYGON ABDE?
(A) 34√3 cm2
(B) 35√3 cm2
(C) 36√3 cm2
(D) 37√3 cm2
(E) 38√3 cm2
Rationale: A regular hexagon consist of 6 equilateral triangle. Each of side 6 cm.
So the area of 1 equilateral triangle is = ¼(√3 a2) = 9√3 cm2
The figure formed by joining polygon ABDE consist of 2 equilateral triangle and 4 half equilateral triangle
Which employs area of 4 equilateral triangle.
So, The area of polygon ABDE = 4*(area of equilateral traingle)
= 4* 9√3 = 36√3 cm2
ANSWER:C
Answer: (C) 36√3 cm2
Question: The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 90 instead of 10 then find the correct average marks?
(A) A)78
(B) B)82
(C) C)92
(D) D)91
(E) E)85
Rationale: correct avg marks = 100+(10-90)/10
avg = 100-8 = 92
Answer is C
Answer: (C) C)92
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
Answer:B
Answer: (B) 10
Question: Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 6. Based on this information, how many gold coins would there be in this collection after the proposed trade?
(A) 50
(B) 60
(C) 180
(D) 200
(E) 300
Rationale: The correct answer is C.
Answer: (C) 180