mathewhe/aqua_rat huggingface dataset:
Question: Joe drives 420 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?
(A) 42
(B) 54
(C) 50
(D) 54
(E) 56
Rationale: t1= 420/60=7 hours
t2=120/40=3 hours
T=t1+t2=10 hours
Avg speed = Total Distance/T
= 540/10 = 54mph=B
Answer: (B) 54
Question: A works twice as fast as B. if both of them can together finish a piece of work in 12 days, then B alone can do it in
(A) 24 days
(B) 27 days
(C) 36 days
(D) 48 days
(E) 50 days
Rationale: Explanation:
B = 2A
2A × A/3A = 12
2A/3 = 12
A = 18 days
B = 2 × 18 = 36 days
Therefore, B alone can finish the work in 36 days.
Answer: Option C
Answer: (C) 36 days
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 15 have taken a course in finance and 14 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 2 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
(A) 12
(B) 8
(C) 5
(D) 4
(E) 9
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 15
Marketing: 14
Which would add up to 51 different attendands, which is not possible.
Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.
51-9= 42
2 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
42-4= 38.
Answer : A
Answer: (A) 12
Question: Jackson invested $200,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
(A) $115,384
(B) $120,000
(C) $121,072
(D) $124,129
(E) $130,000
Rationale: x be the amount invested in account P
0.12*x +(200000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$105,384
hence answer is A
Answer: (A) $115,384
Question: In a class there are 20 boys and 20 girls. In how many ways can a boy and a girl be selected?
(A) 508
(B) 400
(C) 800
(D) 570
(E) 503
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 20 girls in 20 ways
We select a boy and girl in 20 * 20 ways i.e., = 400 ways.
Answer:B
Answer: (B) 400
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 17 1/7
(B) 2/7
(C) 8/5
(D) 4/9
(E) 3/8
Rationale: Explanation:
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
So, both together will finish the work in 17 1/ 7 days.
Answer:A
Answer: (A) 17 1/7
Question: A cab driver 5days income was $45, $50, $60, $65 , $70. Then his average income is?
(A) $58
(B) $42
(C) $65
(D) $48
(E) $62
Rationale: avg = sum of observations/number of observations
avg income=(45+50+60+65+70)/5 = 58
Answer is A
Answer: (A) $58
Question: An isosceles triangle has angles with ratios 1:2:2. What is the measurement of the angle within the triangle with ratio 2?
(A) 36Â°
(B) 46Â°
(C) 72Â°
(D) 92Â°
(E) 100Â°
Rationale: Given that the ratio is 1:2:2 and that the total angle measurement within a triangle is 180Â°, the equation is
1x + 2x + 2x = 180Â°
5x = 180Â°
x = 36Â°
But since we want to find the angle measurement with ratio 2, we multiple x by 2
2x = 2(36Â°) = 72Â°
Therefore, the answer is 72Â° or C.
Answer: (C) 72Â°
Question: A candidate got 40% of the votes polled and he lost to his rival by 5000 votes. How many votes were cast?
(A) 25000
(B) 2028
(C) 2775
(D) 5496
(E) 6851
Rationale: 40%-----------L
60%-----------W
------------------
20%----------5000
100%---------? => 25000
Answer:A
Answer: (A) 25000
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ?
(A) 2013
(B) 2088
(C) 270
(D) 1881
(E) 1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2012) = 2013
Ans: A
Answer: (A) 2013
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
(A) 6
(B) 36
(C) 5
(D) 25
(E) 30
Rationale: Explanation:
(9*12)/3 = 36
ANSWER B
Answer: (B) 36
Question: Find the middle one when The sum of five consecutive even numbers is 65?
(A) 9
(B) 13
(C) 15
(D) 17
(E) 11
Rationale: Let the first number be n
Let the second number be n + 2
Let the third number be n + 4
Let the third number be n + 6
Let the third number be n + 8
n + n + 2 + n + 4 + n + 6 + n + 8= 65
Combine like terms:
5n + 20 = 65
5n = 65 - 20
5n = 45
5n = 45
n = 9
n + 2 = 11
n + 4 = 13
n + 6 = 15
n + 8 = 17
The middle number is 13
Answer: B
Answer: (B) 13
Question: A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
(A) 21 : 32 : 4
(B) 21 : 26 : 4
(C) 21: 12 : 1
(D) 21: 16 : 28
(E) none
Rationale: Sol.
A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28
Answer D
Answer: (D) 21: 16 : 28
Question: Three fill pipes A, B and C can fill separately a cistern in 3, 4 and 6 minutes respectively. A was opened first. After 1 minute, B was opened and after 2 minutes from the start of A, C was also opened. Find the time when the cistern will be full ?
(A) 2 1⁄9 min.
(B) 4 1⁄2 min.
(C) 3 3⁄4 min.
(D) 3 min.
(E) None of these
Rationale: Let cistern will be full in x min. Then,
part filled by A in x min + part filled by B in (x – 1) min + part filled by C in (x – 2)min = 1
⇒ x/3+x−1/4+x−2/6=1
⇒ 9x = 19 ⇒ x = 19⁄9 = 21⁄9 min.
Answer A
Answer: (A) 2 1⁄9 min.
Question: The forth proportional to 20,8,15 is?
(A) 15
(B) 6
(C) 18
(D) 20
(E) 24
Rationale: Let the fourth proportional to 20,8,15 be x
then 20:8::15:x
20x = 8*15
x = 6
Answer is B
Answer: (B) 6
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 228
(B) 240
(C) 188
(D) 266
(E) 281
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: B
Answer: (B) 240
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 60 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
(A) 2hrs, 48mins
(B) 7hrs,
(C) 7hrs, 12mins
(D) 13hrs, 4mins
(E) 14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/60 --> x=1/420--> (time) = (reciprocal of rate) = 392 minutes = 7 hours
Answer: B.
Answer: (B) 7hrs,
Question: A machine puts c caps on bottles in m minutes. How many R hours will it take to put caps on b bottles?
(A) 60bm/c
(B) R=bm/60c
(C) bc/60m
(D) 60b/cm
(E) b/60cm
Rationale: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Answer: (B) R=bm/60c
Question: At the beginning of a year ,the owner of a jewel shop raised the price of all the jewels in his shop by x% and lowered them by x%. The price of one jewel after this up and down cycle reduced by Rs.100.The owner carried out the same procedure after a month.After this second up-down cycle,the price of that jewel was Rs.2304.Find the original price of that jewel(in Rs.)
(A) 2500
(B) 550
(C) 2600
(D) 2650
(E) None of these
Rationale: Solution: Let the original price = y,
After first change, It becomes,
y * (1+(x/100))
After second change, It becomes
y *(1+(x/100))(1-(x/100)) = y(1-(x/100)^2 )
Thus,
x2*y = 106 ------- (1)
x2 = 106/y
Now,
y(1-(106/10000y))2 = 2304(similar to above)
y(1-100/y)2 = 2304
y = 2500.
Answer: Option A
Answer: (A) 2500
Question: By approximately what percent is x greater than 1/2 if (1/2)(x) = 1?
(A) 732%
(B) 560%
(C) 641%
(D) 370%
(E) 300%
Rationale: what percent is x greater than 1/2 if (1/2)(x) = 1?
=> x = 2
% change =[(2 -1/2) /(1/2) ] * 100
= (4 - 1) *100
= 300% approx
Ans ,E
Answer: (E) 300%
Question: Mirun travels the first 3 hours of her journey at 20 mph speed and the remaining 2 hours at 40 mph speed. What is the average speed of Mirun 's travel in mph?
(A) 26mph
(B) 27mph
(C) 22mph
(D) 28mph
(E) 23mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by Mirun = Distance covered in the first 3 hours + Distance covered in the next 2 hours.
Distance covered in the first 3 hours = 3Ã—20=60 miles
Distance covered in the next 2 hours= 2Ã—40=80 miles
Therefore, total distance travelled = 60+80=140 miles.
The total time taken = 3+2=5hours.
Hence, the average speed =140/5= 28mph.
Answer : D
Answer: (D) 28mph
Question: Three fifth of the roads from A to B are at least 5 miles long, and 5/6 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 1/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 11/12
Rationale: So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-2/5*5/6=2/3.
Answer: C.
Answer: (C) 2/3
Question: Each side of a rectangle is increased by 100% .By what percentage does the area increase?
(A) 300%
(B) 400%
(C) 500%
(D) 200%
(E) 600%
Rationale: original area=a*b where a and b are sides
after increase in side increase in area will be=(((2a*2b)-(a*b))*100)/(a*b)=300%
ANSWER:A
Answer: (A) 300%
Question: If the number of boys in a class are 8 times the number of girls, which value can never be the total number of students?
(A) 27
(B) 45
(C) 81
(D) 42
(E) 56
Rationale: Explanation :
Let the number of girls = x and the number of boys = 8x
Then, total number of students = x + 8x = 9x
i.e., the total number of students must be a multiple of 9
From the given choices, 42 cannot be a multiple of 9.
Hence, 42 cannot be the total number of students.
Answer : D
Answer: (D) 42
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 28%
(C) 34%
(D) 39%
(E) 93%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: If four coins are tossed, the probability of getting two heads and two tails is
(A) 3/8
(B) 3/5
(C) 3/9
(D) 3/1
(E) 3/3
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:A
Answer: (A) 3/8
Question: In how many different ways can 5 boys and 2 girls sit on a bench such that the girls always sit together?
(A) 360
(B) 720
(C) 1440
(D) 1800
(E) 2160
Rationale: We can think of the girls as one unit.
The number of ways to arrange 6 units in order is 6!
The girls can have different arrangements, so we multiply this by 2!
The number of ways to sit is 6!*2!=1440
The answer is C.
Answer: (C) 1440
Question: In how many different ways can the letters of the word ‘CAN’ be arranged?
(A) 6
(B) 12
(C) 8
(D) 2
(E) 4
Rationale: A
6
The word SMART has 3 distinct letters.
Number of arrangements = 3!
= 3 × 2 × 1 = 6
Answer: (A) 6
Question: How long does a truck of 200 m long traveling at 60 kmph takes to cross a bridge of 180 m in length?
(A) 36.7
(B) 26.8
(C) 22.8
(D) 21.1
(E) 16.2
Rationale: D = 200 + 180 = 380 m
S = 60 * 5/18 = 50/3
T = 380 * 3/50 = 22.8 sec
Answer:C
Answer: (C) 22.8
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) 2368
(B) 2768
(C) 1121
(D) 4096
(E) 2687
Rationale: Explanation:
Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
Answer:D
Answer: (D) 4096
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back, how far is the place?
(A) 24km
(B) 30km
(C) 48km
(D) 120km
(E) 15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 25
2x+3x = 600
x = 120 km
Answer is D
Answer: (D) 120km
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(3,3)
D=(4,1)
E=(0,8)
(A) 0.75
(B) 1
(C) 0.5
(D) 0.25
(E) 1.5
Rationale: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as C.
Answer: (C) 0.5
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
(A) 25/42
(B) 25/47
(C) 25/48
(D) 25/21
(E) 25/41
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42
Answer:A
Answer: (A) 25/42
Question: Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?
(A) 9
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Explanation:
We have, 2/3 * 2/5 * 3/4 * X = 36
X = 180
Now, 4/5 * X ===> 4/5 * 180 = 144
√144 = 12
ANSWER: B
Answer: (B) 12
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $56. If $2,000 is the total amount invested, how much is invested at 10 percent?
(A) a. $280
(B) b. $800
(C) c. $892
(D) d. $1108
(E) e. $1200
Rationale: 2 equations with 2 unknowns
10x / 100 - 8y / 100 = 56
and
x + y = 2000
Solving these 2 equations, x = 1200 and y = 800
Answer E.
Answer: (E) e. $1200
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.7248
(B) s.4518
(C) s.4518
(D) s.4530
(E) s.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs.7248
Answer: A
Answer: (A) s.7248
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $21?
(A) 33
(B) 35
(C) 37
(D) 39
(E) 41
Rationale: $21 = 3 * $6 + $3
The number of doughnuts is 3*12 + 3 = 39
The answer is D.
Answer: (D) 39
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
(A) Rs.544
(B) Rs. 8112
(C) Rs.820
(D) Rs.639
(E) Rs.897
Rationale: Explanation:
Explanation:
A = 7500(26/25)2 =Rs. 8112
Answer:B
Answer: (B) Rs. 8112
Question: If k > 0, x + 2k = y, and y + 5k = z, what is the ratio between z - x and y - x ?
(A) 3 to 1
(B) 3 to 2
(C) 4 to 3
(D) 7 to 2
(E) 5 to 3
Rationale: y-x = 2k
z-y = 5k
Let's add the two equations together:
z-x = 7k
The ratio of z-x to y-x is 7:2.
The answer is D.
Answer: (D) 7 to 2
Question: Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 29.25
(B) 29.28
(C) 39.25
(D) 29.21
(E) 29.22
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25.A
Answer: (A) 29.25
Question: Two pipes P and Q can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe P is turned off. What is the total time required to fill the tank?
(A) 10 min
(B) 12 min
(C) 14 min 40 sec
(D) 15 min 30 sec
(E) 18 min
Rationale: filled in 4 min = 4(1/15 + 1/20) = 7/15
part = 1-7/15==>8/15
filled by Q in 1 min = 1/20
x=8/15*1*20==> 10 2/3 min==>10 min 40 sec
so tank will be full in (4 min +10 min 40 sec) = 14min 40 sec
ANSWER C
Answer: (C) 14 min 40 sec
Question: If f(2, 3) = 17 and f(2, 4) = 24, what is the value of f(2, 5)?
(A) 107
(B) 127
(C) 147
(D) 33
(E) Cannot be determined
Rationale: Solution:
The function f(a, b) = a3 + b2
f(2, 3) therefore is = 17 and
f(2, 4) = 24
Therefore, f(2, 5) = 33
Answer D
Answer: (D) 33
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 12
(B) 77
(C) 48
(D) 99
(E) 36
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.4 = 1.5 km = 1500 m.
Required time = 1500 * 3/125 = 36 sec.
Answer: E
Answer: (E) 36
Question: A boat covers a certain distance downstream in I hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph. what is the speed of the boat in still Water?
(A) 12kmph
(B) 13kmph
(C) 15kmph
(D) 16kmph
(E) None
Rationale: Solution
Let the speed of the boat in still water be x kmph. Then,
Speed downsteram	= (x + 3) kmph.
Speed upsteram	= (x - 3) kmph.
= (x+3)x1
= (x - 3)x3/2 kmph.
= 2x+6 = 3x-9
x= 15 kmph.
Answer C
Answer: (C) 15kmph
Question: How many integers k greater than 100 and less than 600 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
(A) 40
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Not sure if this is the shortest.. But this is how I did this
There are 8 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. 405 | 504
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 4 sets with 10 such number in each set will give 4 x 10 = 40 integers.
A
Answer: (A) 40
Question: In a container there are two solutions; solution A and solution B in the ratio of 3 : 4. If 8 litres of solution A is added, the ratio becomes 11:12. What is the total quantity in the container after adding the extra 8 litres ?
(A) 96 liters
(B) 104 liters
(C) 94 liters
(D) 92 liters
(E) 112 liters
Rationale: Let Solution A : Solution B be = 3x : 4x.
(Solution A / Solution B) = (3x + 8) / 4x = 11 / 12 =11 / 12
36x + 96 = 44x => 8x = 96 => x = 12.
Solution A + Solution B = 3x + 8 + 4x = 32 + 8 + 48 = 92 liters
Option D
Answer: (D) 92 liters
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 1277
(B) 2977
(C) 1200
(D) 2769
(E) 1971
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer: C
Answer: (C) 1200
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 50 sec
(B) 16 sec
(C) 31 sec
(D) 26 sec
(E) 25 sec
Rationale: The distance to be covered = Sum of their lengths = 200 + 300
= 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18
=10 mps.
Time required = d/s = 500/10
=50 sec.
Answer:A
Answer: (A) 50 sec
Question: Jill has 35 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
(A) 3
(B) 60
(C) 9
(D) 12
(E) 14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 35 1 3/4w = 35w=20The total number of jars = 3w =60Answer: B
Answer: (B) 60
Question: The digital sum of a number is the sum of its digits. For how many of the positive integers 24-90 inclusive is the digital sum a multiple of 7?
(A) 10
(B) 8
(C) 14
(D) 16
(E) 20
Rationale: is there other way than just listing?
25
34
43
52
59
61
68
70
77
86
10 ways..
A
Answer: (A) 10
Question: In a camp, there is a meal for 80 men or 200 children. If 135 children have taken the meal, how many men will be catered to with remaining meal?
(A) 41
(B) 35
(C) 26
(D) 48
(E) 49
Rationale: C
26
There is a meal for 200 children.
135 children have taken the meal.
Remaining meal is to be catered to 65 children.
Now, 200 children 80 men.
65 children = (80 /200)x 65= 26 men.
Answer: (C) 26
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train?
(A) 270
(B) 277
(C) 187
(D) 180
(E) 271
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 18 sec = 18 * 10 = 180 m.
The length of the faster train = 180 m.
Answer: D
Answer: (D) 180
Question: 2+2+ 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =
(A)  2^9
(B)  2^10
(C)  2^12
(D)  2^16
(E)  2^20
Rationale: Let's see that: 2 + 2 is 2^2, then: 2^2 + 2^2 becomes 2 x 2^2 that is 2^3. You follow with the next: 2^3 + 2^3 is equal to 2 x 2^3 that is 2^4. Then is assumed right before 2^8: 2^8 x 2^8 becomes 2 x 2^8 that is 2^9. Option A, 2^9.
Answer: (A)  2^9
Question: During a sale, a store sells 20 percent of its remaining stock each day, without replenishment. After four days, what fraction of its original stock has it sold?
(A) 1/625
(B) 256/625
(C) 61/125
(D) 64/125
(E) 369/625
Rationale: Let's pick a smart number for the initial amount. The store sold 20 percent each day, hmm, after looking at the answer choices 625 is used pretty often, so let's pick it.
1st day: 125 items sold, 500 left
2nd day: 100 items sold, 400 left
3rd day: 80 sold, 320 left
4th day: 64 sold, 256 left
Sum The Sold Items=125+100+80+64=369−−>369/625
Answer E
Answer: (E) 369/625
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.
(A) 1/127
(B) 1/191
(C) 1/138
(D) 1/132
(E) 1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄ = 1/126
Answer: E
Answer: (E) 1/126
Question: From a group of 3 balls and 3 bats, 4 are to be randomly selected. What is the probability that equal numbers of balls and bats will be selected?
(A) 1/5
(B) 2/5
(C) 4/5
(D) 1
(E) 3/5
Rationale: Using the first example, here is the probability of THAT EXACT sequence occurring:
BBbb = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
BbBb = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
E
Answer: (E) 3/5
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
(A) 243
(B) 255
(C) 256
(D) 287
(E) 300
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: (B) 255
Question: Find the value of (√1.21)/(√0.81) + (√1.00)/(√0.49) is
(A) 2.65
(B) 145/63
(C) 155/63
(D) 125/63
(E) 185/63
Rationale: (√1.21)/(√0.81) + (√1.00)/(√0.49)
11/9 + 10/7 => 2.65
Answer is A
Answer: (A) 2.65
Question: A car travels at a speed of 60 miles per hour. How far will it travel in 5 hours?
(A) 425 miles
(B) 625 miles
(C) 300 miles
(D) 225 miles
(E) 625 miles
Rationale: During each hour, the car travels 65 miles. For 5 hours it will travel
60 + 60 + 60 + 60 + 60 = 5 *65 = 300 miles correct answer C
Answer: (C) 300 miles