mathewhe/aqua_rat huggingface dataset:
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 287 m
(B) 178 m
(C) 500 m
(D) 177 m
(E) 188 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: C
Answer: (C) 500 m
Question: The tax on a commodity is diminished by 40% but its consumption is increased by 25%. Find the decrease percent in the revenue derived from it?
(A) 18%
(B) 72%
(C) 25%
(D) 12%
(E) 52%
Rationale: 100 * 100 = 10000
60 * 125 = 7500
10000------- 2500
100 ------- ? =25%
Answer:C
Answer: (C) 25%
Question: The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q ?
(A) 2008
(B) 2009
(C) 2010
(D) 2011
(E) 2012
Rationale: Let the commodity P costs 40 paise more than the commodity Q after n years.
Price of the commodity P in 2001 = Rs.4.20
Since the price of the commodity P increases by Rs 0.40 every year,
Price of the commodity P after n years from 2001 = Rs.4.20 + (n × .40)
Price of the commodity Q in 2001 = Rs.6.30
Since the price of the commodity Q increases by Rs 0.15 every year,
price of the commodity Q after n years from 2001 = Rs.6.30 + (n × .15)
Since the commodity P costs Rs. 0.40 more that the commodity Q after n years from 2001,
4.20 + (n × .40) = 6.30 + (n × .15) + 0.40
=> (40n - .15n) = 6.30 - 4.20 + 0.40 = 2.5
=> .25n = 2.5
=> n =2.5/.25
=10
=> Commodity P costs Rs.0.40 more that the commodity Q after 10 years from 2001.
i.e., in 2011
ANSWER:D
Answer: (D) 2011
Question: If x/2 = y/5 = z/6, then (x + y + z)/x is equal to :
(A) 13
(B) 12
(C) 15/2
(D) 13/2
(E) None of these
Rationale: Explanation :
Solution: Let x/2 = y/5 = z/6 = k => x =2k, y =5k, z = 6k.
.'. (x + y + z)/x = (2k + 5k + 6k)/2k
=> 13k/2k = 13/2
Answer : D
Answer: (D) 13/2
Question: In an examination, the percentage of students qualified to the number of students appeared from school A is 70%. In school B, the number of students appeared is 20% more than the students appeared from school A and the number of students qualified from school B is 50% more than the students qualified from school A. What is the percentage of students qualified to the number of students appeared from school B?
(A) 30%
(B) 70%
(C) 80%
(D) 87.5%
(E) None
Rationale: Solution
Let number of students appeared from school A = 100.
Then, number of students qualified from school A = 70.
Number of students appeared from school B = 120.
Number of students qualified from school B = [150 / 100 x 70] = 105.
Required percentage = [105/ 120 x 100]%
= 87.5%
Answer D
Answer: (D) 87.5%
Question: Two goods trains each 75 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 2.3 sec
(B) 4.2 sec
(C) 48 sec
(D) 7.2 sec
(E) 9 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 75 + 75 = 150 m.
Required time = 150 * 6/125 = 7.2 sec.
Answer:D
Answer: (D) 7.2 sec
Question: The average weight of a group of boys is 30 kg. After a boy of weight 36 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 8
(C) 5
(D) 2
(E) 9
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 36 kg joins the group, total weight of boys = 30x + 36
So 30x + 36 = 31(x + 1) = > x = 5
Answer: C
Answer: (C) 5
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 20 litres of tomato juice?
(A) 2.8 liters.
(B) 2.5 liters.
(C) 8.5 liters.
(D) 2.6 liters.
(E) 2.1 liters.
Rationale: Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
⇒⇒ 10%(20) = 80%(x)
⇒⇒ x = 2.5 liters.
Answer:B
Answer: (B) 2.5 liters.
Question: A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
(A) 4 km/hr
(B) 5 km/hr
(C) 6 km/hr
(D) 3 km/hr
(E) 2 km/hr
Rationale: Rate downstream = 16/2 kmph = 8 kmph.
Rate upstream = 16/4 kmph = 4 kmph.
Speed in still water =	1/2 (8 + 4) kmph = 6 kmph.
Answer : Option C
Answer: (C) 6 km/hr
Question: Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 22 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
(A) 64
(B) 72
(C) 86
(D) 98
(E) 103
Rationale: Use the options.
The options which after getting added to 27 shows a cube of a number could be right.
Here
64+22 = 86
72+22 = 94
86+22 = 108
98+22 = 120
103+22=125 ---(5*5*5)
So we have 103 as the answer!
E
Answer: (E) 103
Question: Goldenrod and No Hope are in a horse race with 8 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
(A) 40320
(B) 20160
(C) 12000
(D) 2400
(E) 2100
Rationale: All 8 horses can finish the race in 8! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 8!/2=20160 different arrangements of finishes where No Hope always finishes before Goldenrod.
Answer: B.
Answer: (B) 20160
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:5
(C) 1:3
(D) 1:1
(E) 1:7
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer:A
Answer: (A) 1:2
Question: A person is traveling at 40km/hr and reached his destiny in 5hr find the distance?
(A) A)200km
(B) B)95km
(C) C)135km
(D) D)80km
(E) E)125km
Rationale: speed = 40km/hr
time = 5hr
distance = 40*5 = 200km
Answer is A
Answer: (A) A)200km
Question: If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 30% of m is equal to what percent of 200% of j ?
(A) 0.35
(B) 3.5
(C) 525
(D) 350
(E) 3500
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
30% of 350, comes out to be 105....
200% of 10 is 20....
(105*100)/20=525....
Ans : C
Answer: (C) 525
Question: A salesman sells two kinds of trousers: cotton and woollen. A pair of cotton trousers is sold at 30 profit and a pair of woollen trousers is sold at 50 profit. The salesman has calculated that if he sells 100 more woollen trousers than cotton trousers, his overall profit will be 45. However he ends up selling 50 more cotton trousers than woollen trousers. What will be his overall profit?
(A) 37.5%
(B) 40%
(C) 41%
(D) 32.33%
(E) None of these
Rationale: Explanation :
Let the cost price of 1 cotton trouser and 1 woollen trouser be ‘C’ and ‘W’ respectively.
Case I: Number of woollen trousers sold is 100% more than cotton trousers.
1.3C+1.5×2×W=1.45(C+2W).
=>0.15C=0.1W.
=>3C=2W.
Case II: Number of cotton trousers sold is 50% more than woollen trousers.
S.P=1.3C + 1.5 x (2W/3).
=>S.P=1.3C+W=2.8C.
And, C.P.=C+(2W/3)=2C.
Profit :-
=>(2.8C-2C)X100/2C.
=>40%.
Answer : B
Answer: (B) 40%
Question: Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?
(A) 70
(B) 90
(C) 60
(D) 80
(E) 10
Rationale: D
80
We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300
D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.
Answer: (D) 80
Question: In a certain code 'BEAMING' is written as 'BFCMHOJ' and 'CLEAR' is written as 'MDESB' How is 'TRAIL' written in that code?
(A) ASKDJS
(B) JKHHGJ
(C) HJGGK
(D) GKJJGG
(E) HGHXA
Rationale: Answer: Option C
Answer: (C) HJGGK
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) 120
(B) 255
(C) 265
(D) 270
(E) 280
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: How many integers from 40 to 200, inclusive, are divisible by 3 but not divisible by 7?
(A) 20
(B) 31
(C) 35
(D) 40
(E) 45
Rationale: We should find # of integers divisible by 3 but not by 3*7=21.
# of multiples of 21 in the range from 40 to 200, inclusive is (189-42)/21+1=8;
53-8=45.
Answer: E.
Answer: (E) 45
Question: The height of two right circular cones are in the ratio 1:2 and their perimeters of their bases are in the ratio 3:4, the ratio of their volume is?
(A) 9:38
(B) 9:31
(C) 9:32
(D) 9:39
(E) 9:35
Rationale: 9:32
Answer:C
Answer: (C) 9:32
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 25 percent of the seeds in the first plot germinated and exactly 30 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 27%
(B) 26%
(C) 29%
(D) 30%
(E) 60%
Rationale: In the first plot 25% of 300 seeds germinated, so 0.25 x 300 = 75 seeds germinated.
In the second plot, 30% of 200 seeds germinated, so 0.30 x 200 = 60 seeds germinated.
Since 75 + 60 = 135 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (135/500) x 100%, or 27%.
Answer: A.
Answer: (A) 27%
Question: If -3 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^5 < 5 – x^2
III. x^4 < x
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
Rationale: I. x^5 < x^2 --> from -3 < x < 0 it follows that LHS<0<RHS, so this statement is true.
II. x^5 < 1 – x --> x^2(x^3+1) < 5 --> positive*negative < 0 < 1, so this statement is also true.
III. x^4 < x --> since -3 < x< 0 means x is negative and x^4 would always be positive, then this statement is false
Answer: B.
Answer: (B) I and II only
Question: A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 10 minutes.
In how much time will he be able to take all the five tablets?
(A) 1 Hour.
(B) 40 min
(C) 50 min
(D) None
(E) Cannot be determined
Rationale: Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:10, third at 8:20, fourth at 8:30 and fifth at 8:40.
Time = 40 min
Answer B
Answer: (B) 40 min
Question: If a choir consists of 2 boys and 5 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
(A) 120
(B) 30
(C) 24
(D) 11
(E) 6
Rationale: There are 6 possibilities:
bbgggggg
gbbggggg
ggbbgggg
gggbbggg
ggggbbgg
gggggbbg
ggggggbb
Think of all 2 boys as a single unit. Together with 5 girls it makes a total of 6 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 6 available positions. If the number of available unique positions is 6, then the number of unique patterns equals 6 as well.
Answer: E.
Answer: (E) 6
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?
(A) (10,000z + 100z(x – y) – xyz)/10,000
(B) (10,000z + 100z(y – x) – xyz)/10,000
(C) (100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: Z * (1+(x/100)) * (1-(y/100))
Z* (100+x/100) * (100-y/100)
(100Z + ZX)/100 * (100-y/100)
[10,000Z + 100 ZX - 100 ZY - XYZ] /10,000
[10,000Z +100Z (X - Y) - XYZ] / 10,000
Choice A
Answer: (A) (10,000z + 100z(x – y) – xyz)/10,000
Question: What is the rate percent when the simple interest on Rs.2000 amount to Rs.320 in 4 Years?
(A) 4.5%
(B) 4.25%
(C) 4%
(D) 4.3%
(E) 4.1%
Rationale: Interest for 1 year = 320/4 = 80
Interest on Rs 2000 p/a = 80
interest rate = 80/2000*100 = 4%
Answer : C
Answer: (C) 4%
Question: A train 110 m long is running with a speed of 27 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 4 sec
(E) 12 sec
Rationale: Speed of train relative to man = 27 + 6
= 33 km/hr.
= 33 * 5/18 = 9.1667 m/sec.
Time taken to pass the men = 110 /9.1667
= 12 sec.
Answer:E
Answer: (E) 12 sec
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.0 cm. What is the area of the triangle?
(A) 28 cm2
(B) 27 cm2
(C) 29 cm2
(D) 25 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.0 * 28/2
= 28 cm2
Answer: A
Answer: (A) 28 cm2
Question: In what time a sum of money double itself at 3% per annum simple interest?
(A) 36 1/3%
(B) 33 1/3%
(C) 33 1/6%
(D) 63 1/3%
(E) 23 1/3%
Rationale: P = (P*3*R)/100
R = 33 1/3%
Answer: B
Answer: (B) 33 1/3%
Question: The distance between two cities A and B is 1140 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
(A) 09 AM
(B) 07 AM
(C) 11 AM
(D) 05 PM
(E) 03 PM
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 1140.
Therefore, 60x + 75(x-1) = 1140.
=> x=9.
So,they meet at (8+9) i.e, 5PM
Answer: D
Answer: (D) 05 PM
Question: Car W and Car Y traveled the same 80-mile route. If Car W took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car W, how many hours did it take Car Y to travel the route?
(A)  2/3
(B)  1
(C)  4/3
(D)  8/5
(E)  3
Rationale: The speed of car W is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: (C)  4/3
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 56%
(B) 57%
(C) 54%
(D) 53%
(E) 52%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = (11628/20400 * 100)% = 57%
Answer B)57%.
Answer: (B) 57%
Question: A 11% stock yields 8%.The market value of the stock is :
(A) Rs. 72
(B) Rs. 137.50
(C) Rs. 112.50
(D) Rs. 116.50
(E) None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 11, investment = Rs.(100/8X11)= Rs. 137.50
∴ Market value of Rs. 100 stock = Rs.137.50
Answer B
Answer: (B) Rs. 137.50
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
(A) 100
(B) 882
(C) 772
(D) 252
(E) 121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter.Answer: A
Answer: (A) 100
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations R could be chosen from this menu?
(A) 10
(B) 20
(C) 40
(D) 80
(E) 100
Rationale: R=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Answer: (C) 40
Question: 2+2+2²+2³ ... +2^9
(A) 2^9
(B) 2^10
(C) 2^16
(D) 2^35
(E) 2^37
Rationale: 2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
so you can notice the pattern... in the end you will have 2^9+2^9, which will give you 2^10
Answer B
Answer: (B) 2^10
Question: A pet store sells dog collars arranged on display such that each of the four different colors of dog collars, green, red, blue, and purple are consecutive in a repeating pattern. If five consecutively displayed collars are purchased, what is the probability that two of the collars are purple?
(A) 1/4
(B) 1/5
(C) 1/16
(D) 1/32
(E) 4/5
Rationale: After green, red, blue, and purple, the next dog collar can be of any given four colours, therefore we have total four possibilites, out of which we need purple i.e. 1 therefore prob is 1/4.
Answer: (A) 1/4
Question: If n = 2.0823 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
(A)  -0.0053
(B)  -0.0023
(C)  0.0007
(D)  0.0047
(E)  0.0153
Rationale: n*=2.08
n*-n=2.08-2.0823
-0.0023
Answer: B
Answer: (B)  -0.0023
Question: The ratio of 2 numbers is 4:6 and their H.C.F. is 8. Their L.C.M. is ?
(A) 20
(B) 24
(C) 52
(D) 96
(E) 60
Rationale: Let the numbers be 4x and 6x
Their H.C.F. = 8
so the numbers are 4*8 , 6*8 = 32,48
L.C.M. = 96
Answer is D
Answer: (D) 96
Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 3hr
(B) 3hr 45min
(C) 4hr 15min
(D) 2hr 1min
(E) 1hr 45min
Rationale: Time taken by one tap to fill the half tank = 3 hr
part filled by the 4 taps in 1hour = 4*1/6 = 2/3
Remaining part = 1-1/2 = 1/2
2/3:1/2::1:x
x = 3/4hr = 45min
Total time taken = 3hr 45min
Answer is B
Answer: (B) 3hr 45min
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 105, then how much amount should C pay as his share of rent?
(A) 35
(B) 27
(C) 25
(D) 15
(E) 55
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=105×9/35=3×9=27
Answer is B.
Answer: (B) 27
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let R be the average rental price for all apartments in the building. If R is $5,600 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $10,400 higher that R, then what percentage of apartments in the building are two-bedroom apartments?
(A) 26%
(B) 35%
(C) 39%
(D) 42%
(E) 52%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 5400 : 104000 -----> 7 : 13
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (7 / 20) * X
percentage of apartments in the building are two-bedroom apartments ---->
(7/20) * 100 ---> 35%
option B is correct
Answer: (B) 35%
Question: At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 35 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 40 km/h. If the distance between City P and City Q is 335 km, at what time will the truck and the car meet each other?
(A) 5:00
(B) 5:30
(C) 6:00
(D) 6:30
(E) 7:00
Rationale: At 2:00 pm, the truck and the car are 300 km apart.
The truck and the car complete a distance of 75 km each hour.
The time it takes to meet is 300/75 = 4 hours.
They will meet at 6:00 pm.
The answer is C.
Answer: (C) 6:00
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.5 per sq m?
(A) 6500
(B) 2779
(C) 2779
(D) 3900
(E) 2781
Rationale: Area = (l + b â€“ d) d
(80 + 60 â€“ 10)10 => 1300 m2
1300 * 5 = Rs.6500
Answer:A
Answer: (A) 6500
Question: What was the day of the week on 28th May, 2006?
(A) Monday
(B) Friday
(C) Saturday
(D) Tuesday
(E) Sunday
Rationale: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
(31[jan] + 28 [Feb]+ 31[Mar] + 30[April] + 28[May] ) = 148 days
148 days = (21 weeks + 1 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.
Given day is Sunday
Answer is E.
Answer: (E) Sunday
Question: If x and y are different integers, both divisible by 7, then which is not necessarily true?
(A) x^2 + y^2 is divisible by 7
(B) x - y is divisible by 7
(C) xy is divisible by 7
(D) x + y is divisible by 7
(E) x + y is divisible by 14
Rationale: Let x = 7k and let y = 7j.
Then x+y = 7(k+j) and k+j could be even or odd.
Thus 7(k+j) is not necessarily divisible by 14.
The answer is E.
Answer: (E) x + y is divisible by 14
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:13. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 19
(B) 17
(C) 13
(D) 10
(E) 12
Rationale: 7*5: 5*x = 7:13
x = 13
Answer: C
Answer: (C) 13
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) 28,009
(B) 28,007
(C) 28,006
(D) 28,000
(E) 28,004
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer:D
Answer: (D) 28,000
Question: What is the area inscribed by the lines y =2, x = 2, y = 10-x on an xy-coordinate plane?
(A) a) 8
(B) b) 10
(C) c) 12
(D) d) 14
(E) e) 18
Rationale: First, let's graph the lines y = 2 and x = 2
At this point, we need to find the points where the line y = 10-x INTERSECTS the other two lines.
For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = 10-x to get y = 10-2 = 8
Perfect, when x = 2, y = 8, so one point of intersection is (2,8)
For the horizontal line, we know that y = 2, so we'll PLUG y = 2 into the equation y = 10-x to get 2 = 10-x. Solve to get: x = 8
So, when y = 2, x = 8, so one point of intersection is (8,2)
Now add these points to our graph and sketch the line y = 10-x
At this point, we can see that we have the following triangle.
The base has length 6 and the height is 6
Area = (1/2)(base)(height)
= (1/2)(6)(6)
= 18
Answer:
E
Answer: (E) e) 18
Question: What is the ratio whose term differ by 25 and the measure of which is 2/7?
(A) A)32:23
(B) B)16:56
(C) C)71:85
(D) D)32:39
(E) E)10:35
Rationale: Let the ratio be x:(x+25)
Then, x/(x+25) = 2/7
x=10
required ratio = 10:35
Answer is E
Answer: (E) E)10:35
Question: A set consists of 18 numbers, all are even or multiple of 5. If 6 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  5
Rationale: {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
18 = 6 + 12 - {Both} + 0;
{Both}=0(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: A.
Answer: (A)  0
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 72 kmph?
(A) 22 sec
(B) 77 sec
(C) 25 sec
(D) 18 sec
(E) 12.5 sec
Rationale: D = 100 + 150 = 250
S = 72 * 5/18 = 20 mps
T = 250/20 = 12.5 sec
Answer:E
Answer: (E) 12.5 sec
Question: If the population of a certain country increases at the rate of one person every 30 seconds, by how many persons does the population increase in 1 hour?
(A) 100
(B) 120
(C) 150
(D) 180
(E) 160
Rationale: Answer = 2 * 60 = 120
Answer is B
Answer: (B) 120
Question: A reduction of 35% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 42
(B) 49
(C) 56
(D) 63
(E) 70
Rationale: 800*(35/100) = 280 ---- 5
? ---- 1 => Rs.56
Answer: C
Answer: (C) 56